Euclid's Father Bearing His Mother Ashore 
on His Back EUCLID'S 
OUTLINE OF SEX 
A FREUDIAN STUDY 
BY 
WILBUR D. BIRDWOOD 
Illustrations by Herb Roth 
NEW YORK 
HENRY HOLT AND COMPANY Copyright, 1922, 
BY 
HENRY HOLT AND COMPANY 
First printing, October, 1922 
PRINTED IN U.S.A. PREFACE. 
The present book has been written because it simply had 
to be written. 
It is little short of amazing that earlier students of psycho- 
analysis should have so completely overlooked the extraordi- 
nary wealth of sex-material contained in the pages of Euclid, 
the Father of Geometry. It cannot be lack of interest, be- 
cause nothing in life fails to interest the true Freudian. 
As the Roman poet has said, Nihil humani a me alienuni - 
" There is nothing human that cannot be explained from the 
standpoint of the alienist." It cannot be lack of diligence, 
because it may be said of the true Freudian that he almost 
works overtime. It cannot be lack of information on the 
subject, because that has never been an insuperable obstacle. 
Under the circumstances, I can only describe the Freudian 
neglect of Euclid as one of the most remarkable cases of 
inhibition on record. 
And yet there is the fact. Euclid, to put it bluntly, reeks 
with sex. In no wrriter of ancient or modern times, with 
the possible exception of Legendre (Elements of Geometry, 
Paris, 1794), and Wentworth and Smith (Plane Geometry, 
for the Use of High Schools), does the theme of the Eternal 
Triangle run so persistently as in Euclid. Even the modern 
French drama succeeds in getting away from the triangle 
now and then; but Euclid, almost never. 
Not that the Father of Geometry did not try. He took 
refuge in parallel lines, for example. But no sooner would 
he draw his parallel lines than Fate, or more properly, the 
Unconscious, compelled him to draw a third line cutting the 
III IV 
PREFACE 
parallels and so bring into existence triangles with their 
vertical angles equal. He resorted to quadrilaterals. And 
again the Unconscious would intervene and make him draw 
a diagonal, dividing the quadrilateral into two triangles. 
Whimsically he once referred to this sex diagonal as the bar 
sinister. 
And so with circles, to which Euclid devoted himself in his 
later books. He was continually circumscribing the circle 
of life around the triangle of sex (See Figure 1), or inscrib- 
ing the circle of life within the triangle of sex (See Figure 2). 
There was no conscious purpose in that. He would start 
off with his circle of life having its center at A (See Figure 3). 
He would move cheerfully along the radii of his circle to 
the circumference at B and C. And then, before he was 
aware of it, he had drawn a chord, BC, connecting the two 
radii and producing ABC - a triangle! 
Fig. 1 
Fig. 2 
Fig. 3 
I believe I have said enough to justify the present modest 
little volume, if modest is the right word. Profounder 
scholars and bolder thinkers are sure to follow where I have 
humbly shown the way. In due time, I have no doubt, the 
virtually inexhaustible sex-content of Euclid will have been 
made available for all students, with special emphasis on the 
Elementary and Kindergarten Grades. 
W. P. B. CONTENTS 
PAGE 
Preface iii 
PART I - GRANDMOTHER 
CHAPTER 
I. Who Was Euclid? 3 
II. Who Was Euclid ? ^continued) 4 
III. His Origins 5 
IV. Infancy and Childhood 7 
V. Dark Days 9 
VI. The Grandmother Complex 11 
VII. Wish-Fulfilments 12 
VIII. The Grandmother Triangle 13 
IX. Doubts 15 
X. The Real Solution 16 
XI. Problems Involving the Grandmother Complex . . 18 
PART II -OEDIPUS 
XII. Who Was Oedipus? 23 
XIII. The Oedipus in All of Us 24 
XIV. The Anti-Oedipus Die Hards 26 
XV. The Rjddle of the Universe 27 
PART III -BALAAM 
XVI. The Ass at the Bridge 31 
XVII. Bridges 33 
XVIII. Equus Asinus Cypriensis 35 
XIX. Balaam 36 
XX. The Ass and the Unconscious 38 
XXI. Subliminal 39 
XXII. Speech 41 
XXIII. Summary 44 
XXIV. Parenthesis 46 
V VI 
CONTENTS 
CHAPTER PAGE 
PART IV -BURIDAN 
XXV. Old Friends 49 
XXVI. Self-determination 51 
PART V -THE NEW ENGLAND ELEMENT IN EUCLID 
XXVII. The Euclidean Style 57 
XXVIII. The Asterisk and the Dotted Line 60 
Bibliography 67 ILLUSTRATIONS 
Euclid's Father bearing his aged Mother ashore . . Frontispiece 
PAGE 
The Grandmother Complex Facing 12 
Balaam and the Ass Facing 36 
The Asterisk Facing 62 PART I 
GRANDMOTHER CHAPTER I 
WHO WAS EUCLID? 
The salient facts in the life of the great geometer, as re- 
corded in the pre-Freudian text-books, are not hard to grasp. 
Typical is the account of Euclid in the New International 
Encyclopedia (New York, 3rd edition, 24 volumes). There, 
in volume 8, page 153, under the title " Euclid," it is stated: 
Nothing is known of his life except that Proclus tells us that 
he lived in the time of Ptolemy I, who reigned b.c. 306-283. 
Quite as convincing is the sketch of Euclid's career in the 
Encyclopaedia Britannica, 11th edition, volume 9, page 879. 
It is from the hand of John Sturgeon Mackay, M. A., LL.D., 
F. R. S. (Edin.), Chief Mathematical Master at Edinburgh 
Academy, 1873-1904; First President of the Edinburgh 
Mathematical Society; author of " Arithmetical Exercises" 
and " Elements of Euclid." 
Professor Mackay tells the story of Euclid with all the 
art of a master of the miniature. He writes: 
We are ignorant not only of the dates of his birth and his 
death, but also of his parentage, his teachers, and the resi- 
dence of his early years. 
Concerning Euclid's residence in his later years Professor 
Mackay intimates that we know nothing. The Britannica 
is an expensive publication, but even at two or three times 
the price, it could not have put the facts about Euclid's career 
more definitely. 
3 CHAPTER II 
WHO WAS EUCLID? (Continued') 
If the foregoing accounts of the life of Euclid should strike 
the reader as somewhat over-condensed, it is not the fault 
either of the New International Encyclopedia or the Encyclo- 
paedia Britannica. Given the methods of historical investi- 
gation prevalent at the time those two admirable works of 
reference were composed, the authors did the best they could. 
