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THE ART or 

Composition 





:«!» A Simple 
AppliGation of 

Dy namie Symmetry 






MlCHELJACoBS 





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ONTARIO COUESE OF ART 

100 McCA'JL ST. 
TORONTO 2B, ONTARIO 




THE ART OF COMPOSITION 



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^'^ McCAUL ST 
^^^Omo 28, ONTARIO 




ESTUDIANTF. <ic BAIl.K 



AFIER A\ OIL PAINTING BV MICHEL JACOBS 



A study in overlapping Root Fours with subdivisions in Roots One and Four 




82790 



0C«OTHY H. HOOVCT IIWAW 
ONTARIO COIUGE Of ART » MMGN 
100 MeCAUl STREET, 
TORONTO, ON. 
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THE 
ART OF COMPOSITION 



^ Simple Application of Dynamic Symmetry 

BY 
MICHEL JACOBS 



8279 



3 




GARDEN CITY NEW YORK 

DOUBLEDAY, PAGE & COMPANY 

1926 






St 



OHTARIO COHERE OF ART 

ICO K'.cCAUL ST. 
TORONTO 2B, ONTARIO 



COPyRIGHT, 1926, BY HICHBL JACOBS. 
ALL RIGHTS RESERVED. PRINTED IN 
THE UNITED STATES AT THE COUN- 
TRY LIFE PRESS, GARDEN CITY, N. Y. 

FIRIT EDITION 



DEDICATION 

Our lives are but a sacrifice} we toil and spin 
to gain a place in the universe. But if we be- 
queath to posterity some beautiful thought, some 
worthy thing, and leave behind the fruits of our 
labour to help those who follow to make the world 
more beautiful, we shall have fulfilled our des- 
tiny. To those who have gone before and who 
have left us their life's work, we give our saluta- 
tions. 

M.J. 



FOREWORD 




HIS book is based on Greek Proportion, which in turn was 
undoubtedly founded on Nature's own laws. Much of 
the information was gathered from "Nature's Harmonic 
Unity," by Samuel Colman, N. A., which was published 
in 1912, and which was one of the first books published 
on proportion in nature; from "Dynamic Symmetry: The 
Greek Vase," "The Parthenon," and other works by Jay 
Hambidge, published from 1920 to 1924; from "Geom- 
etry of Greek Vases," by L. D. Caskey, published in 1922; 
and from the works of D. R. Hay of Edinburgh, Professor Raymond of 
Princeton University, and Professor A. H. Church of Oxford. 

Many writers have put their own interpretation on this system of com- 
position. This is only natural, when you consider the basic principles from 
which they have to draw. The variety of compositional layouts are in- 
numerable. I have only attempted to show some of the possibilities, and 
it is for the artist to work out for himself many more layouts based on this 
system. 

I wish to call to the attention of the reader the fact that this book is only 
intended as a preliminary study of the great principles of Dynamic Sym- 
metry, and I fervently believe and hope that the readers, after they have 
perused these pages, will continue their study with the number of books 
on the subject, and especially the posthumous work by Jay Hambidge 
called, "The Elements Of Dynamic Symmetry." 

Besides the use of this system for artists' composition, I also wish to call 
to the attention of photographers that Dynamic Symmetry can be used to 
great advantage, firstly, by using the Transparent Guides described in this 
book, and secondly, by cutting their photographs so as to conform to dy- 
namic lines and areas, or drawing the dynamic lines on their ground glass. 
Advertising agencies and printers will find that their layouts of type mat- 
ter can be better arranged by the use of this system. 

It can also be used by interior decorators, jewellers, and ceramic workers, 
as well as in other kindred arts. 

My thanks are due to my assistants and pupils, Miss Frederica Thomson, 
Mrs. Eunice Fais, Miss Ruth Radford, and Mr. Louis Amandolare, who 
have helped me with the illustrations and layouts In this book. 

Michel Jacobs. 



tH 



CONTENTS 



INTRODUCTION xviii 

CHAPTER ONE: COMPOSITION IN GENERAL i 

CHAPTER TWO: DYNAMIC SYMMETRY 13 

CHAPTER THREE: DIFFERENT ROOTS OR FORMS AND PRO- 
PORTION OF PICTURES 21 

CHAPTER FOUR: POINTS OF INTEREST 33 

CHAPTER FIVE: WHIRLING SQUARE ROOT 44 

CHAPTER SIX: ROOT ONE 49 

CHAPTER SEVEN: ROOT TWO 60 

CHAPTER EIGHT: ROOT THREE 71 

CHAPTER NINE: ROOT FOUR 77 

CHAPTER TEN : ROOT FIVE 82 

CHAPTER ELEVEN: COMBINED ROOTS 85 

CHAPTER TWELVE: MORE COMPLEX COMPOSITIONS 99 

CHAPTER THIRTEEN: GROUND COMPOSITION IN PERSPEC- 
TIVE, SHOWING THE THIRD DIMENSION 117 

CHAPTER FOURTEEN: COMPOSITION OF MASS, LIGHT AND 

SHADE 120 

CHAPTER FIFTEEN: COMPOSITION OF COLOUR 126 

CHAPTER SIXTEEN: A FEW MATHEMATICS OF DYNAMIC 

SYMMETRY 129 

GLOSSARY , 139 



ILLUSTRATIONS 

PAGE 

EsTUDiANTE De Baile Frotitisftece 

Composition of Mass, Fig. lA I 

Composition of Value, Fig. iB I 

Composition of Line, Fig. iC 2 

Composition of Perspective, Fig. iD 2 

Lines of Action, Fig. 2 3 

Lines of Dignity, Fig. 3 3 

Lines of Rest, Fig. 4 

The Lion, Fig. 5A 

Animals in Action, Fig. 5B 

The Ram, Fig. sC 

The Camel, Fig. 5D 

Even Balance, Fig. 6 

Even Balance with Equal Weight, Fig. 7 

Uneven Balance, Fig. 8 

Even Balance, Weight Subdivided, Fig. 9 8 

Distant Weight against Weight Near Centre, Fig. 10 8 

Weight against Distance, Fig. i i 8 

Weight against Distance Unbalanced, Fig. 12 9 

Weight Subdivided against Distance, Fig. 13 9 

Uneven Balance, Sufficiently Supported, Fig. 14A 10 

Uneven Balance, Not Sufficiently Supported, Fig. 148 10 

Sunflower, Fig. 15 II 

Tangents About to Collide, Fig. 16 14 

Tangents near Edges, Fig. 17 14 

Tangents Overlapping, Fig. 18 14 

Tangents Overlapping and Cutting Edge, Fig. 19 15 

The Suggested Effect of Tangents, Fig. 20 16 

Tangents That are Necessary, Fig. 21 A 16 

Tangents That are Necessary, Fig. 21B 16 

The Indian, Halftone 17 

The Duchess, Halftone 18 

Sequence of Area in Whole Numbers, Fig. 22 19 

Root Two Showing the Diagonals, Fig. 23 21 

Root Two Showing the Diagonals and Crossing Lines, Fig. 24 21 

Root Two Showing the Diagonal, Crossing Line, and Parallel Line, Fig. 25 . . 22 

Root Two Showing the Parallel Lines in All Directions, Fig. 26 22 



xii ILLUSTRATIONS 

PAGE 

Symbols op the Different Roots, Fig. 27 24 

Root One, Fig. 28 25 

Root Two, Fig. 29 25 

Root Three, Fig. 30 26 

Root Four, Fig. 31 27 

Root Five, Fig. 32 27 

Root of the Whirling Square, Fig. 33 28 

Root Five with the Whirling Square Root, Fig. 34. 29 

Roots Two, Three, Four, and Five Outside of a Square, Fig. 35 29 

Roots Two, Three, Four, and Five Inside of a Square, Fig. 36 30 

Root Two with Diagonal and Crossing Line, Fig. 37 32 

The Old Woman Who Lived in a Shoe: based on Fig. 37, Fig. 38 32 

Country Road: based on Fig. 37, Fig. 39 33 

Still Life: based on Fig. 37 33 

Principal and Second Points of Interest, Fig. 41 34 

Principal, Second and Third Points of Interest, Fig. 42 34 

Little Miss Muffet: based on Fig. 42, Fig. 43 34 

The Crystal Gazer, Halftone 35 

The Hillside, Halftone 36 

Root Three Showing Points op Interest in Sequence, Fig. 44 37 

Root Four Showing Points op Interest in Sequence, Fig. 45 37 

Root Five Showing Points of Interest in Sequence, Fig. 46 37 

Root One Containing Two Root Four's, Fig. 47 38 

The Bather: based on Fig. 47, Fig. 48 38 

Root One With Eight Points of Interest, Fig. 49 39 

The Dancer: based on Fig. 49, Fig. 50 39 

Root One with the Quadrant Arc, Fig. 51 39 

Root One with Two Quadrant Arcs and Parallel Lines, Fig. 52 40 

The Old Fashioned Garden: based on Fig. 52, Fig. 53 40 

Pavlowa and Mordkin, Halftone 41 

In the Woods, Halftone 4* 

Showing How to Use Transparent Guides, Fig. 54 43 

Whirling Square Root, Fig. 55 ♦i 

Whirling Squares in Sequence, Fig. 56 44 

Whirling Square Showing Greek Key Pattern, Fig. 57 4$ 

Natural Forms and Designs, Fig. 58 45 

Whirling Square Root with Large Squares Subdivided, Fig. 59 46 



ILLUSTRATIONS xiii 

PAGB 

Resting: based on Fig. 59, Fig. 60 47 

Whirling Square with Root Two in Sequence, Fig. 6i 47 

Root Four with a Root Four in Sequence, Fig. 62 50 

Barnyard: based on Fig. 62, Fig. 63 S° 

Root One Subdivided Into a Root Two and Two Smaller Root Three's, Fig. 64 50 

Sub-Debs: based on Fig. 64, Fig. 65 5° 

The Gipsy, Halftone 5 ' 

The Courtship, Halftone S* 

Root One with Three Root Two's Overlapping with Two Quadrant Arcs, 

Fig. 66 S3 

Tree on the Hill: based on Fig. 66, Fig. 67 S3 

Root One with a Root Two On Top and On Side, Fig. 68 53 

Conventional Design: based on Fig. 68, Fig. 69 S3 

Page of Root Two, Three, Four, Five Inside Root One 5S 

Dynamic Layouts of Photographs of Winter Landscapes 56 

Winter Landscapes, Halftone 57 

Photographs from Nature, Halftone 58 

Dynamic Layouts of Photographs from Nature 59 

Root Two within a Root One, Fig. 70 60 

Illustrative Method of Enlarging in Proportion, Fig. 71 60 

The Diagonal and Crossing Line in Root Two, Fig. 72 and the Root Two in 

Sequence 62 

The Diagonal and Crossing Lines in Root Two and Two Root Two's in Se- 
quence, Fig. 73 62 

The Garden Wall: based on Fig. 73, Fig. 74 62 

Root Two Divided Into Two Root Two's, Fig. 75 63 

Root Two Subdivided Into Eight Root Two's, Fig. 76 63 

Root Two with Roots One and Two in Sequence, Fig. 77 64 

The Toilet: based on Fig. 77, Fig. 78 64 

Root Two with Two Root One's Overlapping Make Three Root One's and 

Three Root Two's in Sequence, Fig. 79 65 

Layout: based on Fig. 79, Fig. 80 65 

The Shop Window: based on Fig. 80, Fig. 81 66 

Root Two with Root One and Two Root Two's Overlapping, Fig. 82 66 

Supplication: based on Fig. 82, Fig. 83 66 

Root Two with Root One on Side Forming Root Two and Root One on End, 

Fig. 84 67 

After the Snowstorm: based on Fig. 84, Fig. 85 67 

Commercial Compositions in Root Two 68 



xiv ILLUSTRATIONS 

PACE 

Layouts of Page 68 69 

Layouts Based on Pace 68 70 

Root Three with Three JIoot Three's in Sequence, Fig. 86 71 

Poke Bonnet: based on Fig. 86, Fic. 87 71 

Root Three's with Three Root Three's and Rhythmetic Curve, Fig. 88 ... . 72 

Composition based on Fig. 88, Fig. 89 7* 

Root Three with Overlapping Root One's and Root Three in Sequence, Fig. 

90 73 

Composition based on Fig. 90, Fig. 91 73 

Layouts in Root Three 74 

Photograph from Nature, Halftone 75 

The Will, Halftone 76 

Root Four with Two Root One's, Fig. 92 77 

Root Four with Two Root One's and Four Root Four's, Fig. 93 78 

Composition: based on Fig. 93, Fig. 94 78 

Root Four with Two Root One's Each Square Containing Two Root Two's 

Overlapping, Fig. 95 79 

Composition based on Fig. 95, Fig. 96 79 

Root Four with Whirling Squares in Sequence and Two Root One'», Fig. 97 80 

Composition based on Fig. 97, Fig. 98 80 

Layouts in Root Four 8 1 

Root Five Containing Two Root Four's and Two Whirling Squares, Fig. 99 • 82 
Root Five Containing a Horizontal and Perpendicular Whirling Square, 

Fig. 100 82 

Layouts in Root Five 84 

Root One with Four Overlapping Root Two's, Fig. ioi 85 

Passing Clouds: based on Fig. ioi. Fig. 102 85 

Root One with Two Root Four's, Fig. 103 86 

Fields: based on Fig. 103, Fig. 104 86 

Root One with Two Root Two's with Superimposed Diagonals, Fig. 105 86 

Edge of the Desert: based on Fig. 105, Fig. 106 86 

Root One with Two Root Four's and Four Root One's, Fig. 107 87 

ConventionalizeU Moon: based on Fig. 107, Fig. 108 87 

Root Two with Two Root Two's and Parallel Lines at All Intersections and 

Diagonals at Left, Fig. 109 88 

Willows: based on Fig. 109, Fig. no 88 

Root Two with Star Layout and Diagonals, Fig. hi ._..... 89 

Bluffs: based on Fig. in. Fig. 112 89 



ILLUSTRATIONS xv 



Root Three with Three Root Three's with Diagonals and Parallel Lines, 

Fig. 113 90 

Pandora: based on Fig. i i 3, Fig. 114 90 

Root Three with Three Root Three's Upright, Parallels, and Diagonals, 

Fig. 115 91 

Conventionalized Elephant: based on Fig. 115, Fig. 1 16 91 

Root Three with Three Root Three's and Numbers of Parallels at Inter- 
sections, Fig. 117 91 

A Border Pattern: based on Fig. 117, Fic. 1 18 91 

Root Three with Six Root Three's Diagonals to the Half, Fig. 119 92 

Commercial Layout: based on Fig. 119, Fig. 120 92 

Peonies, Halftone 93 

Rock of All Nations, Halftone 94 

Root Four with Four Root Four's and Parallel Lines Through Inter- 
sections AND Diagonals, Fig. 121 95 

Composition: based on Fig. 121, Fig. 122 95 

Root Four with Two Root Four's and One Root One Using the Rhythmetic 

Lines, Fig. 123 96 

The Wave: based on Fig. i 23, Fig. i 24 96 

Root Five with Two Root Five's and Rhythmetic Lines, Fig. 125 97 

The Slope: based on Fig. 125, Fig. 126 97 

Whirling Square Root and Diagonals, Fig. 127 98 

Conventional Pattern: based on Fig. 127, Fig. 128 98 

Major Shapes Divided into Complex Forms lOO 

Root Two Divided into Three Equal Parts and Using the Rhythmetic Curve, 

Fig. 1 29 101 

Conventional Landscape: based on Fig. 129, Fig. 130 lOi 

Root Two with Root One on Left Side, Fig. 131 102 

Root Two Showing How to Make the Whirling Square, Fig. 132 102 

Root Two with Whirling Square Root, Fig. 133 103 

Root Two with Four Whirling Squares, Fig. 134 103 

Root Five with Two Whirling Squares Overlapping and a Whirling Square 

ON Each End with Root Two Inside of a Root One, Fig. 135 104 

Composition: based on Fig. 135, Fig. i 36 104 

Root Five and a Root Five at Each End With Diagonals and Parallel Lines, 

Fig. 137 105 

Rolling Ground: based on Fig. 137, Fig. 138 105 

Root Five with a Root Five on Each End with Diagonals from Corners and 

Parallels Through Center Both Ways, Fig. 139 106 

Warrior: based on Fig. 1 39, Fig. 140 106 



xvi ILLUSTRATIONS 

PAOI 

A Form Less Than Root Two with Forms Overlapping, Fig. 141 107 

The Gossips: based on Fig. 141, Fic. 142 107 

Progressive Steps of the Whirling Square Root . 109 

Layouts of Dynamic Poses no 

Dynamic Poses of the Human Figure, Halftone 1 1 1 

Dynamic Poses of the Human Figure, Halftone ill 

Layouts of Dynamic Poses 113 

Layouts of Complex Compositions 114 

Illustrations of Page 114 115 

Layouts in the Whirling Square 1 16 

Perspective of Root One with a Root Two, Fig. 143 1 17 

Composition Based on Fig. 143, Fig. 144 1 18 

Perspective of Root Five with Two Whirling Square Roots, Fig. 14S ' *9 

Composition with Perspective Ground, Fig. 146 119 

Dark Mass Below and Light Mass Above, Fig. 147 I20 

Dark Mass Above and Light Mass Below, Fig. 148 121 

Whirling Square to Show Mass, Light, and Shade, Fig. 149 122 

Whirling Square to Show Mass, Light, and Shade, Fig. 150 122 

Layouts of Ben Day Illustrations 124 

Ben Day Textures 125 

The Reciprocal of Root Two, Fig. 151 131 

Relation of Mass, Fig. 152 131 

The Reciprocals of All Roots 134 

The Square Root of All Roots 135 

Whirling Square Root Outside of the Rectangle, Fig. 153 137 

Whirling Square Root Inside of the Rectangle, Fig. 154 137 

Combined Root Symbols, Fig. 155 138 



INTRODUCTION 




RCHiEOLOGISTS have long since recognized that the 
Greeks useci Dynamic Symmetry, Swa/tci <n)/i/itTpoi in the 
planning of their temples, statuary, paintings, vases, and 
other works of art, but artists have been slow to adopt this 
system mainly because of the belief that it is necessary to 
understand higher mathematics. 

Most books on composition that have been written are 
books of "Don't." I have, therefore, tried to make this 
book a book of construction rather than tell the things to 
guard against. I have tried to show how to construct a work of art so as 
to make the composition a thing of beauty: so that an original conception 
can be carried out in a harmonious arrangement, as a design or decoration, 
without which no work of art is worthy of the name. 

Another reason that I have taken up this task is to connect Dynamic 
Symmetry with other forms of composition long since recognized. Un- 
doubtedly, there are many roads: some intertwine; few diverge to such an 
extent that they cannot be used for the same object. I trust that I have 
made this book so simple that even a child may be able to master the con- 
tents. 

On account of the misunderstanding that Dynamic Symmetry is mathe- 
matical and difficult to understand, I have taken great pains to leave out 
any suggestion of an algebraic or geometrical formula. I have even gone 
so far, in all but the last chapter, to omit letters or numbers to describe 
lines or angles, for fear that the reader might believe, at first glance, that 
it was necessary to understand higher mathematics. 

One often hears of artists who refuse to be guided by any law or rule of 
science and who consider that they are a law in themselves. If they were 
students of psychology, they would see that they are absorbing from others, 
I might even say copying, perhaps subconsciously, but they themselves 
would be the first to deny this accusation. 

Another peculiar fact, those who do not know the laws of nature and 
who do not put them into their work often make a great success in their 
youth through their inherent talent, but in later life fall back in the march 
of progress on account of their lack of early training and absorbed knowl- 
edge. 

Painting and drawing have been taught since the days of Ancient Greece 

by what is known as "feeling." This is all very well, provided that a 

xvii 



xviii THE ART OF COMPOSITION 

sound knowledge of construction, of colour, of perspective, and of composi- 
tion, all based on nature's laws, has been learned and absorbed before "feel- 
ing" is permitted to be expressed. Above all, this knowledge, this 
foundation, must be a part of the artist's subconscious self, so that he does 
not have to think of rules or methods when he is painting. 

If he has not assimilated this knowledge, his work will become stilted, 
mannered, lacking in charm, spontaneity, and "feeling." 

Perspective is used by painters, but they do not necessarily use a ruler, 
compass, or other forms of measurement. Drawing by eye, they are, how- 
ever, guided by the rules of perspective. Dynamic Symmetry should be 
used in exactly the same way. 

I have tried to lead the reader from simple compositional arrangement 
to the more complex, always remembering that the psychological element 
is to be considered, and that man bases his ideas and feelings of art on 
nature's laws. 

In the last chapter, I have given a few geometrical explanations for those 
who wish to delve deeper into Dynamic Symmetry. But I must stress that 
it is not necessary for the artist or photographer to understand the "whys" 
or "wherefores," except that Dynamic Symmetry is based on nature's laws. 
If, however, they are intelligent students, they will not be satisfied with 
working blindly, and will continue the study, in this the most logical and 
most interesting means of arriving at good compositional forms and layouts. 

The little device which I have invented and which I will describe in this 
book, will help, materially, the artist and photographer to use Dynamic 
Symmetry in all his work. It will also help the motion-picture director to 
plan his sets as well as the placing of his principals. 



THE ART OF COMPOSITION 



CHAPTER ONE: COMPOSITION IN GENERAL 




OMPOSITION is one of the means to express to others the 
thought that is in the artist's mind. We can do this with 
colour, with line, mass, form, or with light and shade — 
all of which should be combined to bring out more forcibly 
the idea of the artist. 

We must take into consideration at least six things in 
composing a work of art, whether we paint, photograph, 
model, engrave or work in any medium by which an idea 
is expressed in graphic form. 




FIG. lA. COMPOSITION OF MASS 




FIG. iB. COMPOSITION OF VALUE 



., 



2 THE ART OF COMPOSITION 

1. The placement of the different elements. 

2. The masses or weights so as to get balance. (See Fig. lA.) 

3. Closely allied to this is the composition of values. (See Fig. iB.) 

4. Composition of line. (See Fig. iC.) 

5. Composition of colour. (See Frontispiece.) 

6. Composition of Perspective. This includes ground planning. (See 
Fig. iD.) 

The placing of a certain thing in a picture or on the stage, which, at first 
glance, holds our attention, should be the principal object; the eye should 
then be led to other things which take us from this principal object to 




FIG. iC. COMPOSITION OF LINE 




FIG. iD. COMPOSITION OF PERSPECTIVE 



THE ART OF COMPOSITION 3 

other forms that are associated in a minor key, and which help to express 
the idea, to be in harmony or act as foils or opposition, and which give to 
our mind the sense of completeness. Whistler once said, "Nature was 
made to select from." A work of art is not merely a rendering of nature's 
planning, but an adaptation by which, in a comparatively small area, one 
can convey the impression that nature takes the universe to express. 

The human mind is a very egotistical thing. Our whole existence is 
based on our experience with, sometimes, apparently trivial happenings. 

Man subconsciously thinks of things which happen to him personally. 




FIG. 2. LINES OF ACTION 




FIG. 3. UNES OF DIGNITY 



THE ART OF COMPOSITION 




FIG. 4. LINES OF REST 

For example, the lines of action are the diagonal (or oblique) lines (Fig. 
2); the perpendicular (or upright) lines express dignity and strength (Fig. 
3) j the horizontal (or lying flat) lines, rest (Fig. 4). This is because man, 
when running, is in a diagonal (oblique) position, and when perpendicu- 
lar (upright) he is standing, and when horizontal (lying down) he is asleep 
or at rest. This is not so when we view the lower order of animals, for the 
other animals run in an entirely different line of action from what we do, 
and when they stand, they have also different lines, so we must consider 
that the lines of composition are based on man's egotistical self. (Figs. 5 A, 
SB, sC 5D.) 




FIG. sA. THE LION 



THE ART OF COMPOSITION 




FIG. sB. ANIMALS IN ACTION 




FIG. sC. THE RAM 




FIG. sD. THE CAMEL 



6 THE ART OF COMPOSITION 

There are certain forms which we unconsciously associate with other 
ideas. For instance: an arrowhead immediately makes us feel that we 
should look in the direction in which the point of the arrow is directed. 
The arrow shaft, however, draws our eye to the feather end rather than to 
the point, as we like to feel that the arrow is flying away from us rather 
than toward us. The triangle gives us a feeling of rest and solidity with 
the idea of pointing upward. The circle gives us the sensation of con- 
tinued movement. The square gives us the sensation of solidity. The 
Hogarth lines of grace and beauty give us movement, continuity, and 
rhythm. The cross gives us the feeling of opposing force, and, on account 
of its use for religious purposes, the idea will subconsciously be associated 
with the feeling of piety. As a matter of fact, all form will be associ- 
ated in the mind of the beholder with previous experiences with that form, 
and if our composition partakes of these forms, it will express an idea more 
forcibly than if we did not make use of the subconscious feelings of the on- 
looker. 

In regard to the idea of balance, the seesaw is a very good example. If 
the board extends equally over each end of the centre rest or fulcrum, it 
will balance itself. (Fig. 6.) If we put a child on each end of the seesaw, 
of equal weight, it will also express a perfect balance (Fig. 7), and unless 
some force or weight is used on one end, it will always stay in this even bal- 
ance, but if we put a heavier weight on one end and a lighter weight on the 
other, the heavier end will immediately make the seesaw go down, and like- 
wise raise the other end. (Fig. 8.) 

If, again, we put two children on one end and a heavy person (equal to 
the combined weight of the two children) on the other end, it will also bal- 
ance evenly. (Fig. 9.) 

If we put one of the children toward the centre of the board, the one on 
the longer end will make the balance go down and the other end go up. 

(Fig. 10.) 

If we lengthen one end of the board and make one end short, and put a 
child on the short end, and the other end is long enough, it will balance by 
its own weight. Fig. 11.) 

If we shorten the seesaw on the end with the child and lengthen the other 
end, the child on the short end will be thrown in the air (Fig. 12), and the 
long end will go down; but if we increase the weight on the short end suf- 
ficiently, it will raise the long end to an equal balance. (Fig. 13.) 



THE ART OF COMPOSITION 




FIG. 6. EVEN BALANCE 




FIG. 7. EVEN BALANCE WITIT EQUAL WEIGHT 




FIG. 8. UNEVEN BALANCE 



8 



THE ART OF COMPOSITION 




FIG. 9. EVEN BALANCE WEIGHT SUBDIVIDED 




FIG. JO. DISTANT WEIGHT AGAINST WEIGHT 
NEAR CENTRE 




FIG. II. WEIGHT AGAINST DISTANCE 



THE ART OF COMPOSITION 9 

This gives us a very simple idea of weight, balance, and action, for when 
the seesaw is on equal balance, we have a feeling of rest, and when one end 
of the seesaw is down and the other up, we have a feeling that something is 
going to, or should, happen to make them balance. Each time that we 
leave the board up or down, we feel that it needs something to complete 
the action. 

We can do this also by placing a stick under the long end to apparently 
keep it up in the air, and our mind would be satisfied if this support for 
the long end were heavy enough, in our mind, to hold the board up. 
(Figs. 14A, 14B.) 




FIG. 13. 



WEIGHT AGAINST DISTANCE UNBAL- 
ANCED 






FIG. 13. 



WEIGHT SUBDIVIDED AGAINST DIS- 
TANCE 



10 



THE ART OF COMPOSITION 



All of these examples give you the mechanics of composition, for balance 
in composition is nothing more or less than a feeling of satisfaction of a 
completeness of form. 

Dynamic Symmetry will help us to arrive at an exact equation of these 
balances. 

If we look at the word DYNAMIC and immediately associate it with 
the words dynamite and dynamo, we have an idea that it expresses in the 
word itself, motion. Mr. Hambidge told us that while he named his re- 
discovery "Dynamic Symmetry," 8«i/a/«t oviintTpoi^ the Greeks had them- 
selves already named it by the Greek synonym. It is based on nature's 
leaf distribution and proportion. Everyone must recognize that nature 



«■ 



FIG. 14A. UNEVEN BALANCE SUFFICIENTLY SUP- 
PORTED 




FIG. 14B. UNEVEN BALANCE NOT SUFFICIENTLY 
SUPPORTED 



THE ART OF COMPOSITION ii 

does not move, grow, or exist by accident. It is for us poor mortals to 
discover the secrets of the Master Maker of all things, so as to use them 
for our own purposes and enjoyment. 




PIG. IS. DIAGRAM OF SUNFLOWER POD 

The Royal Botanical Society of London discovered that nature had an 
order of growth which is based on a peculiar form of numbering, strange, 
perhaps, to our present civilization. 

Taking the seeds of a sunflower pod, which they grew in all sizes, they 
found these seeds arrayed in a large spiral form, running from the centre, 
and also in a smaller spiral. (Fig. 15.) Whatever size the sunflower was 



12 THE ART OF COMPOSITION 

grown, the seeds of the large spiral numbered in a certain relation to the 
smaller spiral. They found that if it had fifty-five seeds in the long curve, 
it always had thirty-four in the short one, and if it had thirty-four in the 
long curve, it had twenty-one in the short one. It was always in that rela- 
tion. Then they went further and they found that all nature grew in the 
same way. That leaf distribution and all vegetable growth was based on 
this form of numbering, which is called summation. 

To explain: if we were to write the numbers i, 2, 3, 4, 5, 6, 7, 8, 9, lO, 
1 1, etc., we would be adding one each to the number before. If we say 2, 
4, 6, 8, 10, 12, we are adding two to each number. If we say 3, 6, 9, 12, 
we are adding three, and so forth. If we say i, 2, 3, 5, 8, 13, 21, 34, 55, 
etc., we are adding the sum of the previous number to the last number 
enumerated. This is called counting by summation. I shall adapt an- 
other word to this means of progression, and call it SEQUENCE. We 
know the meaning of the sequence of colour. Why shouldn't we say the 
sequence of form? — for that is the meaning of proportion and composition. 
Using nature as our guide for a means of sequence of form will give to us 
the same feeling of contentment as does sequence of colour. 



CHAPTER TWO: DYNAMIC SYMMETRY 




YNAMIC SYMMETRY means a certain form of com- 
position — a way of building a picture or other object in 
good proportion, so that it is pleasing to the eye. Nu- 
merous ways of getting composition have been tried since 
the world began. Dynamic Symmetry is the method by 
which the Greeks built their temples and their gods. In 
the Middle Ages, a different form of composition was used. 
The Japanese, Chinese, and others used different forms. 
Remember, while Dynamic Symmetry is a wonderful thing, 
it is not the only way of getting a good composition. Dynamic Symmetry 
really means a composition of spaces or areas, one in harmony or sequence 
with another. There is a composition of line, of space (notan, as the Japa- 
nese call it), as described by Dow, and of mechanical balance as described 
by Poor. An artist who wishes to express action, animation, or movement, 
will find that Dynamic Symmetry answers better for all his requirements. 

This form of composition is a composition of action, which does not neces- 
sarily mean that a figure has to be in motion, but simply that the lines or 
masses express motion. In Dynamic Symmetry the compositional forms 
express motion, as in Figs, i to 15. Opposed to this form of composition 
is one called static, or still — a bi-symmetrical composition is often a static 
composition. 

Dynamic Symmetry is really not difficult to learn providing you look at 
it in a simple, common-sense way. Remember, it is not one man's theory 
of composition — it is the Greek form of composition. A Grecian would 
have said, for example, this page was composed in Root two — as we say so 
many inches high and wide. Root One was a square, and from this they 
constructed Roots Two, Three, Four, and Five, etc. Ours is lineal measr 
ure and theirs is a measure of space. 

Dynamic Symmetry composition is not a thing that will make you me- 
chanical, as it bears the same relationship as perspective to composition. If 
you know the laws of perspective, you draw the perspective free hand. 

By drawing a square, you make Root One. The diagonal of Root One 
is the length of Root Two; the diagonal of Root Two is the length of Root 
Three; the diagonal of Root Three is the length of Root Four; and the 
diagonal of Root Four is the length of Root Five, etc. If the Greeks 
wanted to measure the ground of a temple, they would say it was so many 
Root One's, Two's, Three's, or other roots. If you paint a picture and 

13 



H 



THE ART OF COMPOSITION 



use one of the roots for your 
size of canvas, you will have 
a well-proportioned form to 
start With, so far as proportion 
of space to be covered. 

Inside of this form we may 
wish to place a composition, 
and we want to know where 
the objects are to be placed. 
One should think of composi- 
tion as a means of expressing 
an idea based on a psychologi- 
cal reaction of the onlooker, 
and this reaction is based on 
a previous experience, either 
physical or mental. 

If we were to draw two cir- 
cles in very close proximity to 
each other, almost touching, 
our minds would immediately 
feel that two revolving bodies 
were about to collide, as in 
Fig. 1 6. This is what is 
known as tangents in all forms 
of composition. This same 
sensation is given when you 
look at a circle or other form 
about to strike the picture 
frame, as is illustrated in Fig. 