No such limitation, however, rests upon the psychoanalytic 
student of the life of Euclid. All that is necessary is to 
apply to Euclid the method that has yielded such admirable 
results in Freudian studies of Leonardo da Vinci, of Goethe, 
of Mark Twain, of Margaret Fuller, and other notable fig- 
ures. Immediately theje emerges out of the cloud of sup- 
pressions and inhibitions which has gathered about the 
memory of Euclid an amiable and fascinating personality. 
It is necessary only to fill in the sketch presented by the 
International and the Britannica, and the entire career of the 
great geometer rises vividly before us. Let us make the 
attempt. 
4 CHAPTER III 
HIS ORIGINS 
We see Euclid born on the island of Kos in the early sum- 
mer of the year 342 b.c. This fact makes it all the harder 
to understand why he should so frequently be confused with 
another Euclid, who was born in Sicily six hundred years 
earlier, and who attained fame as a wholesale cattle-dealer. 
Euclid was born, then, on the island of Kos, and of a 
native mother, probably a member of the ruling family of 
the Delta Upsilons. Like most Greek gentlewomen of her 
time, she was brought up in complete ignorance of the arts 
of reading and writing, but trained in all the accomplish- 
ments of the complete housewife. She was an adept in the 
preparation of food, with the assistance of a professional 
female cook named Myrtilla, who was probably of Thracian 
origin and had a special gift for fig pastes and stewed tripe 
in honey. Euclid's mother was also expert in the arts of 
spinning and weaving, under the supervision of another 
female slave named Sophronia, a native of Sparta. And 
naturally Euclid's mother was skillful in the care and feeding 
of children, under the guidance of her own old nurse Mel- 
anchthia. 
In short, it can be said of Euclid's mother that she faith- 
fully subscribed to the dictum laid down by Solon that 
woman's place is in the home. 
The father of Euclid was a trader from Crete. On one of 
his voyages, presumably in the open winter of the year 
344 b.c., he was shipwrecked on the coast of Kos, but suc- 
ceeded in making his way to land carrying his aged mother 
5 6 
EUCLID'S OUTLINE OF SEX 
on his shoulder^. This, of course, was the approved method 
of rescuing imperilled parents from fire, flood, and battle in 
old Greek times. 
It may be asked whether it was the custom for traders in 
ancient Greece to take their old mothers with them on their 
voyages, especially as business men in those days frequently 
went in for piracy as a side line. But as we shall see further 
on in this volume, the career of Euclid and the origin of the 
" Elements of Geometry " demand the existence of a paternal 
grandmother. It follows, therefore, that Euclid senior did 
take his aged mother with him on his business trips, and that 
he did carry her to safety through the breakers on his 
shoulders. CHAPTER IV 
INFANCY AND CHILDHOOD 
Euclid was the fifth of seven children, three boys and four 
girls, of whom the two youngest, both boys, did not survive 
infancy. The girls grew up and married well. 
Euclid was fair-haired, big for his years, though with a 
slight tendency to stoop. He had a not unpleasant cast in 
his left eye, and up to the age of four was inclined to stam- 
mer. This last point will be found to be of vital significance 
when we come to consider the familiar Euclidian literary 
style as revealed in mannerisms like 11 Let angle ABC be 
equal to angle DEF," etc. 
The boy's life was of more than normal happiness. It 
naturally would be. The study of Greek came easy to him. 
Latin, Modern History, Manual Training and, of course, 
Geometry, had not yet been invented. 
Spelling and Composition were not difficult. The method 
of writing the Greek language was then in a state of tran- 
sition. The conservatives clung to the fashion of writing 
from right to left. The liberal and radical classes went in 
for the newer method of writing from left to right. The 
boy Euclid wrote in either direction as the fancy seized him 
and it made no difference. 
His schooling, as a whole, was spasmodic. Educational 
theory and methods wrere at that time in rapid flux. It 
was an age of intense experimentation. In the field of His- 
tory, for example, there were several diverse methods of 
instruction. One method insisted on teaching dates without 
facts. Another method specialized in facts without dates. 
7 8 
EUCLID'S OUTLINE OF SEX 
A third method went pretty far in dispensing both with 
dates and facts and concentrated on Trends and Currents. 
Euclid's mother, naturally ambitious for her son, sent 
the boy through all the available experimental schools, with 
the result that the boy attended eleven different educational 
establishments in less than a year and half. Is it any wonder 
that a boy so educated should have devoted his life to 
proving that a straight line is the shortest distance between 
two points? CHAPTER V 
DARK DAYS 
When Euclid was six years old, his father perished in a 
raid upon the island of Kos by the Phi Beta Kappas, a pirate 
tribe inhabiting the adjoining mainland. His mother was 
carried off into captivity, but the lad and his grandmother 
were left behind as of doubtful commercial value. 
Thus arose a Complex between the two which was im- 
measurably strengthened in the course of the next three years. 
When the boy was nine years of age the old lady died, but 
not without, leaving a profound impression on the future 
Proposition 16: " If one side of a triangle be produced, the 
exterior angle is greater than either of interior opposite 
angles." But this is to anticipate. 
Concerning the attachment between the lad and his grand- 
mother - altogether unnatural from the standpoint of psycho- 
analysis - the historian Archilongus has preserved the 
following legend: 
To the end of his life - and Euclid lived to be seventy-six 
years, eight months and odd days, dying of sepsis fol- 
lowing upon a badly ulcerated upper molar - the famous 
geometer devoutly observed the anniversary of his grand- 
mother's death. On that day he would refuse to meet his 
students. He would bathe ceremonially, don a purple robe, 
and comb his beard with special care. He would partake of 
no food whatsoever, but, having sacrificed punctiliously to 
Hermes Mathematikos, he would give himself up to contem- 
plation. 
To his favorite pupil who questioned him on the subject. 
9 10 
EUCLID'S OUTLINE OF SEX 
Euclid explained that he devoted that day to evoking the 
memory of the aged woman who took him, a motherless child, 
to her own heart. She would go out every sundown into 
the olive groves to pick up kindling for a fire - they were very 
poor, Euclid told the disciple. Having given the boy his 
supper, she would croon him to sleep on her lap before the 
hearth. CHAPTER VI 
THE GRANDMOTHER COMPLEX 
An exhibition of exaggerated sentiment, like that just 
described in the aged Euclid whenever he thought of his own 
orphaned childhood and the grandmother who nurtured him, 
might have been regarded by the ancient Greeks or the 
Chinese of today as piety. But Freud has taught us better. 
What the adult Euclid suffered from was unquestionably 
an aggravated case of the Grandmother Complex. 
Here we find ourselves in need of further details about 
the life of Euclid. We experience no difficulty in deriving 
such additional data from the same sources that have served 
us so well in the preceding chapter. 
Euclid first became actually aware of his grandmother 
when he was two years old. She had, of course, entered into 
her grandson's life before that. The old lady frequently 
differed with her daughter-in-law, Euclid's mother, on the 
subject of milk temperatures, pins, colic, talcum, relief for 
the gums, and other issues on which the old generation has 
always been in conflict with the middle generation. It re- 
sulted in the old lady's going to live with one of her married 
granddaughters, who as yet had no children of her own. 
Nevertheless she continued to visit the Euclid household 
daily. When Euclid entered on his third year, a little 
brother was born, and the future mathematician was much 
more freely exposed to the unhampered influence of his 
grandmother. He came to look forward eagerly to her visits. 
11 CHAPTER VII 
WISH-FULFILMENTS 
The reason was a simple one. Grandmother very seldom 
came to call upon the boy without a gift of some kind. 
Usually it was either a bagful of honey-cakes or a basket 
of dried sun-flower seeds, of both of which the little Euclid 
was inordinately fond. Sometimes the old lady would come 
in by the front door and sometimes she would use the back- 
door or the servants' entrance. The reader will do well to 
keep these two doors in mind. 
Also this further fact: At times the little Euclid would 
immediately climb into his grandmother's lap and begin 
munching at the honey-cakes. At other times the two would 
go out strolling on the beach hand in hand. The old lady 
would point across the wine-colored waves to Crete where 
Euclid's father was born and had been, in his time, quite as 
tiny a tot as Euclid was now. The child listened and did not 
understand. But the honey-cakes and the sun-flower seeds 
were delicious. 
Thus the Grandmother Complex was established in that 
young soul. 
12 The Grandmother Complex CHAPTER VIII 
THE GRANDMOTHER TRIANGLE 
We are now in a position to grasp the real meaning of 
what is probably the best known of Euclid's later contri- 
butions to the sum of human knowledge. 
If two triangles have two sides of the one equal to two 
sides of the other, each to each, and have also the angles 
contained by those sides equal to one another, they also have 
their bases or third sides equal; and the two triangles are 
equal; and their other angles are equal; each to each, namely, 
those to which the equal sides are opposite. 
Euclid's demonstration is a model of condensed, if some- 
what dictatorial, literary expression. He says, virtually - 
Fig. 4 
In the above triangles let the line AB be equal to the line 
A'B', and the line AC to the line A'C', and the angle BAC 
to the angle B'A'C; then will the line BC be equal to the 
line B'C', and the two triangles will be equal in every re- 
spect. 
For, superimpose the second triangle on the first. Then 
will the line A'B' coincide with AB and point B' will fall on 
point B. But since the angle B'A'C' is equal to the angle 
BAC, the line A'C' will take the direction of the line AC, 
and point C' will fall on point C. 
13 14 
EUCLID'S OUTLINE OF SEX 
Now, if point B' coincides with point B, and point C' with 
point C, the line B'C' will coincide with the line BC, and the 
two triangles are equal in every respect. Which was to be 
demonstrated; popularly referred to as Q.E.D. CHAPTER IX 
DOUBTS 
This is the way the pre-Freudian text-books in Geometry 
used to present Euclid. Superficially the demonstration was 
adequate. Actually it was devoid of meaning. All sorts of 
doubts were bound to arise. 
For example: if the triangles ABC and A'B'C' are indeed 
equal in every respect, why bother with two triangles? Life 
is short enough as it is. This doubt is one that has perplexed 
generations of high-school students. They have wondered 
why for all practical purposes the world could not get along 
with ABC only. They had their moments, indeed, when they 
felt that they could very well get along without any triangles 
at all; especially at the beginning of the baseball season. 
All through Euclid we find him at great pains to demon- 
strate, by roundabout ways, truths that were either obvious, 
or unimportant, or both. Euclid, for example, lays great 
stress upon the fact that in any triangle any one side is shorter 
than the sum of the other two sides. Yet this truth has 
always been self-evident to a small boy with a bigger boy 
after him; to a dog with a fire-cracker attached to his tail; 
or to a commuter bound for the 7:34. 
It is like trying to prove, by mathematics, that you can 
get a drink in Havana. 
15 CHAPTER X. 
THE REAL SOLUTION 
Such doubts are inevitable if we persist in reading Euclid 
in the old manner. But how if we bring psychoanalysis to 
bear on the problems? 
The triangles with which Euclid was so greatly concerned 
in his later life were not plane triangles but sex triangles. 
In the theorem discussed in the preceding chapter, the 
triangle ABC really represents the infant Euclid's exagger- 
ated emotional reaction to his grandmother. The triangle 
A'B'C' is the later sex-expression of that Grandmother 
Complex. 
In the infant triangle ABC, point A would be the child 
Euclid. He catches sight of his Grandmother coming in 
with the honey-cakes at the front-door, B, or with the sun- 
flower seeds at the side-entrance, C. Then the line BC would 
be the locus or track of the child's appetite. Instead of the 
line BC we might quite as well say Honey-cake-Sunflower 
line. 
What follows is simple. In the adult sex-triangle A'B'C', 
our Euclid sets out from the same point, A', himself. He 
goes on thinking along the line A'B' until the ancient in- 
hibition brings him to a stop at B', the honey-cakes. Or if 
he starts out in another direction, the permanent angle given 
to his infant soul by his grandmother, impels him along the 
line A'C' till the same inhibition brings him to a stop at 
point C', the sunflower seeds. 
Thus the line, B'C', representing the sex life of a mature 
scientist, is predetermined along the old Honey-cake-Sun- 
flower line, BC. 
16 GRANDMOTHER 
17 
Euclid, of course, thought he was inventing Geometry. 
Actually he was rehearsing a vivid anxiety-dream and wish- 
fulfillment of his childhood. Or if we insist on calling it 
Geometry, the very least we can do is to speak of it, not as 
Plane Geometry, but as Complex Geometry. 
This Complex runs all through Euclid; so much we can 
say by way of anticipation. Wherever he demonstrates that 
ABCDXWJZ is equal in every respect to A'B'C'D'W'X'J'Z', 
we are only in the presence of a phenomenon technically 
described, for obvious reasons, as the Przemysl Complex. 
Whenever Euclid asserts that two triangles are equal each 
to each, or two quadrilaterals are equal each to each, or two 
circles are equal in all respects, it is only Euclid's way of 
saying that it is sex of one and half a dozen of the other. CHAPTER XI. 
PROBLEMS INVOLVING THE GRANDMOTHER 
COMPLEX 
Parallel lines are always equidistant from each other. 
A 
C 
B 
D 
In the above parallels, AB represents Euclid, and CD 
represents his Grandmother, walking hand in hand. 
Parallel lines cut by a third transverse line produce inter- 
nal and external angles. 
Fig. 5 
In the above diagram AFE is an external or extraverted 
angle. It represents Euclid watching his Grandmother ap- 
proach with honey-cakes. The angle AFG is an internal 
or introverted angle. It represents Euclid anticipating the 
feel of the honey-cakes inside of him. 