17- 

If we overlap the circle or 
cut it with the frame, our 
mind is immediately associ- 
ated with an idea that the two 
which overlap have passed, 
one over the other (Fig. i8), 
and that the one cut by the 




FIG. 1 6. TANGENTS ABOUT TO COLLIDE 




FIG. 17. TANGENT NEAR EDGE 




FIG. i8. TANGENTS OVERLAPPING 



THE ART OF COMPOSITION 



15 



frame continues indefinitely and suggests the infinite, which is always inter- 
esting to the beholder. (Fig. 19.) In other words, onlookers like to be- 
lieve subconsciously that they are completing the picture themselves. It is 
another form of psychology. The old saying that "things must be taught 
as things forgot" should be carried out in the pictorial arts so that the be- 
holders believe they "had a hand" in the completion of the work. This is 
all, of course, in the subconscious mind. The painter must always figure 
on the psychological effect of his arrangement. 

A very good example of 
the psychological reaction of 
the beholder is the seesaw. 
If one end of the seesaw is 
portrayed in the air, with the 
support in the centre, our 
mind immediately waits for it 
to come down in the return 
action. (Fig. 8.) Especially 
is this so if the end in the 
air is more heavily weighted 
than the one on the ground. 
Whereas, if the seesaw is more 
heavily weighted on the end resting on the ground, and the part that is in 
the air is lighter or without weight, we do not wait for the return of the 
action, we are contented with a sense of finality, and that there will be 
no chance of it coming down again without some added force or weight. 
This should also be carried out, as was explained before, in your picture. 
One is almost tempted to say that composition is nothing more or less than 
the psychological reaction of the beholder j that they are satisfied or dis- 
satisfied with the action that has taken place or been expressed. 

On the other hand, one might wish purposely to express an unpleasant 
theme and would wish to use the tangent, perhaps, to give an idea of a 
catastrophe. (Fig. 20.) Take, for example, two fighters. If a fist of 
one were about to strike the other's head, it would form a tangent and 
would be the correct form for that action. (Figs. 21A, 21B.) 

As I have said, all nature grows in a certain relation, and this order of 
growth in either vegetable or animal life has been found to be in the rela- 
tion in whole numbers of about i, 2, 3, 5, 8, 13, 2i, 34, 55, etc. This is not 




FIG. 19. TANGENTS OVERLAPPING AND CUTTING 
EDGE 






as 



*^ 






i6 



THE ART OF COMPOSITION 



so exact, however, as the rela- 
tion of the numbers Ii8, 191, 
309, 500, 809, 1309, 21 18, 
3427, etc. We will use for the 
present, though a little inaccu- 
rate, the smaller approximate 
whole number summation of i, 
2, 3, 5, 8, 13, 21, 34, ss, etc., 
to show the relationship of 
nature to composition. If we 
draw an oblong which measures 
5 inches by 8 inches, and then 
draw a diagonal, or hypotenuse, 
from the two far corners, and 
crossing this diagonal with a 
line (one end of which rests in 
the corner, and which crosses 
the diagonal line at right an- 
gles) continuing through to the 
opposite side of the oblong, we 
shall have drawn an oblique 
cross in the oblong. 

By drawing a line parallel 
with the side, where the short 
crossing line touches the sides 
of the oblong, so as to form a 
square on one end, you will 
have produced the original 
form of the oblong, but in a 
smaller proportion or sequence 
on the other end. As the origi- 
nal form measured 5 by 8, the 
smaller form will measure 3 
by 5, and if we draw another 
line across where the diagonal 
meets, we shall have a smaller 
form which will measure 2 by 




FIG. 20. THE SUGGESTED EFFECT OF TANGENTS 




FIG. 2i.\. TANGENTS THAT ARE NECESSARY 




FIG. aiB. TANGENTS THAT ARE NECESSARY 




THE INDIAN 



AFTER AN OIL PAINTING BY MICHEL JACX)BS 



In Root Four 




THE DUCHESS 



AFTER AN OIL PAINTING BY MICHEL JACOBS 



In Root Two 




FIG. 22. SEQUENCE OF AREA IN WHOL£ NUMBERS 



20 THE ART OF COMPOSITION 

3, and if we draw again another line, we shall have a smaller form which 
will measure i by 2 inches. (Fig. 22.) By this method, you will see 
that you have made smaller forms in the large rectangle, or forms in se- 
quence which will measure in the summation of i, 2, 3 5, 8 j the same as if 
we strike high "C" or low "C" on the piano. It is the same sound, only 
one is, so to speak, greater in its vibrations than the other. 



CHAPTER THREE: DIFFERENT ROOTS OR FORMS 

PROPORTION OF PICTURES 

TARTING at the beginning to study Dynamic composition, 
one must first learn the so-called roots, these are nothing 
more than squares and oblongs of different proportion. 
While one can make any number of roots, I have only 
shown up to Root 26 in this book, and have used only six 
roots to explain this form of compositional proportion, 
namely. Roots One, Two, Three, Four, Five, and the 
Whirling Square Root. 

To simplify the descriptions of roots and crossing lines, 
we shall designate hereafter: 

• 

The Diagonal: A line, 
drawn from opposite corners 
or any oblique line. (Fig. 
23-) 





FIG. 43. ROOT TWO SHOWING THE DIAGONAL 



A Crossing Line: A line 
drawn from one corner to the 
outside edge, crossing the di- 
agonal (Fig. 24) at right 
angles. 




FIG. 24. ROOT TWO SHOWING THE DIAGONAL 
AND CROSSING LINE 
21 



22 



THE ART OF COMPOSITION 



Parallel Lines: Lines 
drawn straight across the 
form, parallel to the sides or 
ends, at the point where the 
crossing line touches the out- 
side edge through any inter- 
section (Fig. 25) or any line 
parallel to any root boundary, 
(Fig. 26.) 




FIG. «. ROOT TWO SHOWING THE DIAGONAL, 
CROSSING LINE AND PARALLEL LINE 



^ 


""""A 


"sT" 


— ..«.-»««^ 


: W 


/ J 


\ 


^y / 


























! W 


/ * 


\ 


y^ / • 


I \ \ 


/ i 


\ 


y'^ / • 


1 \ ^ 


/ PARAt 


LEL tlNcN 


r / 1 


♦ \ / 


N. 




\ / \ 


\A 


\. 




SX / ( 


4 Y - 


PAOVt, 


JttC UKC 


J \/ » 










> /^ 


y^ 




v/ \ 1 


♦ / ^ 


y^rt-OMi. 


cu UNK 


" \ ■ 


L^j 


\ 




Kj 



FIG. 26. ROOT TWO SHOWING THE PARALLEL 
LINE IN ALL DIRECTIONS 



THE ART OF COMPOSITION 23 

To avoid confusion and to enable the reader to pick out the roots at sight, 
in the different layouts I have adopted the following symbols to designate 
each root. 

The Root One will always be designated by a line made with a series of 
dots: 

The Root Two will always be designated by a line made with a series of 
crosses: ^ ■•-■*• t- .*• .^ «. 

The Root Three will always be designated by a line made with a series 
of dashes: _ _ 

The Root Four will always be designated by a line made with a series of 
angles: <_*-*_ ^ ^ *. «_ 

The Root Five will always be designated by a line made with a series of 
wavy dashes: ^ -»,^^ ^,^ .^^ ...^ 

The Whirling Square Root will always be designated by a line made 
with a series of spirals: ,»»,a »*9.»a»» 

The diagonal and crossing lines as well as lines which do not form an- 
other root will be designated by a straight continuous line. 

By this means, we shall designate and the reader will be able to distin- 
guish readily the roots which are contained in the grand mass. 

If there are two roots, one overlapping the other, for example, a Root 
One containing two Root Four's, they will be designated by a line made 
with a series of dots interposed with the angle: <_ -^ .*-.--..«— .<- 
or, as another example, if a Root One contained a Whirling Square Root 
it would be designated by a line made with a series of alternate dots and 
spirals: »•»•••»• «••••••••< 

Another example would be, if a Root Three contained two other roots, 
a Root Two and a Whirling Square Root, it would be designated by a cross, 
a spiral, and a dash: .+. — ^ -»- — •© -♦- 
(See Fig. 27 for all of these symbols.) 

In addition to these markings, wherever possible, I have also designated 
the root by the number of the root. The Root One I have marked S, which 
stands for a square, and the Whirling Square will be known as W.S.; the 
other roots by the number of the root and also in the captions under each 
illustration the roots used. 



24 THE ART OF COMPOSITION 



DOOT5 

.ONE 

^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^^^ jr\NO 

THREE 

^ ^^ ^ ^^ ^ ^^ ^^^ ^ ^FOUR 

_ ^ ^^^^^^^^^ FIVE 

• «e.,ee«c.e<.«ec«WHIRLING SQUARE 
COMBINATION OF TWO ROOTS -- 
ROOT ONE and TWO. ^.^.^.^.^.^.^.^.^.^.^.^ 

♦• ONE and THREE 

♦♦ ONE and FOUR . ^ . ^ . ^ .*_ .^ . -t_ . ^ .-._.*_ .i^ .*_ . 

♦♦ ONEand FIVE ..^.^w.-v^.-^...^ .-~^ .-^. ^.^^ 

" ONEand the WHIRLING SQUARE ...<i.. 

- TWOandTHREE-e - ^ - ^ - ^--.._ - - --^-^- 
TWOdnd FOUR ^ ^ _H ^ ^ -^ -H -- -H - -H^ ^ ^ H- -H H-^ +^ 
TWOdndi iVc .^.xbv -«- -o^^ 'vv..^. <w-«-'v»..^ /v^.^. 'w.^ ^w,^ •.'v.^./M—^. 
TWOandthe WHIRLING SQUARE ^e_^.e__e^«_^«^«-^ 

•• THREEand FOUR _.< * ^ ^ ^ ^- 

THREEdndFlVE ^ 

'• THREEandtheWHIRLING SQUARE-* _e _e_«_« _e_ 

FOURandFIVE. ^ ^^x ^^^^^^^ ^^^ 

FOURdnd the WHIRLING SQUARE^ e-^e ^e^e^^^o^ 
FIVE andthe WHIRLING SQUARE^ « ^e.^e— G->^r 

FIG. J7. SYMBOLS OF THE DIFFERENT ROOTS 



THE ART OF COMPOSITION 



25 



FIG. 28. ROOT ONE 



Root One — It is easily understood that 
if you multiply one side of a unit square 
by the other side, you will get the unit one: 
I X I = I } so we say the square is Root 
One (as in Fig. 28.) (See Glossary for 
definition of Square Root.) 



Root Two — If we measure the diago- 
nal, or hypotenuse, of a square we get the 
length of Root Two, and the side of the 
square itself is the other sidej for example, if we take a square measuring 
3 inches (7.65 centimetres), we find the diagonal measures about 4^4 inches 
(10.20 centimetres). By making an oblong measuring about 3 X 4^4 
inches (7.65 X 10.20 centimetres), we have constructed a Root Two rec- 




■ 4 'A Inches fl0.20Cent(metep3)- 

FIG. 29. ROOT TWO 



26 



THE ART OF COMPOSITION 



tangle, or oblong j if the measurement is done with a compass, you do not 
need to know the number of inches. By simply putting one point of the 
compass on the corner of the square and the other point on the opposite far 
corner, you will have the length of Root Two. (Fig. 29.) 

Root Three — By putting the compass points on the two opposite far 
corners of Root Two, you will find out the length of Root Three, and of 
course, the width will be the width of the same square. This Root Three 
will measure about 3 X 534 inches (7.65 X 13.40 centimetres) as in Fig. 
30) if we use the same base line of three inches. 




5'A Inches dOAO Centimeters) 

FIG. 30. ROOT THREE 

Root Four — By again putting the compass points on the two opposite 
far corners of Root Three, you will find out the length of Root Four, and 
again the width will be the size of the original square. This Root Four 
will measure about 3X6 inches (7.65 X 15. 30 centimetres), using the 
same square. Two Root One's equal a Root Four (as in Fig. 31), and one 
half of a square measures a Root Four. 

Root Five — By once again putting the compass point on the two oppo- 
site far corners of Root Four, you will find out the length of Root Five, 
again using the width of the original square: 3 inches. This Root Five 



THE ART OF COMPOSITION 



27 



will measure about 3 X 6"/i6 inches (7.65 X 17.70 centimetres) as in 
Fig.32. All the other roots can be drawn in the same manner. 



^ 

^ 
^ 
^ 

'ft 

^f 
J^ 

.«» 
u^ 

gr- 

Ih 
If 

t 
^ 

1 fU 



-6- Inches (l5.30Centimeters)- 

FIG. 31. ROOT FOUR 




6'Vi6 Inches (17.70 Centimeters) 
FIG. 32. ROOT FIVE 



28 



THE ART OF COMPOSITION 



The Whirling Square Root — This root is a little different from all of 
the foregoing roots. We find out this by taking a square and marking off 
half of one side; we measure the diagonal of this half, using the same 3-inch 
square. This diagonal will measure 3^ inches (8.65 centimetres). By 
adding the half of the square to the length of this diagonal, you will have 
the length of the Whirling Square Root; using again the width of the 
original square for the small end, the Whirling Square Root will measure 
3 X 4^'^ inches (7.65 X 12.50 centimetres), as in Fig. 33. 



V* 



do 



£ f»6<i G &a i66»a tf0<;«6so& 009 



<o; 



« 

•if t9 • 




«««<>•• 9909 99999009999999 999 999^99990 O-OOSOOSOOOSS 09> 

4% Inches(l3.50&ntimeters) » 



FIG. 33. ROOT OF THE WHIRLING SQUARE 



Another way to form the root of the Whirling Square is to take a square, 
and from the centre of one side draw a half circle j this arc will touch the 
corners of the square. This will give you a Whirling Square Root on each 
end, and the whole form will be a Root Five. By taking away one of the 
small Whirling Square Roots or oblongs, you will have a Whirling Square 
Root, which is a square and a Whirling Square. So, you see, the Root Five 
and the Whirling Square Root are closely related, as in Fig. 34. 



THE ART OF COMPOSITION 



29 





FIG. 34- ROOT FIVE WITH THE WHIRLING SQUARE ROOT 



Putting the Roots Outside of a Square — All of the roots can be 
placed outside of a square by drawing a square, taking a diagonal of the 
square or Root One and laying it along the base of the square and drawing 
the oblong or rectangle ; again laying down the diagonal of Root Two, you 
will get the length of Root Three ; again laying down the diagonal of Root 
Three you will have the length of Root Fourj and again laying down the 
diagonal of Root Four, you will have the length of Root Five, as in Fig. 35. 




FIG. 35. ROOTS TWO, THREE, FOUR, AND FIVE OUTSIDE OF THE SQUARE 



30 



THE ART OF COMPOSITION 



Putting the Roots Within a Square — All of the roots can be placed 
within a square by the following method. Draw a square and with a com- 
pass make a quarter circle, called an arc, the two ends resting in opposite 
corners, and by drawing a diagonal from the opposite two corners, you will 
cross this quarter circle or arc at the centre; then, by drawing a line parallel 
with the top side and base of the square, you will have formed Root Two 
within the lower part of the square, as in Fig. 36 

By again drawing a diagonal line from the corner of the square to the 
corner of the Root Two oblong thus formed within the square, you will 
draw the parallel line to form Root Three where this diagonal crosses the 
quarter circle. Again drawing the diagonal line from the corner of the 
square to the corner of this Root Three, you will know where to draw the 
parallel line to form Root Four. And again drawing the diagonal line 
from the corner of the square to the corner of the Root Four rectangle thus 
formed, you will have formed Root Five. Wherever the diagonal crosses 
the arc is the place to draw the parallel line to form the root as in Fig. 36. 

Any of these root rectangles, or oblongs, 
will be found to be a good proportion for 
your canvas, or board, on which to draw or 
paint your pictures, and as a guide for the 
photographer in cutting his print. 

It must be remembered that Roots One, 
Two, Three, Four, Five, etc., bear a rela- 
tionship one to the other. For example, 
Root One, we have seen, contains all the 
other roots, and, likewise. Root Five con- 
tains all the other roots, so that, by using 
two or more of these roots, one within the 
other, we have a perfect sequence of area. 
In the following chapters I will show how this relationship of the different 
roots is used to form various compositional layouts. 

A very simple method of finding out what is the root of any shape would 
be to use a compass on the small end, measure off the square on the long 
side, point off Root Two, then, with a compass, take the diagonal of Root 
Two, lay off Root Three, etc. 

If you wish to measure with a ruler, you could take the measurement of 
the long side of the oblong or rectangle and divide it by the short side. 




FIG. 36. ROOTS TWO, THREE, FOUR, 
AND FIVE INSIDE A SQUARE 



THE ART OF COMPOSITION 31 

This would give you the symbol number of the root, or as it is called 
the Reciprocal. For example, if the oblong measures 3 by 4% and you di- 
vided this by 3 (the length of the short side), it would give you 1.41 +. 
You would know this to be a Root Two rectangle. (See Proportion of 
Roots, Chapter Sixteen.) Another example: if the rectangle meas- 
ured 5 by 7.07 1 inches and you divided it by the short side, namely 5 inches, 
the result would again be 1.4 142. This would show that it was also Root 
Two. If you have a form which measures 3 by 6 inches and you divide 
the long side by fhe short side (6 divided by 3 is 2.000), you know that this 
is the number which shows that the proportion is a Root Four. 