18 GRANDMOTHER 
19 
Every point in the circumference of a circle is equidistant 
from the centre. 
Fig. 6 
In the above diagram the center C is Grandmother on the 
rare occasions when she forgot to bring the honey-cakes. The 
circumference EEE is Euclid giving Grandmother a thorough 
examination from every point of view and hoping against 
hope. 
Note: The circumference of a circle is equal to 3 1/7 times 
the diameter; at least, in the very best circles. 
A straight line is the shortest distance between two points. 
A B 
In the above diagram A is Euclid and B is Grandmother, 
and the line AB represents Euclid making a bee line for 
Grandmother, this being the shortest distance between two 
points. 
Things equal to the same thing are equal to each other. 
Example: The Eighteenth Amendment can be explained 
only in terms of sex, and Michelangelo is explainable only 
in terms of sex. Therefore, the Eighteenth Amendment and 
Michelangelo are identical. 
A 
B PART II 
OEDIPUS CHAPTER XII 
WHO WAS OEDIPUS? 
Advanced students of psychoanalysis have, of course, 
recognized for a good many pages back the true nature of 
the Grandmother Complex. They have understood that the 
Grandmother Complex is only another form of the Oedipus 
Complex; only much more so. 
For the benefit of beginners in psychoanalysis it may be 
permitted to explain just what is this Oedipus Complex, in 
a few brief but vivid words. 
The Oedipus Complex is the neural mix-up which accounts 
for the familiar fact that children are more strongly attracted 
to the parent of the opposite sex. The son is fonder of his 
mother; the daughter is more strongly drawn to her father. 
But to say fonder is to put it mildly. At bottom every 
Freudian knows that every normal son would like to see his 
father dead and every normal daughter would like to see 
her mother dead. This pleasant truth has been established 
by the special researches of Freud's famous collaborator, 
Friedrich Jung. Hence the expression, the Jung Generation. 
The name for this charming little Complex comes, of course, 
from Oedipus. He is known in Greek legend as the hero of 
three exceptionally difficult feats: he slew his own father; 
he married his own mother (both in ignorance, to be sure); 
and he answered the riddle of the Sphinx, which no one before 
him had been able to solve. 
The story of Oedipus was utilized by the Greek dramatists 
for a number of tragedies. The Greeks called them tragedies 
because the Greeks lived in the days before Freud and were 
the slaves of certain established prejudices concerning the 
proper relations between parents and children. Today we 
would call these plays Social Comedies. 
23 CHAPTER XIII 
THE OEDIPUS IN ALL OF US 
• The basic truth of the Oedipus Complex is confirmed by 
everyday experience. Approximately one-half of my readers, 
for example, must at some time have been little boys. Such 
readers will have not the least difficulty in recalling their 
experiences with measles or scarlet fever. Upon such occasions, 
when they were particularly feverish or otherwise ill-at- 
ease, they almost invariably called for Mother. It is 
also a well-authenticated fact that wounded soldiers in their 
delirium most frequently call for their mothers. 
On the other hand, those of my readers who were once 
little girls, will recall that on occasions during the summer 
vacation when they were confronted by a strange dog, or 
an infuriated hen, or a cow whose intentions wTere doubtful, 
they almost invariably called for Daddy. 
The author may be pardoned for citing an instance of the 
Oedipus Complex from his own experience. He will never 
forget how during his bitter struggles with the first book of 
Euclid, it was almost invariably his father who insisted that 
the boy finish his prescribed lessons before he went to bed, 
whereas his mother would argue that the boy had had a 
hard day, and it was more important for him to be in bed by 
nine o'clock, not forgetting to brush his teeth before retiring. 
There were other times when the boy would turn to his 
father for assistance in arriving at the truth that from any 
point outside of a line only one perpendicular can be drawn 
to that line. His father would begin buoyantly enough. 
24 OEDIPUS 
25 
He would study the text for a minute or two. Then his face 
would grow stern and he would remind the boy roughly that 
it was dishonest for a school boy to solicit help in preparing 
his home-work. 
His mother, on the contrary, would either help him out 
with the perpendicular or else say that it was time to go to 
bed, not omitting the tooth-brush. As a result, all through 
high-school the author recalls that his feelings for his mother 
were much more tender than for his father. 
To be sure, it did not go so far as the boy's wishing 
that his father were dead. But he did have dreams in 
which his father used to ride an old-fashioned bicycle on a 
tight-rope, condemned to solve innumerable problems about 
a perpendicular from a point in the handle-bar to said tight- 
rope. CHAPTER XIV 
THE ANTI-OEDIPUS DIE HARDS 
The Oedipus Complex has not been without its critics. 
They argue that frequently a little boy when pursued by a 
mad hen, will call for Daddy instead of Mother. They cite 
the case of little girls who, in dangerous proximity to a 
strange cow, will call for Mamma. But such examples must 
be dismissed as irrelevant. 
Neither is there much force in the contention that sons are 
more attached to their mothers because of a protective male 
instinct, and daughters are more attached to their fathers be- 
cause of a feminine mother-instinct. Everybody has been 
saying this for thousands of years and it therefore cannot be 
true. 
The only real difficulty we encounter is in the case of 
young children, who are asked by visitors wrhom they like 
better, Mother or Daddy, and who reply, 111 like Mamma and 
Daddy best." The explanation of this will most likely be 
found in a super-Oedipus Complex. 
26 CHAPTER XV 
THE RIDDLE OF THE UNIVERSE 
One apparent omission we do encounter in the handling 
of the Oedipus Complex by the psychoanalysts. They never 
touch upon the story of Oedipus and the riddle of the 
Sphinx. 
It will be recalled that the Sphinx asked Oedipus: What 
animal walks on four feet in the morning, on two feet at 
noon, and on three feet at night. Oedipus replied that the 
animal is Man; he crawls on all fours in infancy, walks 
erect in manhood, and leans upon a staff in old age. 
Up to recently this answer may have been deemed sound 
enough; but now we see it to be false. For if Freudianism has 
taught us anything, it has taught us that man is an animal 
who never walks erect, but is always crawling around in 
the mud. 
As a matter of fact, psychoanalysis does concern itself with 
the riddle of the Sphinx without mentioning it by name; 
and with a certain difference. 
In the old Greek legend, Oedipus discovered the answer to 
the riddle. 
In our own psychoanalytic science Oedipus is himself the 
answer. 
What is life? Oedipus Complex. What is thought? 
Oedipus Complex. What is health, disease, love, hate, 
cruelty, martyrdom? Oedipus. What is art, literature, war, 
the pulpit, the professor's chair, the bacteriologist's micro- 
scope? Oedipus. Why does the writer write, the engineer 
build, the mathematician draw figures, the poet sing, the 
27 28 
EUCLID'S OUTLINE OF SEX 
subway guard howl, the conservative conserve, the radical 
protest, the middle-of-the-road man stay in the middle? 