Inversely, if you wish to know the measurement of the long side of any 
root and you know the dimension of the short side, multiply the short side 
by the number of the root that you wish to use, called the Reciprocal, as 
shown in Chapter Sixteen; this will give you the length of the long side. 
These measurements are only approximate, and are used only to make the 
idea more comprehensible to the beginner. 



CHAPTER FOUR: POINTS OF INTEREST 




SIMPLIFIED FORMS AND LAYOUTS IN ROOTS ONE, TWO, THREE, FOUR, 
AND FIVE 

N THE preceding chapter, we have found out the propor- 
tion to make our picture forms that are pleasing to the eye 
in the major shape. We now shall find where to place the 
principal points of interest. 

By taking Root Two instead of starting with Root One, 
we shall have 
a simpler 
form to ex- 
plain the be- 
ginning of Dynamic Sym- 
metry composition. As we 
explained in the previous 
chapter. Root One is a com- 
bination of two Root Four's 
and can be divided up into 
many more forms, and is a 
little harder to study at the 
outset than the Roots Two, 
Three, and Four. So, as I have said above, we will start with finding out 
the principal points of interest in Root Two. 

By drawing an oblong which we know to be Root Two, as is explained in 
the previous chapter, we take the diagonal of a square; this diagonal would 

be the length of Root Two, as 
is illustrated in Fig. 29. After 
drawing a diagonal from the 
two far corners, cross it with 
an oblique line one end of 
which rests in the corner, 
crossing the diagonal line at 
right angles, continuing 
through to the opposite side 
of the oblong, as is illus- 
trated in Fig. 37: where these 
FIG. 38. THE OLD woMA^N WHO uvED IN A two lincs cross will be one 

32 




FIG. 37. 



ROOT TWO WITH DIAGONAL AND 
CROSSING LINE 




THE ART OF COMPOSITION 



33 




of the artistic centres of the rectangle. It will be, of course, understood 
that the diagonal may be drawn from the opposite corners, and the cross- 
ing line, or, as it is known, the line "squaring the diagonal," may be 

drawn from any one of the four cor- 
ners. Also, the oblong may be upright 
or lying on its side, as is illustrated in 
Fig. 38, Fig. 39, and Fig. 40. 

Any one of these points of interest may 
be considered as principal points of interest. 
If we were to draw the diagonal and 
cross it on the top and bottom, we would 
have two points of interest, one of which 
wc will call the principal and the other the 
secondary point of interest in Sequence. 
(Fig. 41.) Again, we can take the oblong 
and draw on it both diagonals and all four 
of the short crossing lines to make it look 
like Fig. 42, 

You will notice on this illustration that 

FIG. 39- COUNTRY ROAD , , J * J • * 4.I, • • 

I have designated one pomt the prmci- 
pal point of interest, another the second point of interest, another the 
third point of interest, and another the fourth point of interest. To 
explain this matter further, I would refer you to Fig. 43 which shows you 
a simple composition based on the idea of taking the points of interest in 
Sequence. 

We have shown now a sim- 
ple way of getting points of 
interest in the flat plane in 
Root Two. This same lay- 
out may be applied to Roots 
Three, Four, and Five (as in 
Figs. 44, 45, 46). 

When placing the object in 
the principal point of interest, 
it is very good to follow, more 
or less, the lines of the compo- 
sitional construction, namely, p,g ^„ 5^jll life 




34 



THE ART OF COMPOSITION 




FIG. 4«. PRINCIPAL AND SECOND POINTS OF 
INTEREST 




FIG. 4*. 



PRINCIPAL, SECOND, THIRD, AND FOURTH 
POINTS OF INTEREST 





FIG. 43. LITTLE MISS 
MUFFET 




THE CRYSTAL GAZER 



AFTER AN OIL PALXTING BY MICHEL JACOBS 



In Root Two 




THE HILLSIDE 



AFTER AN OIL PAINTING BY MICHEL JACX)BS 
A form less than Root Two 



THE ART OF COMPOSITION 



37 




FIG. 44. ROOT THREE SHOWING POINTS OF INTEREST IN 
SEQUENCE 




FIG. 45. ROOT FOUR SHOWING POINTS OF INTEREST IN SEQUENCE 




FIG. 46. ROOT FIVE SHOWING POINTS OF INTEREST IN SEQUENCE 



38 



THE ART OF COMPOSITION 




FIG. 47. ROOT ONE CONTAINING 
TWO ROOT FOUR'S 



the diagonal and the short crossing line. It is not necessary, however, to 
make the composition exactly on these lines. The composition would be- 
come too mechanical if this were done. Perspective is used by an architect 
in a different way than by a painter. The architect's drawing is hard, cold 

and mechanically perfect, whereas the 
painter's perspective is free and bold and 
more artistic. Remember that Dynamic 
Symmetry has the same relation to compo- 
sition and proportion that perspective has 
to any painting, photograph, or stage set. 
The Root One, as I explained before, 
contains two Root Four's. This could be 
used in a number of ways; the more com- 
plicated ones 1 will take up later. Divid- 
ing the square in half, and drawing the 
diagonal through each of the halves, and 
squaring the diagonal, as is illustrated in 
Figs. 47 and 48, would give you two points of interest, which could be con- 
sidered as principal and secondary. I have also shown a simple sketch 
based on this idea. 

Continuing to make this Root One useful for a composition with the two 
Root Four's which it contains, divide each 
one of these Root Four's, the same as we 
did with the Root Two, with both the 
diagonals of each Root Four and the cross- 
ing lines; we now have eight places to 
select from as our principal points of in- 
terest and seven points of interest in Se- 
quence. We also have a number of 
crossing lines which we can use more or 
less in our composition, as is illustrated in 
Figs. 49 and 50. 

Another way that we could use Root 
One would be to draw the diagonal line, 
and then, with a compass, draw a quarter circle to find out 
the smaller roots inside of a square, as we explained in Chap- 
ter Three, we would have lines as illustrated in Fig. 51. [|^ 




THE ART OF COMPOSITION 



39 



Now, if we draw a line where the quarter circle crosses the diagonal, as 
if we were going to find out the Root Two (as is explained in Fig. 36, Chap- 
ter Three), and if we do this on both sides and ends, we shall have a lay- 
out of lines for a composition which will be as is shown in Fig. 52. We can 



•^•T- ■•••» — T "^r? 


^t^^-f'r—vr—f—r^ 


r\- 


l/V 


'ks^. 


K><S 



FIG. 49. ROOT ONE WITH EIGHT 
POINTS OF INTEREST 




FIG. 50. THE 
DANCER 



select any one of the points as a principal point of interest, 
and the other ones to be points of interest in Sequence, as 
is illustrated in Fig. 53. There are many different ways 
of using all the roots, which will be explained later. 
The few compositional layouts which I have given are for the beginner. 



$>5^ 


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t.£ 


%h 


^ 




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^vL 


^ 


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FIG. 51. 



ROOT ONE WITH A QUAD- 
RANT ARC 



40 



THE ART OF COMPOSITION 




FIG. 52. ROOT ONE WITH TWO 
QUADRANT ARCS AND PARAL- 
LEL LINES 






FIG. 53- THE OLD 

FASHIONED 

GARDEN 




I wish here to suggest a method whereby the different roots and layouts 
can be kept for future reference, which will help the painter to correct the 
original drawing without again making the layout for the original picture. 

If you take a number of small transparent guides about two or three 
inches in width, each one with the different roots drawn upon it with water- 
proof drawing ink, and draw the crossing lines, the diagonal, and parallel 
lines which you wish to use, now holding this within a few inches of the eye, 
and standing off a few feet from the picture, you will be able to judge 
the corrections to be made in your painting to make it conform nearer to 
the root line or mass. These small guides can be kept for future reference 
for other compositions. This will do away with the task of each time 
drawing a separate layout on the canvas. In Fig. 54 is an illustration show- 
ing how this system can be used. 

For those who desire them the Pri-matic Art Company, of New York, 
have made up, under my direction, all the layouts contained in this book 
printed on transparent guides. 




ANNA PAVLOWA AND MICHAEL MORDKIN AFTER AN OIL FAINTING BY MICHEL JACOBS 

In Root Two 




IN THE WOODS 



AFTER AN OIL PAINTING BY MICHEL JACOBS 

In overlapping Root Ones 



THE ART OF COMPOSITION 



43 




FIG. 54. SHOWING HOW TO USE TRANSPARENT GUIDES 



CHAPTER FIVE: THE WHIRLING SQUARE ROOT 




E REMEMBER that the Whirling Square Root was made 
by taking the half of a square, drawing the diagonal of this 
half, and adding half of the square to the length of this 
diagonal to form one side of the oblong or rectangle. 
(Fig. 55.) Taking this oblong or rectangle and drawing 
into it a diagonal and the crossing line, and by drawing a 
line where the crossing line touches the outside of the ob- 
long, we will form, as we have said before, a square on one 
end and a reproduction of the same form on the other end 

in a proportion similar ecr oe,^ &».«.€, o«.e,e«, e^ce-e-e. e- 

to the major shape. 

By drawing the parallel 

line again, so as to form 

a Sequence of squares, 

we will have produced 

a compositional layout 

in Dynamic Symmetry 

of the Whirling Square 

as is shown in Fig. s^- 
We have mentioned, 

in the previous chapters 




<> 

4 




FIG. 55. WHIRLING SQUARE ROOT 

that nature grows in an order of summation, and we have produced in Fig. 
56 the Whirling Square Root in Sequence. If we draw diagonal lines 
crossing the squares, we shall have produced a Whirling Square similar to 
the Greek key pattern, which is so well known. If we connect these corners 
^e..«,.e..ft-e.-e.-e..a,.«,.e..e.-a<. »<«,.».•&. (s..(5..c.-&.«fc;^ with a continuous line, 
^ ^ c * ^y"^^ ^ w^ shall have a spiral in 

* » \ ? -'■'o ? ^^^ same proportion as 

the Greeks use on their 
«.«.^.v Ionic column, as in Fig. 

57- 

We, of course, know 

the effect of centrifugal 
force, one of nature's 
phenomena. We have 
all seen the pinwheel 
WHIRLING SQUARES IN SEQUENCE ^^row off fire from a 

44 




THE ART OF COMPOSITION 45 

central point, showing us this spiral in many beautiful compositional forms. 




FIG. S7. WHIRUNG SQUARE SHOWING GREEK KEY 
PATTERN 

We often see this spiral reproduced in nature. Look at the illustrations 
in Fig. 58 for some of these. 




FIG. s8. NATURAL FORMS AND DESIGNS 



46 



THE ART OF COMPOSITION 



We now wish to know how to use nature's way of making rhythmic curves 
which is well recognized in the scientific world and is called a logarithmic 
curve. Many scientists have studied this phase of nature's laws, but the art- 
ist is not interested in knowing the mathematical side of it, but simply 
how to reproduce it. It can be drawn outside of an oblong or square, but, 
for the present purposes, it is not necessary to do this, as at present we are 
only interested in producing it inside of a certain area. 

Besides giving you these facts as to how to reproduce this Whirling 
Square in the Whirling Square Root, we can reproduce it in any other root. 
This is very important, much more important, I believe, than is generally 
understood by students of Dynamic Symmetry. All composition, in no 
matter what root, should partake somewhat of this flowing, rhythmic, com- 
positional form: in the mind of the author. 

Perhaps it is a new departure from the generally accepted ideas of Dy- 
namic Symmetry, but to me it is a kernel of beauty, the essence of aesthetic 
feeling, which takes from Dynamic Symmetry the things we have seen 
heretofore of hard, cold, straight, angular lines. I cannot stress forcibly 
enough the great importance of always keeping this Whirling Square or 

spiral in mind. 

It combines and an- 
swers perfectly the 
well-known Hogarth 
lines of grace and 
beauty, and while in 
this chapter we will 
only take up the sim- 
pler forms, in a later 
chapter, it will be 
shown how this won- 
derful spiral can be 
used in compound 
forms that will help 
us to get rhythmic lines in beautiful proportion. One of the ways in 
which the Whirling Square can be used would be to take this form 
and draw the layout or plan, as in Fig. 57, and then to compose a 
picture using the eye or centre of the Whirling Square as our prin- 
cipal point of interest, radiating the lines more or less from this 




FIG. 59- 



WmRLING SQUARE ROOT WITH LARGE SQUARE 
SUBDIVIDED 



THE ART OF COMPOSITION 



47 



centre, and using other points as second and third points of interest, etc. 

This is done by first dividing the large or first square in half, drawing the 

diagonal in each half, and crossing the diagonal with the crossing line and 

parallel line, as shown in Fig. 59. In Fig. 60 we have shown a composition 




FIG. 61. WHIRLING SQUARE WITH ROOT TWO IN 
SEQUENCE 

based on this layout. Another simple method by which the Whirling 
Square Root can be used would be to draw the Whirling Square, and on 
the large, square end, draw a diagonal making a quadrant from the two 
opposite corners. This will produce (as was explained in Chapter Three, 



48 THE ART OF COMPOSITION 

Fig. 36, and Chapter Four, Figs. 51 and 52) a Root Two inside of a square. 
There is shown in Fig. 6 1 this layout carried out. 

You will notice that we have used as much of the curved lines as we 
thought would carry out the idea, both of the spirals and of the quarter 
circle or quadrant, and also the straight line. 

It may now be seen that you can divide this square or the other squares 
in Sequence into other roots to be contained in this Whirling Square Root. 

In a later chapter, we will take up the proposition of making more than 
one Whirling Square within a Whirling Square Root. 



CHAPTER SIX: 
ROOT ONE 



SIMPLIFIED COMPOSITIONS BASED ON 




O PLACE a composition in a square, as we have explained 
in the previous chapter, you can divide the square into 
two Root Four's, or you can draw a diagonal and draw a 
quarter circle or quadrant arc finding out where the Root 
Two would come. Or you could use the Root Three in- 
side of the square, or the Root Five. If you use any one 
of these roots in the square, you will have the balance of 
the square to contend with. Some of the methods of do- 
ing this are explained in the following. 
Remember, it is not always necessary to follow the straight lines of the 
Dynamic layout, and often the curve or spiral is more pleasing, as it gives 
rhythm, besides placement and line. It will be understood that, of course, 
the spiral can be used in all roots, not alone in the Whirling Square Root, 
and the principals laid down in the Whirling Square Root are applicable to 
all roots. 

Drawing a square and dividing it in half with a line drawn through the 
centre will give us two Root Four's. If we draw the diagonal through one 
of these halves and the crossing line, we shall have found out a point of 
interest which we will consider as the principal point of interest, and divid- 
ing the other half in the same manner to make the crossing line in the 
opposite corner will make the secondary point of interest. If we draw a 
line where the crossing line meets the boundary of one of the Root Four's 
and make a Root Four in Sequence, we shall have produced a layout, as 
is shown in Fig. 62. An illustration is also shown in Fig. 63 based on this 
layout. 

Another way of the many of using the Root One or square, would be to 
draw a diagonal making the quarter circle to make Root Two, as is ex- 
plained in Chapter Three, Fig. 36. Taking this Root Two and drawing 
the diagonal, then squaring the diagonal with the short line, we shall have 
a point of interest which we will call the principal point. The part that 
is left after making Root Two we can divide in half and draw the diagonal 
and our crossing line to get the secondary point, as is shown in Fig. 64. 
In Fig. 65 is shown a composition based on this layout. 

Another way that the Root One can be used would be to draw both 
diagonals of the square and draw two Root Two's at right angles to each 
other as before directed by means of two quadrant arcs or quarter circles, 

49 



50 



THE ART OF COMPOSITION 




FIG. 62. ROOT ONE WITH ROOT 
FOUR IN SEQUENCE 





FIG. 64. ROOT ONE SUBDIVIDED 

INTO ROOT TWO AND TWO 

SMALLER ROOT THREE'S 





THE GYPSY 



AFTER AN OIL PAINTING BY ARTHUR SCHWIEDER 
A double whirling square in a form less than Root Two 




THE COURTSHIP 



AFTER AN OIL PAINTING BY ARTHUR SCHWIEDER 
In Root Two 



THE ART OF COMPOSITION 



53 



taking the points where the Root Two line and the quadrant arcs cross, 
drawing an upright line and drawing another diagonal to half of the part 
that was left after making the Root Two within the square, and drawing 
two more diagonals to half of the Root Two, as is shown in Fig. 66. In 
Fig. 67 is shown a composition based on this layout. 




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^ 


s 



FIG. 66. ROOT ONE WITH THREE 

ROOT TWO'S OVERLAPPING 

WITH TWO QUADRANT ARCS 



FIG. 67. TREE ON A HILL 



A very beautiful conventional layout can be made in Root One by draw- 
ing four quadrant arcs and reproducing two Root Two's, as in the previous 
paragraph, where we make the two roots overlap, only this time we repro- 
duce the Root Two at the side and on the top ; then drawing two centre cross 
lines, as is shown in Fig 68, with the design carried out in Fig. 69. 




/ ^SmS' R^^s^ 


1 



FIG. 68. ROOT ONE WITH A ROOT 
TWO ON TOP AND ON SIDE 



FIG. 69. CONVENTIONAL DESIGN 



54 THE ART OF COMPOSITION 

Many combinations using the Root One, more or less simple or complex, 
can be made. The more difficult ones will be explained in Chapter Thir- 
teen. 

A few divisions of a Root One will be seen on page $5- 



THE ART OF COMPOSITION 



55 







PAGE OF ROOTS TWO. THREE, FOUR, AND FIVE INSIDE ROOT ONE 



56 



THE ART OF COMPOSITION 



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DYNAMIC LAYOUTS AIX IN RO<grpprWO ^OJ^PHOTOGRAPH REPRODUCTIONS ON 




WINTER LANDSCAPES By ALFRED T. FISHER 

Photographed from nature in Root Two 





PHOTOGRAPHS FROM NATURE By FRANK ROY KRAPRIE, S. M., F. R. P. S. 

In Roots One, Two, Three, and Four 



THE ART OF COMPOSITION 



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ROOT FOUR 




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ROOT TWO 



ROOT TWO 



ROOT THREE 






ROOT ONE ROOT ONE ROOT ONE 

DYNAMIC LAYOUTS OF PHOTOGRAPH REPRODUCTIONS ON OPPOSITE PAGE 



CHAPTER SEVEN: 
ON ROOT TWO 



SIMPLIFIED COMPOSITIONS BASED 





OOT TWO can be drawn as was explained in Chapter 
Two in two ways: either outside of a square or inside of a 
square. The best way to form Root Two or oblong out- 
side of the square, without referring to mathematical means, 
would be to measure the diagonal of a square. This will 
give you the length of Root Two. (Illustration Fig. 29.) 
If you wish to know the mathematical measurement, I 
would refer you to Chap- 
ter Sixteen, where all the 
formulas are given. 

To construct Root Two inside of a 
square as we have explained in the previ- 
ous chapters, you would draw a diagonal 
in the square and make the quadrant arc 
or quarter circle} where this line crosses 
the diagonal, we would draw a parallel 
line, as is explained in Chapter Two. This 
form is Root Two. The balance of the 
square can be thrown aside. (Fig. 70.) 
For my own purposes, I have many 
times drawn the roots in the following way: Taking a sheet of paper 
of any size, and drawing the root I wished by using the square, either 

inside or outside 
method, and plac- 
ing this measured 
root on the larger 
surface or canvas 
that I intended 
to use, I drew the 
diagonal through 
the opposite cor- 
ners. This is one 
of the methods 

riG. 71. lU-USTRATIVE METHOD OF ENLARGING IN PROPORTION Used by modcm 

illustrators to get an enlargement. It is very simple, very practical, and 

does away with all mathematical means. (Fig. 71.) 

60 



FIG. 70. 



ROOT TWO WITHIN 
ROOT ONE 




THE ART OF COMPOSITION 61 

After we have decided on the measurements of Root Two, we can place 
our composition. It is, of course, taken for granted that you have some 
idea to express, and that you have already conceived of the general effect 
that you want to get. Remember that Dynamic Symmetry is only a means 
of making your own conception more beautiful j it will not give you a con- 
ception, although it may suggest the arrangement. If you work for a short 
time with Dynamic Symmetry, your conceptions will naturally partake of 
compositional forms that will readily adapt themselves to some form of the 
innumerable Dynamic layouts. 

It is for you to choose, after your first conception has been formed, which 
particular grid or layout you wish to use; which particular thing you wish to 
stress and make the principal point of interest, which the second, third, 
etc. For example, you may be drawing or photographing a landscape, you 
may have houses and trees and lakes, any one of these three objects 
could be placed in the principal point of interest, depending on what 
your original conception of the subject was or how the ladscape impressed 
you. This is the artists' feeling which is individual, and is, of course, 
real art. 

Many students of Dynamic Symmetry have been led to believe that by 
drawing the lines of Dynamic Symmetry they can get an idea or conception. 
This, in my mind, is a mistake. The conception must come first j then 
use Dynamic Symmetry to perfect the arrangement. 

Taking the Root Two, we can use many simple forms or layouts, one of 
which would be to draw the diagonal, drawing the squaring line through 
the diagonal, and then dividing the remaining part in the same manner, 
as is illustrated in Fig. 72. After we have made the two Root Two's, one 
on each side of the large Root Two (this root divides exactly into two 
Root Two's) we can again draw the diagonal in the smaller ones, finding 
out the points of interests in each. One of these may be selected as the 
principal point of interest and the other as the secondary. The remaining 
parts of the smaller Root Two's we can divide into two equal parts (again 
two Root Two's) as is shown in Fig. 73. In Fig. 74 is shown an illustration 
based on this compositional layout. 

Root Two divides itself exactly into two equal Root Two's by means 
of drawing the diagonal and the crossing lines, as is shown in Fig. 
75. 



THE ART OF COMPOSITION 




FIG. 72. THE DIAGONAL AND CROSSING LINE IN 
ROOT TWO AND THE ROOT TWO IN SEQUENCE 




FIG. 73. THE DIAGONAL AND CROSSING LINES 

IN ROOT TWO AND THE TWO ROOT TWO'S 

IN SEQUENCE 




FIG. 74- THE GARDEN WALL 



THE ART OF COMPOSITION 



63 



Drawing two diagonals and making the star layout by crossing the diago- 
nals in both places, and then by drawing a line through the intersection and a 
parallel line through the length of the oblong, you will have made eight 
divisions which will all be Root Two's, and the two halves will also be two 
Root Two's in greater Sequence} and again, you will find four Root Two's, 
so that this layout really gives you one large Root Two which contains two 
Root Two's. These smaller Root Two's also contain four Root Two's. 
The major form contains also eight Root Two's, as is shown in Fig. 76. 



kflVe 







> 



FIG. 75. ROOT TWO DIVIDED INTO TWO ROOT 
TWO'S 





/ ' \ 
/ 1 \ 

/ * \ 

\ / 1 \. / 

\ J / 
1 \ * / 
' \ J / 

1 \/ 





FIG. 



76. ROOT TWO SUBDIVIDED INTO EIGHT 
ROOT TWO'S 



64 



THE ART OF COMPOSITION 



Another method of using a simple composition inside of a Root Two 
would be to form a Root One or square at the side, and in the remaining 
part to draw again a square in the smaller proportion, or Sequence. This 
would make a small square and a Root Two in smaller proportion of Se- 
quence. If we draw a quadrant arc or a quarter circle from the far cor- 
ners of the large square and cross this with the diagonal line, we shall have 
found the place where again the Root Two will be inside the square. If 
we draw the diagonal and crossing lines in the small Root Two, we shall 
have the point which we can make one of our points of interests. This 
layout would then look like Fig. 77. In Fig. 78 is shown an illustration 
based on this layout. 




FIG. 77. 



ROOT TWO WrrH ROOTS ONE AND TWO 
IN SEQUENCE 




FIG. 78. LA TOILETTE 



THE ART OF COMPOSITION 



65 



Another very simple composition inside of a Root Two would be to make 
a square, as we did in the previous layout, but this time make Root One's on 
both sides, one overlapping the other. This would then look like Fig. 79. 
If we take three of the Root Two's thus formed and draw the diagonal 
with a crossing line and draw the diagonals in three of the squares that re- 
main, we will have a layout which will look like Fig. 80. In Fig. 81 is 
shown a composition based on this layout. 



j.*.^' 



r 

f 

f 

f 
t 



•f 
t 



. ^.^.••.•^•^r 



FIG. 70. ROOT TWO WITH TWO ROOT ONE'S 

OVERLAPPING MAKE THREE ROOT ONE'S AND 

THREE ROOT TWO'S IN SEQUENCE 




FIG. 80. LAYOUT 



66 



THE ART OF COMPOSITION 




Another simple method of using a Root Two woiild be to draw a square 
within the Root Two and in this square draw two Root Two's overlapping 
each other. This would give you the layout shown in Fig. 82. In Fig. 
83 is shown a composition based on this layout. 




FIG. 82. ROOT TWO WITH ROOT 

ONE AND TWO ROOT TWO'S 

OVERLAPPING 



THE ART OF COMPOSITION 



67 



Another compositional layout can be made by drawing the square on 
one end of the Root Two, and dividing the remaining part into a square 
and a Root Two, and making the principal point of interest on the centre 
of the diagonals of the square and the secondary point of interest in the 
smaller square, as is shown in Fig. 84. There is shown in Fig. 85 a com- 
position based on this layout. On page 70 are shown a few layouts in 
Root Two. 

You can readily understand by these that the combinations are inex- 
haustible. In Chapters Thirteen and Fourteen, there is shown the com- 
bination of putting other roots and more complex compositions within the 
Root Two. 




FIG. 84. ROOT TWO WITH ROOT ONE ON SIDE 
FORMING ROOT TWO AND ROOT ONE ON END 




68 



THE ART OF COMPOSITION 




Kuppenneimerl 

GOOD CLOTHES 



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The John P. Gross i> c«. 

PMIUkO(LPMW P». 



SoUvbigrneUliQuestm 



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TXe fua in sports 
lies ia tie ma ke ~ 

OAV/eCA 
SKATES. 





Its Just WondeiHil 

IVORY 

f SOAP 




COMMERCIAL COMPOSITIONS IN ROOT TWO 



THE ART OF COMPOSITION 



69 







70 



THE ART OF COMPOSITION 




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LAYOUTS BASED ON PAGE 69 



CHAPTER EIGHT: ROOT THREE 



HIS root is found by the di£Ferent methods shown in Chap- 
ter Two, either outside of the square or inside of the square. 
If it is necessary to find out the size of a canvas desired, it 
can be done by means of the small size root as is explained 
in Chapter Seven and drawing the diagonal through the 
corners to get a larger proportion of the same root — 
the same method that an illustrator uses to enlarge his 
sketch, as is illustrated in Fig. 71. One can also find 
the root desired by using the transparent layouts, as 
before described. 

Taking a Root Three, draw the diagonals and the squaring lines on both 
ends, crossing both diagonals. This will give you three Root Three's. On 
the lower Root Three draw two uprights where the diagonal crosses the 
parallel line. On the upper Root Three, divide in half and draw two 
diagonals to meet at the centre, as is shown in Fig. 86. In Fig. 87 there is 
shown a composition based on this layout. 





FIG. 86. ROOT THREE WITH THREE 
ROOT THREE'S IN SEQUENCE 



FIG. 87. POKE BONNET 



72 



THE ART OF COMPOSITION 



Another compositional layout in Root Three would be to draw the two 
diagonals and the two crossing lines (as in the previous example), making 
three Root Three's. In the lower Root Three, draw a Whirling Square, 
as is shown in Fig. 88. In Fig. 89 there is shown a composition based on 
this plan. 




FIG. 88. ROOT THREE WITH THREE 

ROOT THREE'S AND RHYTHMIC 

CURVE 



FIG. 89. 



COMPOSITION BASED 
ON FIG. 88 



Still another method of laying out Root Three would be to draw a 
square on one side and a square on the opposite side. These will overlap 
each other at the centre. In other words, you would have two Root One's 
overlapping in a Root Three. Draw both diagonals in both squares, and 
in one square reproduce Root Three on the right-hand side, as is shown in 
Fig. 90. In Fig. 91 is shown a composition based on this layout. 

It can be readily understood that the number of plans or layouts are too 
numerous to mention. The foregoing is only to give you some idea of 
some of the layouts. 

On page 74 there is shown a number of layouts in Root Three. 



THE ART OF COMPOSITION 



73 




FIG. 90. 



ROOT THREE WITH OVERLAPPING ROOT ONE'S AND 
ROOT THREE IN SEQUENCE 



B THEARTOF COLOR 

ffln these days of technical know— 
leii^ an^ scientific accuracy, 
Itis a rfreat -wonder that the artist 
still follows the old law of colors 
and their complementaries as dem- 
onstrated by Newton and Drevfsto; 
based on the theory that red, blue, 
and yellow are primary colors,and 
^reen, purple, and orange are sec- 
ondary, me theory has lond since 
been discarded Tby scientists and 
tbfi new theory adopted as laid 
down by Young-Helmnoltz- Tyndall 
onthe spectrum 

When we see an object that is 
a certain color in a white li^ht the 
shadows of that object assume a 
color that b toward the coroplemen 
larytothe cdor oftheli^htedf side. 



B omm. CONTENTS ™™ Q 

CHAPTER TWO COLOR FIRST FOR ART STUDENTS 
CHAPTER Siy COLOR FOR THE PORTRAIT PAINTERS 
CHAPTERSEVENCGLORFORTHE LANDSCAPE PAINTERS 
CHAPTEREIGHT SUNLIGHT OUTDOORS AND IN 
CHAPTER TfN REFLECTED COLORS IN WATFR, 
CHAPTER TWELVE COLOR FOR COLOR PRINTERS 
CHAPTER FIFTEEN COLOR AS APPLIED TO DESIGNERS 
CHAPTER SIXTEEN COLOR AS APPLIED TO FLOWERS 
CHAPTER EIGHTEEN COLOR. DYING AND BATIK.. 
mnjcmi LIST OF ILLUSTRATIONS mnnnnm □ 

Color combtaation.3-- brilliant cotaptctrveat^rtea-' 
Color comb{nationS"aeutraliusd cotapLementane) 

Color cotnfcinatioas ■•bar monies in- brilliant 

Color combiaations--9pUt complementaries in orays 
Color e-onxtinatio as -split complementaries in l»ill>*< 

Scintillation, charts aKowind'broloen color 

The color of ihadows - still lite 

PorHrAlt-thc violet vail •».•. ... . 

landscape-aututn.n. cHan^esto winter 

Color Cotnbinattoits Continued tnon-ochrdn«» 
Color combinations contiuued frabicde»i^n"* 

Land .scape Idyl of a sumnters &on 

Neutralued complemeniarles '•• 



b^ 



ItllllllllllllD 



^ 



FIG. 91. COMPOSITION BASED ON FIG. 90 



74 



THE ART OF COMPOSITION 




LAYOUTS IN ROOT THREE 




PHOTOGRAPHED FROM NATURE By FRANK ROY FRAPRIE, S. M., F. R. P. S. 

In Root Two 




V- 






1 


V 1> 














V' 




S 













THE WILL 



AFTER AN OIL PAINTING BY ARTHUR SCHWIEDER 
A form less than Root Two using whirling square motif and star layout 



CHAPTER NINE: ROOT FOUR 




OOT FOUR is two squares laid alongside of each other, 
as is shown in Fig. 92. If we take this Root Four and 
draw the diagonals and the squaring lines and the parallel 
lines to the base, we shall have made two squares and four 
Root Four's inside of this large oblong, as is shown in Fig. 
93. There is shown an illustration in Fig. 94 based on this 
plan. 

Another interesting compositional layout can be made 
by taking the two Root One's which Root Four contains, 

and dividing them with each of the diagonals and squaring the diagonals, 

and on both of these diagonals drawing ^ 

the quadrant arc or quarter circle, which 

will produce two Root Two's in each 

square, one overlapping the other, as is 

shown in Fig. 94. There is shown a com- 
position in Fig. 96 based on this layout. 
Another compositional form would be I 

to take the Root Four and lay ofF the t 

Whirling Square Root by taking the com- • 

positional layout in Fig. 93, which will f 



give half of the square. The crossing 
line, in that instance, would give the length 
of the Whirling Square if added to half of 
the square, as was explained in Chapter 
Five on the Whirling Square Root. This 
will give, inside of the Root Four, a large 
and a smaller Whirling Square Root and f 
two Root One's. If we divide this Whirl- \ 
ing Square Root by a diagonal and the ; 
crossing line completing the smaller form 
in Sequence, we will have a compositional 
layout, as is shown in Fig. 97. In Fig. 98 fig. 
there is shown a composition based on this 
layout. 

Numbers of compositional layouts of Root Four are shown on page 81, 
so that it will not be necessary to give a separate explanation of each. 