Oedipus. 
Implanted in man is this passion for finding a single 
answer to the riddle of everything. At different times the 
answer has been providence, fate, chance, fire, wrater, air, 
earth, the atom, the electron, the amoeba. Often it has been 
ouija, the violet ray, internal bathing, the Kneipp cure, 
mineral oil, bran, Fletcherism, the bicycle, the automobile, 
the Soviet, the simple life, the daily dozen, the solar plexus. 
Always it has been a single magic word to satisfy all of 
the Sphinx's questionings. 
Today Freud has given us the real answer, the all-suffi- 
cient answer. What is anything, and why, and how? Ans. 
Oedipus. PART III 
BALAAM CHAPTER XVI 
THE ASS AT THE BRIDGE 
I believe I have by this time convinced the open-minded 
reader that there is hardly a page in the " Elements of 
Geometry " that will not yield rich treasures of sex meaning to 
the searcher equipped with the proper psychoanalytical tools. 
But I have reserved, until this moment, consideration of one 
particular Proposition in the 11 Elements " which seems to me 
to sum up the entire Freudian gospel as it was anticipated and 
exemplified by Euclid. 
This Proposition occurs very early in Book I, and is 
usually stated as follows: 
7/ two sides of a triangle are equal, then the angles opposite 
these sides are equal. 
In the history of mathematics this celebrated proposition 
has come to be known as the Pons Asinorum, or the Bridge 
of Asses. 
The phrase is not altogether a happy one. The reader 
at first sight would assume that a Bridge of Asses is a bridge 
peculiarly adapted for crossing by an Ass. Whereas Euclid's 
intended meaning is just the opposite. It is a bridge that an 
Ass cannot cross, try how he may. 
The common explanation of the Pons Asinorum is that 
this is the Proposition where the slow-witted student of 
Euclid is brought to a standstill. Hitherto he has managed 
to stumble along with more or less difficulty. But when 
confronted with a triangle with two equal sides the dunce 
shies, balks, and refuses to cross. Either he transfers 
from Geometry to Comparative Literature, or else he changes 
31 32 
EUCLID'S OUTLINE OF SEX 
to a new school where emphasis is laid on Character 
Development. 
With all due modesty, however, I am compelled to state 
that this interpretation of the Bridge of Asses, so long en- 
dorsed by greater scholars than myself, is nevertheless to 
be rejected out of hand. To accept the common explanation 
would be to take the very heart of sex out of Euclid, as I 
shall now proceed to show. 
Scholars and mathematicians would never have been con- 
tent to regard the Bridge of Asses as a mere humorous 
epithet for the stupid school boy, if they had only stopped 
to consider one simple fact: In all literature and in all 
common speech both Ass and Bridge are words steeped in 
sex significance. They are erotic symbols par excellence, or 
as we should put it in English, pure and simple. CHAPTER XVII 
BRIDGES 
The Bridge as a symbol of eroticism is so obvious and so 
familiar as to call only for the briefest consideration. 
The Bridge is plainly the transition period from childhood 
to adolescence. That period corresponds with the eighth grade 
in the elementary schools and the first year of high school. 
In the study of mathematics it is the period when the 
student passes from arithmetical problems in carpeting floors 
and papering rooms at so much a square yard (excluding the 
windows), to the first principles of Euclid. 
The Pons Asinorum would thus come very near the period 
when early adolescence is filled with the vague yearnings 
and perplexities to which psychoanalysis has given us the 
key. 
This controlling sex connotation I discern without difficulty 
in " The Bridge of Sighs," and " I Stood on the Bridge at 
Midnight," which mistaken parents are accustomed to regard 
as an affliction when recited by their offspring, instead of 
recognizing them and welcoming them as the expression of a 
vital urge. But I am not quite prepared to go with some 
eminent members of the Left Wing of Psychoanalysis who 
discern the same sex-significance in " London Bridge is Fall- 
ing Dowm." 
There can be no doubt, however, about the real meaning 
of other famous Bridges. 
Horatius at the Bridge, defending the young Roman civil- 
ization against the much older civilization of the Etruscans, 
33 34 
EUCLID'S OUTLINE OF SEX 
is really a sex inhibition or a sex transition, as we may prefer 
to regard it. 
The great Natural Bridge in Rockbridge County, Virginia, 
is just what its name implies, natural; that is to say, sexual. 
The shot fired by the embattled American farmers at the 
Bridge at Concord, Mass., in 1775, is the exact parallel to 
Horatius. Emerson knew what he was talking about when 
he described it as the shot heard round the world: it was 
sex explosion. 
The four bridges which span the East River, namely, 
Brooklyn Bridge, Manhattan Bridge, Williamsburg Bridge 
and Queensborough Bridge, connect the two most important 
sections, that is to say, sexions, of Greater New York. 
A separate chapter might be written about the Bridge in 
Dentistry, both in itself and in relation to the Crown and 
the Root. But time presses. CHAPTER XVIII 
EQUUS ASINUS CYPRIENSIS 
Concerning the Ass in general or as the philosophers might 
say, the Ass sub specie aeternitatis, it is necessary to repeat 
only what I said a little while ago. 
This familiar animal has in all ages and all climes been a 
symbol of eroticism, together with the Bird, the Cat, the Don- 
key, the Eagle, the Fur-bearing Seal, the Giraffe, the Hyena, 
the Irra wady Woodpecker, the Jaguar, the Kangaroo, the 
Llama, the Mesopotamian Fish-Hawk, the Narghili, the Ox, 
the Penguin, the Quadriga, the Rhinoceros, the Swan, the Tour- 
niquet, the Uganda, the Vituperative Buzzard, the Weasel, 
the Xingu, the Yuban, and the Zebra. 
It remained for the Romans to coin a phrase about the 
Ass, descriptive of the fact that by means of erotic symbols 
we can attain the truth that lies beyond the stars: Per 
Asspera ad Asstra. 
35 CHAPTER XIX 
BALAAM 
We may now pass on to an examination of a few of the 
most celebrated erotic Asses in history. 
The field is both extensive and crowded; and anything like 
an exhaustive study is, of course, out of the question. Our 
investigation may well begin with the earliest specimen on 
record which fortunately happens to be also the most typical 
and famous example of the species. 
This is, of course, Balaam's Ass, as we first encounter him 
in Numbers, XXII, 22-33, and subsequently in all world 
literature. 
The story of Balaam and his Ass may be briefly rehearsed 
for the benefit of those readers whose restricted leisure has 
not brought them into contact with the ancient literature of 
the Hebrew people. 