» 

L 



ROOT FOUR WITH TWO 
ROOT ONE'S 



77 



78 



THE ART OF COMPOSITION 




FIG. 93 
ROOT 



ROOT FOUR WITH TWO 
ONE'S AND FOUR ROOT 
FOUR'S 



FIG. 94- 



COMPOSITION BASED 
ON FIG. 93 



THE ART OF COMPOSITION 



79 




FIG. »5. ROOT FOUR WITH TWO ROOT ONE'S, EACH SQUARE CON- 
TAINING TWO ROOT TWO'S OVERLAPPING 



Thonl^^ivm^ Joy 



^iocolAtes 
J Joy h Give 




FIG. 9«. COMPOSITION BASED ON 
FIG. 9S 




8o 



THE ART OF COMPOSITION 



r 
r 
r 
f 
f 
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r 




FIG. 97. ROOT FOUR WITH WHIRLING SQUARES IN SEQUENCE AND 

TWO ROOT ONE'S 




THE ART OF COMPOSITION 



81 











' .^^^ ^ 












LAYOITTS IN ROOT FOUR 



CHAPTER TEN: ROOT FIVE 




HE Root Five oblong or rectangle is, perhaps, one of the 
most interesting of all of the roots. It is the one, I believe, 
on which the whole of Dynamic Symmetry is based. Some 
of the forms in Sequence into which it can be divided are 
as follows: 

A Root Five can contain two Whirling Squares and two 

Root Fours. (Fig. 99.) 
It can be divided into one Whirling Square horizontal 

and one Whirling Square perpendicular. (Fig. roo.) 



» ■»■"%%* W^ ll^l% ^ W 



'~1 



FIG. 99- 



ROOT FIVE CONTAINING TWO ROOT FOUR'S AND TWO WHIRLING 
SQUARES 



>«.».w». 



"^ ■*»»|« ^ »<^«W ^ •» 









FIG. 100. ROOT FIVE CONTAINING A HORIZONTAL 

WHIRLING SQUARE 
82 



AND PERPENDICULAR 



THE ART OF COMPOSITION 83 

A Root Five rectangle can be divided into a square and two Whirling 
Square Roots. (Fig. 34.) 

Many more of these combinations with other roots can be made with a 
Root Five. This root is also peculiar, as it will give us the dimensions of 
the human figure based on the idea that the human figure can be enclosed 
in two Root Five's laid alongside each other. 

The proportions of the human figure have been explained by Mr. Jay 
Hambidge in the Diagonal so thoroughly that I must refer the reader again 
to "The Elements of Dynamic Symmetry" for this information, as this 
book is intended only as a book of composition. 

The student, for years, has been taught at first to draw from the antique, 
and until the advent of Dynamic Symmetry, we considered the figures of 
the Greeks to be taken from life, but we now know that they were con- 
ventionalizations based on the ideal, using Dynamic Symmetry to get the 
placement of the different members of the human body. From my ex- 
perience, I find that it is much better to start the student drawing from 
life, and later on, after he has learned Dynamic Symmetry, to apply his 
life drawing and anatomy, together with Dynamic Symmetry measurements, 
to the perfection of his design. 

On page 84 you will see a number of layouts using some of the different 
divisions of Root Five. 



^ 



THE ART OF COMPOSITION 








lAYOUTS IN ROOT FIVE 



CHAPTER ELEVEN: COMBINED ROOTS 




E HAVE already, in the preceding chapters, taken up in 
a simplified way the making of one root within another, os- 
ing the diagonals and the squaring lines, etc., of each root 
to get our composition. In this chapter we will take up a 
few more of the combined roots in Sequence, as was ex- 
plained in the preceding chapters. Root One could con- 
tain two Root Four's, or a Root Two, or a Root Three, or a 
Five, making these inner roots by means of the quadrant 
arc or quarter circle and the diagonal. All of these roots 
could be used at one time, if so desired, inside of the major Root One. 

It will be very easy to trace the roots which each grand form contains 
by the symbols which have been explained in Chapter Three, "Different 
Roots or Forms and Proportion of Pictures." (Fig. 27.) 

Fig. 10 1 shows a layout in Root One with the diagonals with two quad- 
rant arcs, and where these lines cross, we shall have produced two Root 
Two's overlapping each other, and by drawing upright lines at the same 
intersection, we shall have produced two Root Two's in the opposite direc- 
tion overlapping each other. 




y ^C^^H^ "i jyiH I ~> ■■ ~ f ■ I 

■* j[ J ^ ~ i ~) Fid ■ j \i k i J F 



FIG. loi. ROOT ONE WITH FOUR FIG- »»»• PASSING CLOUDS 

OVERLAPPING ROOT TWO'S 

By drawing two crossing lines through centres we shall have made the 
Root One contain four Root One's also nine smaller Root One's. In Fig. 
102 a composition is shown based on this layout. 

In Fig. 103 a compositional layout is shown also in Root One with the 
diagonals} dividing this Root One in half we shall have two Root Four's. 
If we draw the two diagonals in each one of these Root Four's and draw 

«5 



86 



THE ART OF COMPOSITION 



parallel lines where the diagonals of the individual Root Four's cross, we 
shall have made a star layout, as is shown in Fig, 104, where there is a com- 
position based on this layout. 




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FIG. 103. 



ROOT ONE WITH 
ROOT FOUR'S 



TWO 



FIG. 104. FIELDS 



In Fig. 105 is shown a layout also in Root One, with a Root Two 
and a space left over. By following the symbols of the Root Two, this 
can be readily understood. 





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TwS'S AND. SUPERIMPOSED 
DIAGONALS 



FIG. 106. EDGE OF THE DESERT 



Taking now the Root Two so formed, and dividing it in half, we shall 
have made two Root Two's, because the line that crosses the diagonal meets 
the outer edge of the square exactly in the centre. As we know, a Root 
Two contains two Root Two's, and knowing this, we can draw cross lines 
each time through a Root Two and always produce the same form. Then, 



THE ART OF COMPOSITION 



87 



over this, we can again consider the Root One and superimpose another 
layout by drawing the diagonal of the Root One, and the diagonal of the 
remaining space from the Root Two, which was previously drawn, and all 
the other diagonals, as is shown; this will give us the layout, with an il- 
lustration based on this compositional form in Fig. 106. 





ro6¥'four's and four root 

ONE'S 



FIG. 108. CONVENTIONALIZED MOON 



In Fig. 107, we again take the Root One, drawing four quadrant arcs 
and a complete circle, dividing the square in half, and one half again, giv' 
ing us two squares and two Root Four's. The upper right-hand square, 
or Root One, we have divided so that it will contain one large Root Two 
and one small Root One and a small Root Two laid horizontally. It will 
be noted that the small Root Two divides into four Root Two's by the lines 
already drawn. This can be readily traced by the symbols of the dot for 
Root One and the spiral for the Rhythmic Curve. A composition based on 
this layout is shown in Fig. 108. 

In Fig. 109, we have taken a Root Two as our major shape. Drawing 
the diagonals and the crossing lines, we shall have produced two Root 
Two's, side by side, and if we draw parallel lines at the intersections and 
diagonals at the left, where these lines bisect, we shall have made a layout, 
as is shown. A composition based on this layout is shown in Fig. no. 

In Fig. Ill, we again take the Root Two and draw the diagonals and 
the crossing lines; this gives us again the so-called star layout. Then, by 
drawing the parallel line so as to make two Root Two's, we superimpose a 
layout at the intersections by making uprights where the diagonal and 



88 



THE ART OF COMPOSITION 



crossing lines meet. Then, by drawing two parallel lines at the inter- 
sections of the diagonal and the crossing line, and by drawing diagonals, 
we shall have made the layout, as is shown. Fig. 1 1 2 shows a composition 
based on this layout. 




FIG. lOO. ROOT TWO WITH TWO ROOT TWO'S AND 

PARALLEL LINES AT ALL INTERSECTIONS AND 

DIAGONALS AT LEFT. 




FIG. no. WILLOWS 



THE ART OF COMPOSITION 



89 




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FIG. 112. BLUFFS 



In Fig. 1 1 3 we have taken the Root Three and divided it by the diagonals 
and the crossing lines, making three Root Three's by drawing the parallel 
lines. In the two side Root Three's, which are in Sequence, we have 
again drawn the diagonals. In the left-hand Root Three, we have crossed 
the diagonal by a series of lines at the intersections, and drawn two parallel 
lines through the major shape, also at the intersections. In Fig. 114 there 
is shown a composition based on this layout. 

Fig. 1 15 is also a Root Three with the diagonals in the major shape, and 
also in the upper and lower Root Three's thus formed. Uprights have 
been traced through the intersections and through the centre with diagonals 
connecting the centre with the uprights. In Fig. 116 there is shown a com- 
position based on this layout. 

In Fig. 117, also a Root Three, by drawing again the three Root Three's 
in Sequence in the same manner as before explained, and drawing the 
diagonals and parallels at intersections, you will have completed the lay- 
out. In Fig. 1 1 8 is shown a composition based on this layout. 

Fig. 119 is also a Root Three with six Root Three's and diagonals to 
the half for a newspaper or magazine layout. The various shapes shown, 



90 



THE ART OF COMPOSITION 




FIG. 113. ROOT THREE WITH THREE ROOT THREE'S WITH 
DIAGONALS AND PARALLEL UNES 



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FIG. lis. ROOT THREE WITH THREH 
ROOT THREE'S UPRIGHT, PARAL- 
LELS AND DIAGONALS 



FIG. Ii6. CONVENTIONALIZED 
ELEPHANT 





FIG. 117. ROOT THREE WITH 
THREE ROOT THREE'S AND NUM- 
BERS OF PARALLELS AT INTERSEC- 



FIG. J 1 8. A BORDER PATTERN 



92 



THE ART OF COMPOSITION 



of course, have each a relation to the other, on account of using the Dy- 
namic lines. This must always be true. In Fig. 1 20 is shown a composi- 
tion based on this layout. 





FIG. 119. ROOT THREE WITH SIX 

ROOT THREE'S AND DIAGONALS 

TO THE HALF 



FIG. 120. COMMERCIAL LAYOUT 



Fig. 121 is a Root Four which shows the major shape divided into four 
Root Four's by drawing the two diagonals with the crossing line and the 
parallel line, also a parallel line through the centre; by drawing upright 
lines through the intersections with the diagonals you will have completed 
this layout. In Fig. 122 is shown a composition based on this layout, which 
shows that it is not always necessary to follow straight lines, but the line 
can be curved in the form of the Whirling Square to make a rhythmic 
composition. 

In Fig. 123 is shown a Root Four with the spiral lines; by drawing the 
diagonal and the crossing of the diagonal, you will have produced a Root 
Four on each end and a Root One in the centre. By drawing a parallel at 




PEONIES 



AFTER AN OIL PAINTING BY MICHEL JACOBS 
In overlapping Root Ones 




ROCK OF ALL NATIONS 



By MICHEL JACOBS 



Modeled in bronze in Root Four 



THE ART OF COMPOSITION 



95 



the intersection of the diagonals, and by cutting the lines up with the spiral, 
you will have completed the layout with rhythmic lines, but not in the 
dimensions of the Whirling Square which has been carried out in a compo- 
sition in Fig. 124. 

In Fig. 125, you have a Root Five divided up into two Root Five's, one 
on each end, by means of the diagonal and the crossing line, and the rhyth- 
mic line drawn from the intersection in the left-hand upper corner. This 
layout has been carried out in composition in Fig. 126. 

Fig. 127 shows the Whirling Square Root with a composition based on 
this layout. (Fig. 128.) This last composition shows the possibility of 
combining the rhythmic, flowing line with Dynamic Symmetry. 



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FIG. 121. ROOT FOUR WITH FOUR 
ROOT FOUR'S AND PARALLEL LINES 
THROUGH INTERSECTIONS AND DI- 
AGONALS 



FIG. 



COMPOSITION BASED ON 
FIG. 121 



96 



THE ART OF COMPOSITION 




FIG. 123. ROOT FOUR WITH TWO ROOT FOUR'S AND ONE ROOT ONE 
USING THE RHYTHMIC UNES 



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FIG. 124. THE WAVE 



THE ART OF COMPOSITION 97 




FIG. 135. ROOT FIVE WITH TWO ROOT FIVE'S AND RHYTHMIC UNES 




FIG. 136. THE SLOPE 



98 



THE ART OF COMPOSITION 




FIG. 127. WHIRLING SQUARE ROOT AND DIAGONALS 




FIG. 128. CONVENTIONAL PATTERN 



CHAPTER TWELVE: MORE COMPLEX COMPOSITIONS 



E HAVE seen in the previous chapter a method whereby we 
used more than one root in the major shape. In this chap- 
ter, we will take up both two and three roots in the major 
shape. It will not be necessary to describe in detail 
why we have drawn each of the lines in the individual il- 
lustrations, as I believe, now, that the reader is conversant 
with the general scheme, but I wish to call to the attention 
of the student of Dynamic Symmetry a few cardinal 
points. 

Any major shape may contain other roots which may be found by drawing 
the diagonal, squaring the diagonal, and by drawing the parallels where 
this crossing line meets the outside of the large formj and also the major 
shapes may be divided in many ways, as is shown on page lOO. • 




Root One: 

It can contain all the other roots by means of drawing the quadrant 
arc or quarter circle, drawing the diagonal and the parallel line at inter- 
sections leading from Root Two down to Root Five. 

The Root One also can be divided into four equal parts making four 
Root One's, so that one root can overlap another root. For example, 
you can get two Root Two's in a square by having one overlap the other. 

Also, this Root One can be made to contain two Root Four's by divid- 
ing the square in half so that each one of these Root Four's would contain 
two Root One's. 

Each one of these smaller forms or forms in Sequence, as we know 
them, can be divided with the diagonal, the squaring line, and the parallel 
line. 
Root Two: 

It can contain two Root Two's by simply dividing the length in half, 
or by drawing the diagonal, the crossing line, and the parallel line. 

The Root Two can also be divided into three equal parts by making 
the parallel line pass through the intersection of the crossing line and 
the diagonal, and by making the rhythmic curve, as is shown in Fig. 129. 

In Fig. 1 30 is a composition based on this layout. 

The Root Two can also be divided into four Whirling Square Roots, 
one overlapping the other, by means of making the square on one end 
of Root Two, as in Fig. 131, dividing this square into four smaller 

99 



100 



THE ART OF COMPOSITION 






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MAJOR SHAPES DIVIDED INTO COMPLEX FORMS 



THE ART OF COMPOSITION 



101 




FIG. 129. ROOT TWO DIVIDED INTO THREE EQUAL 
PARTS AND USING THE RHYTHMIC CURVE 




FIG. 130. CONVENTIONAL LANDSCAPE 



102 



THE ART OF COMPOSITION 



squares, taking the half of one of these small squares, finding out the 
diagonal of the half, and making a Whirling Square Root in one corner, 
as in Figs. 132 and 133, and repeating it in the other three corners, as in 

Fig. 134- 

A few of the many subdivisions or forms in Sequence will be found 
on page 70. 



FIG. J31. ROOT TWO WITH A ROOT ONE ON SIDE 



r—- "• — 




-t* J 



FIG. 132. 



ROOT TWO SHOWING HOW TO MAKE 
THE WHIRUNG SQUARE 



THE ART OF COMPOSITION 



103 



i 













FIG. 133. HOOT TWO WITH WHIRLING SQUARE 
ROOT 






• •«•••« 't ' 



«-. ,V^c .. *r T ..'....■.*. ^ i 

FIG. 134. ROOT TWO WITH FOUR WHIRUNG 
SQUARES 



104 



THE ART OF COMPOSITION 



Root Three: 

It can be divided into three equal divisions, as is shown on page 71. 

Numbers of diflFerent forms can be drawn into this Root Three, and 

many have been shown on page 74. 
Root Four: 

It can be divided into two Root One's or four Root Four's, as is shown 

on page 78. Each one of the Root One's can be divided in their turn 

by all the subdivisions as shown on page 55 under Root One. On page 

81, many layouts are shown within Root Four. 
Root Five: 




FIG. 13s. ROOT FIVE WITH TWO WHIRLING SQUARES OVERLAPPING AND A 
WHIRLING SQUARE ON EACH END WITH ROOT TWO INSIDE OF A ROOT ONE 




THE ART OF COMPOSITION 



105 



It is a very important root. It can be divided into five equal partsj 
each one of the lesser forms will be Root Five's. 

It can be divided into one square and two Whirling Square Roots, as 
is shown on page 29. Each one of these forms in Sequence can be 
laid out or subdivided, as is shown under their respective headings in 
this chapter. 

We could take each one of these Whirling Square Roots and form the 
Whirling Square Root in Sequence, as is shown in Fig. 135. By look- 
ing at this illustration, you will see that we have combined in the Root 
Five two Whirling Square Roots, one Root One and one Root Two. In 
Fig. 136 there is shown an illustration based on this layout. 




FIG. 137. ROOT FIVE WITH A ROOT FIVE AT EACH END WITH DIAGONALS AND 

PARALLEL LINES 



?/T ^^ I ' ^^ ^y^"^'^^^ 



FIG. ij8. ROLLING GROUND 



io6 



THE ART OF COMPOSITION 



In Fig. 137 is shown a layout in Root Five by means of the diagonal, 
the crossing line, the parallel line, and numbers of diagonals in the forms 
so constructed j and in Fig, 138 is shown an illustration based on this 
layout. 

In Fig. 139 is shown another composition in Root Five, which is also 
made with the diagonal, crossing line, parallel lines, and numbers of 
diagonals differently arranged from those in the preceding layout. In 
Fig. 140 there is shown a composition based on this layout. 
Whirling Square Root: 

It is extremely interesting on account of its association with Root Five, 





FIG. 139- "- 

ROOT FIVE ON EACH END WITH 
DIAGONALS FROM CORNERS AND 
PARALLELS THROUGH CENTRE 
BOTH WAYS 



FIG. 140. WARRIOR 



THE ART OF COMPOSITION 



107 



which is the basis of all Dynamic Symmetry. As I have shown under 
Root Five, two Whirling Square Roots and a square make a Root Five. 
I have shown on page 1 1 6 a number of subdivisions and arrangements of 
the Whirling Square Root. Any one of these subdivisions can, of course, 
have the diagonals, the crossing line, and the parallel line. On pages 
114 and 115 I have shown a number of different layouts with illustra- 
tions based on them which can be readily understood at this time. 

In Fig. 141 there is shown a shape which is less than a Root Two, to 
demonstrate that it is possible to use, if necessary, a form which does 
not fit any of the roots. In Fig. 142 there is shown an illustration 
based on this layout. 




FIG. 141. 



A FORM LESS THAN ROOT TWO WITH 
FORMS OVERLAPPING 




FIG. 14a. THE GOSSIPS 



io8 THE ART OF COMPOSITION 

I trust that the reader, at this time, understands sufficiently the principals 
of Dynamic Symmetry to know that it is possible to make innumerable lay- 
outs and combinations of forms to suit the conception of the artist, and 
in closing this chapter, I wish to emphasize the fact that it is always neces- 
sary first to visualize the conception. Even go so far as to draw the picture, 
or, at any rate, the sketch, with your original conception fresh in your mind. 
Then, finding out which of the roots and Dynamic lines will more nearly 
carry out your idea, change the line so that it will come nearer to the Dyna- 
mic line. 



THE ART OF COMPOSITION 



109 





4 5 

PROGRESSIVE STEPS OF THE WHIRLING SQUARE ROOT 



no 



THE ART OF COMPOSITION 





ROOT TWO 



ROOT THREE 



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ROOT TWO 




ROOT FOUR ROOT FOUR 

DIAGRAMS OF DYNAMIC POSES OF THE HUMAN FIGURE 



I 




DYNAMIC POSES OF THE HUMAN FIGURE 




DYNAMIC POSES OF THE HUMAN FIGURE 



THE ART OF COMPOSITION 



113 



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ROOT THREE 



ROOT FOUR 



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ROOT FOUR 




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ROOT FOUR 
DIAGRAMS OF DYNAMIC POSES OF THE HUMAN FIGURE 



114 



THE ART OF COMPOSITION 







LAYOUTS OF COMPLEX COMPOSITIONS 



I 



THE ART OF COMPOSITION 



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ILLUSTRATIONS OF COMPLEX LAYOUTS 



ii6 



THE ART OF COMPOSITION 




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LAYOUTS IN THE WHIRLING SQUARE ROOT 



CHAPTER THIRTEEN: GROUND COMPOSITION IN 
PERSPECTIVE SHOWING THE THIRD DIMENSION 

E HAVE seen in the preceding chapters the composition or 
arrangement of masses so as to make a decoration in the two 
dimensions. Of course, the idea of design or pattern 
which all modern pictures should have is very important, 
whether they are painted in the subjective, which is just 
the spirit of the thing, or objective, which is a more or less 
literal translation of realistic forms. The picture must 
have a pattern, in the same way as a piece of cloth or other 
material. 

This is especially true in the subjective form, and is more noticeable in 
the two dimensions, but it is also necessary to have a pattern in the ground, 
in the third dimension. This is very obvious in sculptural or architectural 
work, but it is also necessary on the canvas or paper. 

The better way to understand this problem would be to draw a parallel 
perspective, or, as it is sometimes known, one point perspective, and in this 
perspective drawing lay out the root, and inside this root lay off your diag- 
onals and your crossing lines. In Fig. 143 there is shown a perspective 
drawing with a Root One or square laid out with the diagonal and the 
quadrant arc in perspective with a parallel line which shows the Root Two. 




romj or oi»T«NCt 



»OINT Of >»gHT 



pamof pi>TMici 



» 




nC. 143. PERSPECTIVE OF ROOT ONE WITH A ROOT TWO 



m 



ii8 



THE ART OF COMPOSITION 



I have drawn this illustration in scale the better to convey the idea in mind. 
But, of course, the artist will not use any mathematical measurements for 
his picture, but will approximate the placement of these lines so as to arrange 
his ground composition in the three dimensions to the best advantage. Fig. 
144 is a composition based on this layout. In Fig. 145 there is shown a 
Root Five in perspective divided by two Whirling Square Roots with the 
spiral or Whirling Square designated. In Fig. 146 there is carried out a 
composition based on this layout. 




FIG. 



COMPOSITION BASED ON 
FIG. 143 



THE ART OF COMPOSITION 



119 



If the reader wishes to go to the trouble of making a layout on trans- 
parent paper of the root that he wishes to use in two dimensions, holding 
this up in front of the perspective layout in the third dimension, he will have 
one overlapping the other. 

I suggested in Chapter Four that the artist make different roots with dif- 
ferent layouts on transparent guides with waterproof ink. If he holds 
these up to the eye (as was explained in that chapter), standing off from 
the picture, he will be able to judge immediately the corrections to be made 
in the original sketch or painting, making it conform nearer to the root he 
wishes to use. 



•ami OF OtSTAMCt 



POINT OP SMHT 



PCINT Of DurAMCt 




FIG. 145. PERSPECTIVE OF ROOT FIVE WITH TWO WHIRLING SQUARE ROOTS 




FIG. 146. COMPOSITION WITH PERSPECTIVE GROUND 



CHAPTER FOURTEEN: 
LIGHT, AND SHADE 



COMPOSITION OF MASS, 




S WE explained in the first part of this book and illustrated 
with the seesaw, the weight or mass of any composition 
must be considered. While Dynamic Symmetry will give 
you the placements of the principal points and other points 
of interest in Sequence, and will give you, to a certain 
extent, the shape of the masses to be followed (as closely 
as possible to the original conception of the artist), it must 
always be remembered that the weight of these masses 
would throw your picture off balance if they were not 
considered. 

For example: if we were to take a layout and paint the principal point of 
interest a gray, and another part, which we intended to keep as a minor 
point of interest, a black surrounded by a white mass, the principal point of 
interest would not hold our attention. 

It must always be borne in mind that the greatest contrast in black-and- 
white value will attract the eye. Sometimes we put a very light highlight 
into a dark mass, and sometimes the reverse — putting a dark mass into a 
light area: either one of these methods will hold the eye. 




FIG. 147. SUPPLICATION TO ZEUS. (DARK MASS BELOW AND UGHT MASS 

ABOVE) 



THE ART OF COMPOSITION 



121 




FIG. 148. WAR. (DARK MASS ABOVE AND LIGHT MASS BELOW 

Then, again, the texture will either attract or will not hold your atten- 
tion. For example: a black-and-white stripe of heavy lines wide apart 
will hold the eye, and a dotted line will give atmosphere. Oblique lines 
will not attract as much attention, or hold up in the foreground as much as 
the perpendicular or horizontal. On page 125 I have shown you a few 
textures reproduced by means of the Ben Day process, to remind you of 
these textures in the composition. 

Another example of balance or weight of composition, as we explained 
with the seesaw, is that one large mass can equal two or more smaller 
masses. (See Fig. 9.) 

If the large mass of dark colour is used in the composition at the lower 
part or near the ground, and the light mass in the upper parts, it will give 
a feeling of rest and solidity. (Fig. 147.) If the reverse of this is done, 
and the dark mass is in the upper part and the light mass below, it will give 
a feeling of overbalance or action, which is sometimes desired. (See Fig. 
148.) 



122 



THE ART OF COMPOSITION 



Another thing that must be borne in mind is that a very dark mass will 
seldom balance a very light mass, except, as we have said before, that the 
dark mass is in the lower parts of the picture, as is shown in Fig. 147. 




FIG. 149. WHIRLING SQUARE TO SHOW MASS. LIGHT AND SHADE 

Combining Dynamic Symmetry with light and shade, one will see in Figs. 
149 and 150 two roots of the Whirling Square. Both of these have been 
carried in Sequence to the smaller Whirling Square and darkened to show 
the effect of the graduation of dark and light. 







FIG. ISO. WHIRLING SQUARE TO SHOW MASS. LIGHT, AND SHADE 



THE ART OF COMPOSITION 123 

This leads the eye from the larger spiral in mass to the smaller form, 
and vice versa. 

Lines which surround masses, if very dark, will appear to be part of the 
background, whereas, lines which are very light or lightly drawn will ap- 
pear to be part of the figure itself. 

The lighting of any picture should, of course, always be considered. 
The greatest illumination is arrived at by keeping all details out of the 
lighted side, putting the shadows in also without detail. The more simply 
the forms are expressed, the more light will be shown. 

It is generally a good idea to put details only in a picture in the half 
tones. This will give broadness and strength. 

Distances are expressed in black and white in numbers of different ways. 
If the picture contains only black and white, distances can be shown by 
making the objects diminish in size as they recede. If the half tones are 
to be used, you will find that the lights must be darker and the darks must be 
lighter as they diminish and disappear into the distance. Likewise, the 
darks are darker and the lights are lighter as they advance to the fore- 
ground. 

In closing this chapter, I wish to call to the attention of the artist that the 
entire work must be m the same atmosphere. To see an object very much 
stronger than its entire surroundings does not satisfy j it must be a part of 
the whole. If the picture is expressed in dark tones, many of the objects 
can be dark, but if expressed in light tones, it is not good to make a staccato 
note of one extreme dark. 

Charcoal will be found to be the easiest medium with which to try out 
black-and-white mass composition. 



124 



THE ART OF COMPOSITION 



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rl^IS 


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I^YOUTS OF BEN DAY ILLUSTRATIONS 



THE ART OF COMPOSITION 



12? 








tiiif'i:S-!:~i '^ihi:.M.'. 




BEN DAY TEXTURES 



CHAPTER FIFTEEN: COMPOSITION OF COLOUR 




ATURE does not paint in black and white. All the world 
is full of colour. Even the blackest material will reflect 
some colour, and when we make a drawing in black 
and white, we have only said part of the truth; we have 
only given a conventional idea of our whole conception. 
We can also express an idea in black and white and one 
other colour. This also is only a conventional adaptation 
to suggest to the beholder a little more of our conception. 
It was mentioned in the previous chapter that, besides 
painting objectively, which is painting nature as it really is, or as near as 
our pigments will permit us, there is another form of painting which, per- 
haps, is more assthetic, which is getting the spirit of the thing, in colours 
which are only possible in our imagination, in a subjective style. It is the 
form of art which the Japanese, Chinese, Egyptians, and other peoples 
adapted and developed thousands of years ago. To-day our occidental 
minds are striving to work out this phase of art. Perhaps it is the kernel 
of all the modern schools. 

In this subject form of painting, our imaginations carry us into the Ely- 
sian Fields; we can make ourselves as one of the gods, we can create; we 
can become a builder of things that do not already exist. Besides creating 
forms in this theme of art, we can originate in colours that are indeed 
strange, we can arrange colours contrary to all our previous coceptions of 
how nature is painted. We can make a sky: green, purple, red, blue, yel- 
low, any colour, in fact, that we desire. We can make our trees any colour 
in the spectrum. We must be careful in doing this that our creations arc 
based on nature's laws. If the artist will create original conceptions on the 
Dynamic Symmetry lines (as I have explained in the foregoing chapters) 
and will base his colour combinations also on nature's laws, in harmonies, in 
contrast, in split complementaries, etc., the sensation will be agreeable to 
the beholder. 

In "The Art of Colour" and "The Study of Colour," I have gone deeper 
into this subject. Colour combinations are nothing more than colour com- 
positions. Those who have read these books will understand what I mean 
when I say that a picture can be in two colours and two complementaries, or 
three colours and three complementaries, or a harmony of three, four, or 
five, or a split complementary of one against two, one against three, two 

against three, and one against six. These combinations and all the thou- 

126 



THE ART OF COMPOSITION 127 

sands that I have mentioned in the two books will be found to be pleasing. 
Of course, these colour combinations often are conventional arrangements, 
but this is the new art which many are striving to create. 

If we are painting objectively, colour arrangements must conform more 
or less to the object we are painting from, but in subject painting or object 
painting, we must always be careful that the main points of interest and the 
other points of interest attract our eye in Sequence, for the eye does not 
like to be distracted by two or more principal points of interest in one pic- 
ture, except in certain large decorations where it is impossible to take in the 
whole picture at one glance. 

Certain colours will always attract our eye more than others, especially 
as our pigments are not all as brilliant as nature's own spectrum. The red 
and orange, perhaps, are the two colours that first attract our eye. The 
yellow and scarlet would rank next. The crimson, yellow-green, and green 
next} the purple and blue-green next; the blue next; and the violet and 
blue-violet last. These are called sometimes advancing and receding col- 
ours. All colours can be made to advance or recede by surrounding them 
with other colours that are complementary, of mdre or less brilliancy. 

Aerial perspective has also to do with colour composition. We must al- 
ways remember the atmosphere changes all colours; and that the object, as 
it recedes, will partake somewhat of the colour of the atmosphere; the 
lighted side does not do so as quickly as the shadow. Then, again, it makes 
a difference what the colour of the object is, for a red object would have a 
purple shadow: this shadow would disappear more quickly into the dis- 
tance than would the red, whereas the blue-violet object would vanish into 
the atmosphere colour more quickly than would the shadowy side. For a 
fuller explanation of this phenomenon I would refer you to Chapter 
Seven of "The Art of Colour." 

How much of each colour to use in a picture depends on which colour 
we are going to paint the principal point of interest and the points in Se- 
quence. If we are using harmonies, it would be pleasing to use an even 
distribution of all colours, but if we are making a composition in contrasting 
colours, we can either paint the large masses in harmony and the comple- 
mentary colours in the smaller masses, or we can put a colour with its com- 
plementary in juxtaposition. This holds good also with split complemen- 
taries where the larger number of colours can be used in harmony in the 
large masses and the smaller number of split complementaries in the smaller 



128 THE ART OF COMPOSITION 

masses, or each set of complementaries with their mutual complementary. 

If a colour is neutralized or gray and we wish to have an even distribu- 
tion of weight of colour, we could use larger masses of the gray or neu- 
tralized colour and smaller masses of the brilliant tone. 

If an object is brilliantly coloured in a large mass, all the surrounding 
objects will be influenced by this colour, and all other colours around it will 
partake of a colour toward the complementary in the same way that a 
shadow also partakes of a colour toward its complementary, clockwise or 
counter-clockwise on the spectrum circle. 



CHAPTER SIXTEEN: A FEW MATHEMATICS OF 
DYNAMIC SYMMETRY 




HIS chapter is written only for those who wish to study 
Dynamic Symmetry from a geometrical point of view and 
prove the correctness of the theory. It is not essential to 
the artist. 

As I explained in the Foreword and Introduction of this 
book, I purposely left out any mathematical or geometrical 
reference in explaining Dynamic Symmetry. The task has 
been, perhaps, a little more difficult, on account of my 
determination not to use any signs, letters, or anything 
that might be misconstrued by the casual reader, by which he might be led 
to believe that Dynamic Symmetry was purely mathematics. 

But in this chapter I am going to give some very simple data to those 
who wish to delve deeper into the "whys and wherefores." Of course, it 
will be impossible to go as deeply into this subject as Jay Hambidge has 
done in his book called "The Greek Vase" or in "Elements of Dynamic 
Symmetry," but perhaps those who have studied the preceding chapters 
will be better able to take up the task which apparently seems so difficult at 
the outset. After the first understanding of Dynamic Symmetry, the books 
of Jay Hambidge and Samuel Colman are wonderful explanations of the 
Greek form of composition, and I trust that some of the readers of this 
book will study and verify the compositional layouts illustrated in "The 
Greek Vase" and in "Elements of Dynamic Symmetry." 