When the Israelites, on their way from Egypt towards the 
promised land, reached the frontiers of Balak, King of Moab, 
that ruler was naturally alarmed by the overwhelming 
strength of the invaders. He therefore sent messengers in great 
haste to the celebrated wizard Balaam, with the urgent re- 
quest that Balaam hasten to the court of Balak and curse 
the Israelites for him. 
Balaam, after some delay marked by a number of vivid 
dreams, inhibitions, and frustrated wish-fulfilments, con- 
sented to undertake the journey to Balak's court, and 
mounted his Ass for that purpose. 
What follows is pure Freudianism. The Ass immediately 
became aware of the presence of an angel blocking the road. 
36 Balaam and the Ass BALAAM 
37 
Balaam, on the other hand, remained in dangerous ignorance 
of the obstacle. 
Difficulties ensued. First the Ass turned aside into a 
field. Then he crushed Balaam's foot against the wall of 
the abutting vineyard. Then he fell prostrate in the road. 
Meanwhile Balaam was cruelly engaged in repressing the 
Ass's desires with his heavy staff until the inevitable neurotic 
discharge occurred; the mouth of the Ass was opened and he 
addressed his master in a few well-chosen words with the 
precise tenor of which we are not particularly concerned. 
The significant fact is that the Ass did break into speech. CHAPTER XX 
THE ASS AND THE UNCONSCIOUS 
11 The significant fact is that the Ass did break into speech." 
For stressing this point the author of the present volume 
has at least two compelling reasons. One may be called 
personal. His own emotional reactions to the vocal Ass in 
the Balaam epic are so strong that to abstain from utterance 
on the subject would be to practice inhibition of a most dan- 
gerous kind. Feeling as I do about Balaam, it must be 
either the fullest and frankest kind of speech or else an 
inevitable nervous breakdown. 
The second reason has to do with the public and with its 
right to the Truth. It is my sincere conviction that I have 
discovered the Truth about Balaam's Ass, and to withhold 
that Truth from the world at large would be a social crime. 
It is every man's inescapable duty to give the public what 
it wants, even if it wants the Truth, as it occasionally does. 
38 CHAPTER XXI 
SUBLIMINAL 
Consider, then, the two basic elements in this Balaam- 
Ass epos: the fact that it involves an Ass and the fact that 
the Ass is represented as speaking for publication. 
On the first point I have possibly said enough when I 
have shown that the Ass is in himself a pure erotic symbol. 
Whenever in history or legend or poetic fantasy we come 
across the Ass as a central figure, we may feel confident that 
it is a case of Cherchez la femme. 
But why is the Ass, aside from his innate eroticism, so 
splendid an embodiment of the Freudian idea? The answer 
is simple. The Ass is also the perfect type of the Uncon- 
scious. 
The Ass is the traditionally patient beast of burden. He 
carries his rider on his back precisely as the Unconscious 
carries the real burden of our conscious mental life. The 
Ass submits to the rein, the whip, the staff, the spur, as 
though he were dependent for his very existence on the good 
will of his master. So the Unconscious submits to checks 
and controls as though it existed by sufferance of the Intelli- 
gence, instead of actually carrying the Intelligence on its 
back, so to speak. 
But, when the need arises, the Ass, like the Unconscious, 
will balk, rear, kick out, and in the extreme, send his rider 
head foremost to the ground. In the final test the Ass and 
the Unconscious have little difficulty in telling the rider, 
whether it be Man or Intelligence, just where he gets off. 
And now consider Balaam and the contrast. The Ass is 
39 40 
EUCLID'S OUTLINE OF SEX 
supposedly a stupid, reticent, patient beast of burden, bound 
down to humdrum duties. Balaam, on the other hand, is a 
wizard, a seer, a something of a prophet. He has the gift 
of eloquence. He has the power to bless and curse. The 
legend in Numbers XXII represents him even as in com- 
munication with God. . . . 
And yet when it comes to the ultimate test between primi- 
tive instinct and the Unconscious, as typified in the Ass, and 
conscious pride of Intellect, as typified in Balaam, it is the 
Ass who wins out. It is Balaam who gets his foot crushed 
against the wall, and is dragged through the brambles, and 
ends by biting the dust. And the lesson is reinforced by a 
few illuminating remarks from the hitherto inarticulate Ass. 
And so it always has been in the last resort. Whenever 
the tyranny of the Intelligence becomes unendurable, the Ass 
grows vocal. CHAPTER XXII 
SPEECH 
What vernacular did the Ass employ in addressing the 
prophet Balaam? Presumably the Hebrayic. 
The bray of the Ass has a poignant symbolism that far 
outstrips in significance its physical carrying power. It is 
penetrating in something more than the ordinary sense. It 
penetrates into the deeper meaning of life. The Ass is vocal 
but not local. He is universal. 
The Ass's bray is universal precisely for the reason that it 
is monotonous. Like the Unconscious, the Ass expresses 
himself in only one key, and for the very simple reason that 
there is only one key to the mystery of life - Unconscious 
Sex. 
Compare the splendid universal monotone of the Uncon- 
scious Ass, with the confused diversity of the human voice. 
It is the difference between a real world-language and Babel. 
The human voice has developed an extraordinary variety 
in its attempt to express the supposed variety of the Scheme 
of Things. It has developed rhythm, tone, pitch, timbre, 
modulation, inflection. It has developed scales and gamuts. 
It makes use of sharps, flats and naturals. It has sought 
refinement of expression through breves, semibreves, crotchets, 
quavers and demisemiquavers. It has even invented that 
mysterious thing called " temperament " which is supposed 
to add a new meaning to the normal effect of the physical 
sound vibrations. 
And it is all vanity. 
The human voice believes that it has fitted the proper 
41 42 
EUCLID'S OUTLINE OF SEX 
intonation to the proper sentiment. It has one tone for love, 
another for pity, another for terror, another for mercy, an- 
other for affection, another for self-sacrifice, another for 
cruelty, another for courage, another for cowardice. And it 
proceeds on the pathetic assumption that when it utters these 
diversified sounds it is mirroring a corresponding reality. 
The human voice actually believes that there are different 
things called love, pity, terror, mercy, affection, self-sacrifice, 
cruelty, courage, cowardice. 
The Ass knows better. He has only one tone because he 
knows that there is only one Reality, and its name is Venus 
Cytherea. 
The human voice sings, shouts, weeps, lilts, groans, ejacu- 
lates, cheers, ululates, lullabies, chants, curses and exhorts, 
under the impression that it is responding to different stimuli. 
The Ass knows there is only one stimulus, and it is the 
Cyprian Aphrodite, or to give her the older name, Astarte, 
that is to say, Asstarte. 
So he brays. 