In the first chapter, the different roots were explained and how to form 
them, and how, by means of the diagonal, to make the smaller forms in 
summation. I took the liberty of naming them "SEQUENCE OF. 
FORM." The basis of the area of each root is measured in what is known 
as square root. Of course, all those who have studied geometry and alge- 
bra know that the square root of i is i. This is called Root One. A quan- 
tity which, taken twice as a factor, will produce the given quantity. Thus 
the square root of 25 is 5, because 5 X 5 = 25; so also % is the square root 
of %, since % X % = %; a:^ is the square root of x* since x^ X x'' = x*; 
A -|- X is the square root of or + 2ax + x^, and so on. When the square 
root of a number can be expressed in exact parts of one, that number is a 
perfect square, and the indicated square root is said to be commensurable. 
All other indicated square roots are incommensurable. In other words, the 
square root is one of two equal factors of a given number. Thus 2 is the 

129 



130 THE ART OF COMPOSITION 

square root of 4, x of x'. The following illustrates the method of finding 
the square root of 576, which is 24: 









V576 


(20 








400 


4 


2 X 


20 = 


40) 


176 


24 


(40 


+ 4) 


X4 


= 176 





Quantities which when multiplied together produce unity are called, in 
mathematics, Reciprocals. Thus, the reciprocal of i is i. The reciprocal 
of 2 is .50, and also, reversed, .50 is the reciprocal of 2. In other words, 
the reciprocal of a quantity is the quotient resulting from the division of 
unity by the quantity. 

The square of Root Two is one side multiplied by unity to get the 
area of the rectangle, and we find that the reciprocal is I.4I42''', which is 
an indeterminate fraction. 

Taking the side of the rectangle as one (this would not necessarily mean 
one inch, or one mile, or one yard, but simply that you take the short side 
of the rectangle as the unit), you would find that the long side measured 
1.4142+ times the short side. The number 1.4142+ is called the recip- 
rocal, because, multiplied by itself, it would give you the Root Two. We 
must always remember that Dynamic Symmetry deals with areas and not 
with line. The Root Two rectangle contains two rectangles of the same 
shape in a smaller Sequence. In other words, its reciprocal is equal to 
half the whole. (See Fig. 151.) Likewise, the major form is the recip- 
rocal of the smaller form in Sequence. In the same way, one half is the 
reciprocal of 2 and 2 is the reciprocal of the half. 

Another way to show the relationship of form would be to draw a Root 
Two rectangle and alongside of this Root Two draw a square. Now, if we 
draw a small square which measures the width of the Root Two on the side, 
we will find that this smaller square will be exactly one half in area to the 
large square, and we see that, while Root Two is incommensurable in line, 
it is commensurable in area. (See Fig. 152.) So we see that the lesser 
square is the reciprocal of the greater square, and likewise, the greater 
square is the reciprocal of the lesser square. Thus, though the ends and 



THE ART OF COMPOSITION 



131 



1.4M2 




FIG. 15". THE RECIPROCAL OF ROOT TWO 



4 
4 
4 
4 
i 
4 
4 
4 
4 
♦ 



t 
4 






FIG. 152. RELATION OF MASS 



132 THE ART OF COMPOSITION 

the side are incommensurable in line, they are commensurable in area. The 
ends and side of this rectangle is i or unity to the square root of 2, or i to 
1. 4 1 42+ which is an indeterminate fraction. 

Therefore, we find that all the roots can be designated in the same man- 
ner as we have just designated Root Two. Before giving you the recip- 
rocal of all the roots, I would like to show you the reciprocal of Root Two 
which is 1.4142+ multiplied by itself as follows: 

1.4142+ X 1.4142+ = 

1.4142+ 
1.4142+ 



28284 
56569 
14142 
S656S 
14142 



1,99996164 

The small discrepancy is, of course, accounted for by the end of the frac- 
tion being dropped. 

The reciprocal of all roots is given below. In other words, if any one 
of these numbers is multiplied by itself, it will give you the root, i. e. 
1.4142+ X 1.4142+ = 2 or 2 X2 = 4. 

The reciprocal of Root One is i.ooo 

The reciprocal of Root Two is 1.414+ 

The reciprocal of the Whirling Square Root is 1.6 18+ 

The reciprocal of Root Three is i-yj^"*" 

The reciprocal of Root Four is 2.000 

The reciprocal of Root Five is 2.236+ 

The reciprocal of Root Six is 2.449+ 

The reciprocal of Root Seven is 2.645+ 

The reciprocal of Root Eight is 2.828+ 

The reciprocal of Root Nine is 3.000 

The reciprocal of Root Ten is 3.162+ 



THE ART OF COMPOSITION 133 

The reciprocal of Root Eleven is 3.316+ 

The reciprocal of Root Twelve is 3.464''" 

The reciprocal of Root Thirteen is 3. 605+ 

The reciprocal of Root Fourteen is 3.741 + 

The reciprocal of Root Fifteen is 3.872+ 

The reciprocal of Root Sixteen is 4.000 

The reciprocal of Root Seventeen is 4.123+ 

The reciprocal of Root Eighteen is 4.242+ 

The reciprocal of Root Nineteen is 4.358+ 

The reciprocal of Root Twenty is 4.472+ 

The reciprocal of Root Twenty-one is 4.582+ 

The reciprocal of Root Twenty-two is 4.690+ 

The reciprocal of Root Twenty-three is 4.795+ 

The reciprocal of Root Twenty-four is , . .4.898+ 

The reciprocal of Root Twenty five is 5.000+ 

It must always be kept in mind that these numbers do not mean inches, 
centimetres, or squares, but mean the proportion which is always the samej 
whether in the major shape or in the minor shapes or forms in Sequence, 
the geometrical relation will be constant. As we have explained, a rec- 
tangle whose side is expressed by the unit one and whose other side is ex- 
pressed by 1. 4 1 42 or the square root of two, in which a diagonal or hypote- 
nuse is drawn, both angles thus formed are equal ; and if a crossing line is 
drawn through this hypotenuse so as to form four right angles, and a paral- 
lel line drawn where this line meets the side of the rectangle, the form so 
constructed will be also a Root Two. 

This diagonal or hypotenuse or oblique line and the crossing line, to- 
gether with the parallel, is a very important element in Dynamic Symmetry 
and can be reproduced in all roots. It will be noticed that, in all roots, this 
major rectangle and minor rectangle will be exactly in the proportion of 
the square root, i. e.: In Root Two the smaller square will be exactly one 
half. In the Root Three it will be one third. In the Root Four it will 
be one fourth, and in the Root Five, one fifth, as is illustrated on page 135. 

The ratio of 1.6 18+ is used with unity to make a rectangle, which is di- 
vided by a diagonal, crossing lines, and the parallel to make a Whirling 
Square which is based on nature's design and which will make the logarith- 
metic curve. This can be done in two ways within the root of the Whirling 



134 



THE ART OF COMPOSITION 




ROOT 2 



I 



L 



WMRLMG SQUARE 



aoox 3 



I... 



I 
I 
I 
I 
I 
I 
I 
I 
I 



I 



4 



noOT * 



1 

r 

r 



noor 9 



RECIPROCALS OF ALL ROOTS 



THE ART OF COMPOSITION 

1.4» »•.*» 



135 





1.733. 




THE SQUARE ROOT OF ALL ROOT RECTANGLES 



136 THE ART OF COMPOSITION 

Square, and also outside the rectangle, whose reciprocal is 1.618+. If you 
will draw a square whose side measures 4. 50 centimetres, laying off half 
the square and finding the diagonal of this half, adding this to half the 
square to make the Whirling Square Root, you will have a rectangle whose 
side will measure 7.236 centimetres. If we draw the diagonal and the 
crossing lines together with the parallel line, bringing down the forms in 
Sequence, and draw the Whirling Square around the outside of the rec- 
tangle, as is shown in Fig. 153, we shall have completed the logarithmetic 
spiral, or Whirling Square, outside the rectangle. 

If we now draw another square which measures 5 centimetres and make 
the Whirling Square in the same way as we did in the preceding paragraph, 
we shall have a rectangle whose side measures 8.20 centimetres plus or 
minus. 

Now, if we draw again the diagonals and the crossing lines and draw the 
Whirling Square inside the rectangle connecting up the hypotenuse of each 
square, we shall have a Whirling Square which will measure identically 
with the Whirling Square in the preceding paragraph, but turned obliquely, 
as is shown in Fig. 154. Both of these rectangles have a ratio of 1.618+. 

It is much more important to the artist to be able to do this inside of the 
Major Form, although, in "The Greek Vase," Jay Hambidge did not show 
this, to my knowledge. 



THE ART OF COMPOSITION 



137 




FIG. J 53. WHIRLING SQUARE ROOT OUTSIDE OF THE 
RECTANGLE 




FIG. IS*. WHIRLING SQUARE ROOT INSIDE OF THE 
RECTANGLE 



138 THE ART OF COMPOSITION 



COMBINED ROOT SYMBOLS 

one: and TWO and THREE. ^_.H 1 *- 

ONEdhd TWO and FOUR . -». * »- -«-.-»- ^ 1- 

ONEdndTWOandFIVE .^.^.^ -.wv...^- ^^.-t- 
ONEdndTWOandtheWHIRUNG SQUARE .^ e ._4- c .-^«.- 

ONEand THREEand FOUR .-^ ^ ^ ^.-^.. 

ONEand THREEand FIVE . *^. — ^ -^. — -»/»'. — *^« — vt/v_ 

ONEand THREEand the WHIRLING SQUARE — c — e « — 

ONEdud FOUR and FIVE .a—^va, .^_^*/». .^_^x/v.^ — yx/v.^_yx«.^. ^_ . 
ONEand FOUR and the WHIRLING SQUARE .-u_ e . -<_e .-.-c-t. 
ONEand FIVE dnd+he WHIRLING SQUARE . ^ c . .^ « . .^ e . 

TWO and THREEand FOUR ^_-l_ ^._- H-<^f — -^-»- — 

TWO^ndTHREEandF^\/E., ^-, • ^^— ^^-^- 

TWOandTHREEandtheWHIRLING SQUARE ^.-e ^_e +-e- 

THREEand FOURand FlVE-^^_*_- 1--^ — ^^^_<-^ 

THREEand FIVE andtheWHIRLlNG SQUARE — ^* wa « 

FOURand FIVE andthe WHIRLING SQUARE<-^« -.-^ e _ 

FIG. ISS 



GLOSSARY 

Balance: A picture so arranged that the objects balance each other either dynami- 
cally or statically. A composition which gives us a satisfaction of mechanical 
rest or continued movement. 

Commensurable: Measurable by a common unit. Proportionate. 

Crossing line: A line drawn from one corner the opposite from which the diagonal 
is drawn, through the diagonal line touching the outer side of a rectangle. 

Diagonal: A line drawn from two opposite corners. An oblique line. The hypote- 
nuse of a rectangle. A straight line showing two opposite vertices. 

Dynamic Symmetry: A form of composition and proportion which was used by the 
Greeks and Egyptians. 

Horizontal: On a level. In the direction of or parallel to the horizon. Flat. 
Plane. 

Hypotenuse: The long side of a right-angled triangle. 

Incommensurable: Not measurable by a common unit. Opposite of commensurable. 

Logarithmetic : A curve which progresses in width from the centre or eye in a 
certain ratio. This ratio is based on nature's law of growth as found by the 
Royal Botanical Society. See illustration of sunflower, page ii. 

Oblong: Having one principal axis longer than the other or others. 

Parallel: Not meeting or intersecting, how far soever extended: said of straight 
lines or planes. 

Parallel line: Any line, either perpendicular or horizontal which is parallel to the 
sides or ends of a rectangle. 

Parallelogram: A quadrilateral whose opposite sides are parellel. 

Perpendicular: Upright or vertical. 

Points of interest: The place in a picture which first attracts our eye. The object 
which shows the important conception. It is found at the intersection of the 
crossing line and the diagonal of any rectangle in Dynamic Symmetry. 

Second point of interest: The object which we next are conscious of after seeing 
the principal point of interest. It should not attract our eye before the principal 
point of interest does. It can be placed at the intersection of any crossing 
line in Sequence to the principal point of interest. 

Third point of interest: The object which is placed in Sequence to the first and 
second jjoint of interest. 

Fourth point of interest: The object which leads us from the major points of 
interest. 

Fifth point of interest: An object of not much importance which leads us in 
Sequence from the major points of interest. 

Quadrant arc; A part of a circle, the two ends resting in opposite comers to the 
diagonal. 

Quotient: The result obtained by division; in arithmetic, a number indicating how 
many times one number or quantity is contained in another. 



140 THE ART OF COMPOSITION 

Eectangle: A parallelogram whose angles are right angles. An oblong or square. 

Bight angle: An angle formed by two straight lines which intersect each other 
perpendicularly. 

Boot One: A square i X i. Its reciprocal is i. The Root One can contain any 
one of the other roots. Dividing it in half will make two Root Fours. The 
other roots are found inside of a square by means of a quadrant arc or quarter cir- 
cle and the diagonal. 

Boot Two : A rectangle which can be divided into two equal parts, both parts form- 
ing Root Two in Sequence or lesser magnitude. Its reciprocal is 1.414+. 
The diagonal of Root One is the length of Root Two. 

Boot Three: A rectangle which can be divided into three equal parts, each one of 
the three parts forming a Root Three in Sequence or form of lesser magnitude, 
in the same proportion. Its reciprocal is 1.732+. The diagonal of Root Two 
is the length of Root Three. 

Boot Four: A rectangle which can be divided into four parts each one of the four 
parts forming a Root Four in Sequence or form of lesser magnitude, in the 
same proportion. Its reciprocal is 2. The diagonal of Root Three is the 
length of Root Four. 

Boot Five: A rectangle which can be divided into five equal parts each one of the 
five parts forming a Root Five in Sequence or form of lesser magnitude, in 
the same proportion. Its reciprocal is 2.236+. The diagonal of Root Four is 
the length of Root Five. 

Boots Outside of a Square: These are found by measuring the diagonal, taidng 
this as the length of the Root Two. 

Bule of Three : The product of the extremes is equal to the product of the means. 

Sequence : The process of following in numbers each related to the other. A num- 
ber of things related to each other considered collectively. A series. 

Square: A figure having four equal sides and four right angles. A rectangle whose 
sides are equal. 

Square Boot: A quantity which, being taken twice as a factor, will produce the 
given quantity. Thus, the square root of 25 is 5, because 5X5 = 25. When 
the square root of a number can be expressed in exact parts of I, that number 
is a perfect square, and the indicated square root is said to be commensurable. 
All other indicated square roots are incommensurable. One of two equal factors 
of a given number. Thus 2 is the square root of 4, x of x*. 

Star layout; Inside a rectangle lines drawn from opposite corners or hypotenuse 
and crossing lines drawn at right angles to the hypotenuse. 

Summation: A form of numbering which is adding the preceding number to the 
following number such as 1, 2, 3, 5, 8, 13, 21, or 1.4142, 2.4142, 3.8284, 6.2426. 

Symmetry: A due proportion of several parts of a body to each other, or the union 
and conformity of the members of a work to the whole. Symmetry arises from 
the proportion, which the Greeks called analogy, which is the relation of conform- 
ity of all parts of certain measure. 



THE ART OF COMPOSITION 141 

Whirling Square Boot: This root is found by taking half of a square, drawing the 
diagonal across this half, and adding this to half the width of the square. A 
Root Five contains two Whirling Square Roots and a square. The Whirling 
Square is the form of the logarithmetic curve which is based on Nature's growth 
and leaf distribution. 



The Art of Colour 

Third Edition 

A Book of Exceptional Clarity and Scope 



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It is a peerless encyclopedia of colour, written in a clear, 
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For artists, architects, designers, and students of art, it sums 
up a vast amount of valuable information that might otherwise 
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The most complete and comprehensive treatise on colour in its 
various phases and uses that has ever been written. 

Price, $7.50 



M^j^i^^TM 



Published by 

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Garden City New York 



The Study of Colour 

fVith Lessons and Exercises 
2nd Edition in Two Volumes 

by 

Michel Jacobs 

For the Artist For the Student For the Craftsman 

The lessons in this book are the development of years of 
experience in the Metropolitan Art School, the result of careful 
selection, graded in order of difficulty, and covering the subject 
thoroughly and carefully. It is a theoretical textbook on colour 
with practical lessons and exercises, and covers the course taught 
today in the Metropolitan Art School of New York. 

Those who are familiar with Michel Jacobs's first book, "The 
Art of Colour," cannot afford to be without this new work. "It is 
no longer a theory, it is a proven fact." 

The price has been made moderate so as to be within the reach 
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Vol. I. Lessons, Bound Separately. . . .$2.50 For Instructors 

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If the art student would execute the lessons which the book 
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Published by 

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Garden City New York 



BorOTHY H. hoover IIMARY 
ONTARIO COLLEGE Of ART & DESIGN 
ICO MeCAUl STREET, 
TORONTO, ON. 
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F' 



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is 






SMTATtlC 






NC JACOBS, MICHEL. 
740 THE ART OF COM- 
J23 POSITION. 
REF. 

Oi«.A.iiiJ CuLLEt^E Or h..i 

1C?0 ;AcCAUL ST. 
TO.^ON.O 2B, ONTARIO