The human voice, in its quest for truth, stutters, whispers 
to itself, encourages itself, scolds itself, gasps with awe, 
breaks into babble with the joy of understanding, says " I 
have it! " says " Goldarn it! " spends itself, in other words, 
upon shadows and appearances. 
The Ass knows better. He does not whistle when things 
are going fine under the lens of his microscope. He does 
not ejaculate when something new swims within the field of 
his telescope. He does not groan when things go wrong on 
his electromagnetic weighing-scales. He does not shout wrhen 
things begin to precipitate in his bacteriological test tube. 
He does not swear when the two halves of his new iron bridge 
run out of true by a quarter of an inch. He does not halloo 
when the two halves of his Vehicular Tunnel meet within 
half an inch. The Ass knows that there is only one answer. 
It is She of the groves and the High Places - with compli- BALAAM 
43 
cations. It is Cybele, Oedipus, Aphrodite, Narcissus, and 
the Maenads. It is all in the family. 
So he brays. 
The human voice tries to utter its sense of the manifold- 
ness of life, and it only succeeds in developing the complicated 
symptoms described in the programme notes of the Phil- 
harmonic Symphony Orchestra. 
The Ass asserts the essential sex-unity of the universe. 
He brays. CHAPTER XXIII 
SUMMARY 
Before we say farewell to Balaam it will be of service to 
restate the significance of this Freudian epos. The story 
of Balaam is the story of sex. The evidence may be mar- 
shalled in a few brief statements. 
The King of Moab is terrorized by an invading host 
of Israelites coming from the west. But we know that the 
West has always been a symbol of sex. 
The King of Moab summons to his aid a wizard from the 
east. But the East has always carried a peculiar sex-signifi- 
cance. 
The King of Moab in his letter to Balaam doubtless re- 
ferred to the invaders as like unto a thundercloud from the 
north. The North has always had an erotic significance. 
The King of Moab, in this same letter, probably described 
the invaders as like unto a host of grasshoppers from the 
south. But the South can be said to be almost synonymous 
with sex. 
The Israelites, fleeing before their Egyptian foes, crossed 
a desert. All Freudians know what a desert means. 
The Israelites also encamped at the foot of a sacred moun- 
tain. All Freudians know what a mountain means, especially 
a sacred one. 
The Israelites at various times came into contact with 
cloven rocks, burning bushes, golden calves, arks, tablets, 
inspired men, inspired women, traitors, rebels, sinners, saints, 
manna from the heavens, grapes from Eshcol, rivers, oases, 
tents, droves, Amalekites, Peruzzites, Jebusites, etc. But 
44 BALAAM 
45 
to any one who knows what's what in Freud, it is hardly 
necessary to point out just what is meant by cloven rocks, 
burning bushes, golden calves, arks, tablets, saints, sinners, 
manna, grapes, rivers, droves, Jebusites and Peruzzites. 
When Balak, King of Moab, felt impelled to curse the 
Israelites, it is clear that he suffered from an anti-Israelite 
Complex. 
When Balak was afraid to tackle the job himself but sent 
for Balaam to do the cursing, he was plainly suffering from 
an Inferiority Complex. 
When Balak insisted on Balaam's coming, in spite of the 
latter's refusal, he was plainly the victim of a Wish-fulfil- 
ment. 
When Balaam refused to come the first time, and hesi- 
tated the second time, he was plainly suffering from a bad 
case of Inhibition. 
When Balaam sought his heart for counsel, he was obvi- 
ously the victim of a bad case of Introversion. 
When Balaam belabored the Ass with his staff and found 
himself in the ditch as a result, he was just as plainly a 
victim of Extraversion. 
When Balaam lifted up his voice and said, " How beautiful 
are thy tents, 0 Israel," he was giving utterance to an Incest 
Complex. 
The Ass was the only actor in the whole affair who was 
immune from inhibition, repression or complex. He spoke 
right out in meeting. CHAPTER XXIV 
PARENTHESIS 
In passing, I cannot refrain from voicing my astonishment 
at the fact that students of Freud have hitherto given so 
little attention to the Bible. 
Prejudice must not blind us to the fact that the book is 
simply crammed with the raw material of psychoanalysis. 
The few humble results I have derived from the story of 
Balaam are an index of what might be done by others with 
more time on their hands. I have but scratched the surface. 
The Song of Songs alone ought to be worth a million dollars 
to any trained Freudian scholar and practitioner. 
No other book can touch the Bible for its wealth of ma- 
terial on sleep, visions, and dreams. Though a chronic suf- 
ferer from insomnia, I can testify to having repeatedly put 
myself to sleep by repeating all the generations from Adam 
to Zerubbabel. 
Sleep, dreams, visions, hysterias, ecstasies, inhibitions, com- 
mandments, complexes, fulfilments, frustrations-the list 
is virtually inexhaustible. I will content myself with only 
one point which demonstrates the sympathetic attitude of 
the Book as a whole to the psychoanalytic world-outlook. 
This is the emphatic Biblical assertion, that the ideal span 
of man's life is three score years and ten. 
It is only another way of saying when a man has finished 
being a sexagenarian, life has very little further meaning. 
46 PART IV 
BURIDAN THE FORDNEY COMPLEX 
Par. 25. Coal-tar products: Acetanilide not suitable for medicinal 
use, alpha-naphthol, aminobenzoic acid, aminonaphthol, aminophene- 
tole, aminophenol, aminosalicylic acid, aminoanthraquinone, aniline oil, 
aniline salt, anthraquinone, arsanilic acid, benzaldehyde not suitable for 
medicinal use, benzal chloride, benzanthrone, benzidine, benzidine sul- 
fate, benzoic acid not suitable for medicinal use, benzoquinone, benzoyl 
chloride, benzyl chloride, benzylethylaniline, beta-naphthol not suitable 
for medicinal use, bromobenzene, chlorobenzene, chlorophthalic acid, 
cinnamic acid, cumidine, dehydrothiotoluidine, diaminostilbene, dianisi- 
dine, dichlorophthalic acid, dimethylaniline, dimethylaminophenol, 
dimethylphenylbenzylammonium hydroxide, dimethylphenylenediamine 
dinitrobenzene, dinitrochlorobenzene, dinitronaphthalene, dinitrophenol, 
dinitrotoluene, dihydroxynaphthalene, diphenylamine, hydroxyphenylar- 
dinitrotoluene, dihydroxynaphthalene, diphenylamine, hydroxyphenyl- 
arsinic acid, metanilic acid, methylathraquinone, naphthylamine, 
naphthylenediamine, nitroaniline, nitroanthraquinone, nitrobenzaldehyde, 
nitrobenzene, nitronaphthalene, nitrophenol, nitrophenylenediamine, 
nitrosodimethylaniline, nitrotoluene, nitrotoluylenediamine, phenol, 
phenylenediamine, phenylhydrazine, phenylnaphthylamine, phenylgly- 
cine, phthalimide, quinaldine, quinoline, resorcinol not suitable for medic- 
inal use, salicylic acid and its salts not suitable for medicinal use, 
sulfanilic acid, thiocarbanilide, thiosalicylic acid, tetrachlorophthalic 
acid, tetramethyldiaminobenzophenone, tetramethyldiaminodiphenyl- 
methane. 
48 CHAPTER XXV 
OLD FRIENDS 
Just about six hundred years ago there lived in France a 
philosopher and logician by the name of Jean Buridan. His 
claim to a place in history and to a portion of the strictly 
limited space at my disposal may be said to rest upon the 
back of no less than two Asses. Buridan must thus be re- 
garded as the outstanding eroticist of the Middle Ages. 
Of the two Buridan examples of the species Asinus, one 
animal is by an extraordinary coincidence - but I personally 
think it more than a coincidence - our old Euclidean friend 
the Ass at the Bridge. 
Buridan, too, had his Pons Asinorum, but he made use of 
him in the field of logic and not of mathematics. 
My readers are no doubt aware that in Logic they have 
a form of reasoning, or, if you wish to call it so, a form of 
entertainment, knowm as the Syllogism. The Syllogism is 
composed of a major term, a middle term, and a minor term, 
and the idea is to cross from the major term to the minor 
term by means of the middle term. 
Now, there are syllogisms wThich are so simple that fre- 
quently there is no need to state the middle term; the ordi- 
nary logician can leap straight across from major to minor. 
Buridan, however, always insisted upon inserting the middle 
term, and it is supposed that he did it for the convenience of 
the Grade Ass student in Logic. 
There is thus a notable difference between Euclid's Pons 
Asinorum and Buridan's Pons Asinorum. Euclid's Bridge 
of Asses was one which an Ass could not cross. (See 
49 50 
EUCLID'S OUTLINE OF SEX 
page 31.) Buridan's Bridge was built especially for the 
facilitation of Ass traffic. Euclid, in other words, believed 
in the inhibition of Asses, while Buridan believed in the liber- 
ation of Asses. But the important thing is that they both 
recognized the significance of the animal. CHAPTER XXVI 
SELF-DETERMINATION 
However, the Buridan Ass who crossed the bridge is by 
far the less celebrated of his two specimens. The Buridan 
animal that enjoys universal fame is the Ass of the Haystacks. 
Jean Buridan in philosophy was what is called a Deter- 
minist. That is to say, he believed that man's conduct is 
entirely guided and determined by external forces. To 
illustrate this point Buridan imagined an Ass placed at a 
precisely equal distance between two precisely equally attrac- 
tive haystacks. It was Buridan's contention that an Ass, so 
conceived and so dedicated, would find it impossible to make 
up his mind between the two piles of hay and would slowly 
but surely perish of starvation. 
The true meaning of Buridan's Ass is, of course, just the 
reverse of this commonly accepted version. Buridan did 
not really mean that the Ass, or Man, was bound to be per- 
manently inhibited. He was merely anxious to point out 
the dreadful results of inhibition if carried too far. By the 
Ass starving to death he did not mean physical death, but 
psychic breakdown, neurosis. 
Buridan, if he were living today, would have been all in 
favor of psychoanalyzing the Ass. He would discover the 
particular Complex developed by the Ass in early foalhood, 
bring that Complex to the surface of consciousness, and thus 
cast it out. 
Thereupon the Ass would head without loss of time for one 
of the two haystacks. Having consumed it, he would turn 
his attention to the other haystack. 
51 52 
EUCLID'S OUTLINE OF SEX 
The Broadway Complex 
The Messrs. Lee and J. J. Shubert Present 
CECIL LEAN and CLEO MAYFIELD 
IN 
"THE BLUSHING BRIDE" 
Books and Lyrics by Cyrus Wood 
Based on a Play by Edward Clark and Mark Swan 
Music by Sigmund Romberg 
Staged by Frank Smithers 
Musical numbers arranged by Jack Mason 
Orchestra Under the Direction of Al Goodman 
Scenes by Watson Barratt 
The Entire Production Under the Personal Direction of Mr. J. J. Shubert 
Miss Lorraine's Gowns by Madame Frances 
The sable and ermine wrap worn by Miss Lorraine in the Third Act 
executed by C. C. Shayne and Co. 
All gowns and costumes by Anna Spencer, Inc., Designs of Shirkey 
Braker, Personal Supervision of Miss Anna Spencer 
Boy clothes by Knox Uniforms from Brooks Co. 
Shoes from I. Miller 
Scenery designed and executed by Clifford Pember. Painted by Berg- 
man. Built at Selwyn Studio. 
Motion pictures by Shackleford. BURIDAN 
53 
It is asserted by the pre-Freudian text-books that there is 
really no mention in Buridan's extant works of either the 
Ass at the Bridge or the Ass of the Haystacks, and it is sug- 
gested that both Asses were, so to speak, saddled upon him 
by his enemies. But from the standpoint of the Freudian 
analysis the mere fact that a thing is not so does not prove 
that it isn't so. We shall be safe in continuing to think of 
Buridan as being himself the mediaeval bridge between the 
ancient eroticism of Euclid and the eroticism of today. 
We may call Buridan, in fact, the Pons Asinorum between 
the classic and the modern world. PART V 
THE NEW ENGLAND ELEMENT IN EUCLID CHAPTER XXVII 
THE EUCLIDEAN STYLE 
All of us are acquainted with the phenomenon of what the 
older psychology used to call diffidence or shyness. (See 
W. S. Gilbert, The Mikado, Act II.) We know today that 
shyness in adults is the result of inhibition or repression in 
childhood. 
The stigmata of the diffident man are familiar. In com- 
pany he either stutters or yells. Either it is impossible to 
get him to talk or else it is impossible to choke him off. He 
is alternately panic-stricken or terrifyingly Napoleonic. 
When he is silent it is the Inferiority Complex. When he 
refuses to be flagged it is the Defense Complex. The louder 
he talks the more he is on the defensive. 
Thus it was with Euclid. Remember his childhood of sup- 
pressions. Remember his enslavement to the Honeycake 
Complex and the Sunflower Complex. You will then under- 
stand the peculiar literary style of the Euclid we meet in 
the " Elements." 
It is a hard-bitten^ dogmatic, finger-pointing, bumptious 
style, with its " Let A and C be the two points," its abrupt 
" Draw a line from F to G," its " Now's " and " Then's " and 
" Therefores," its self-satisfied, smug, almost smirking 
" Q.E.D.'s." 
We find Euclid at his characteristic best, or worst, in the 
following: 
57 58 
EUCLID'S OUTLINE OF SEX 
Theorem 
A straight line perpendicular to one of two parallel planes 
is perpendicular to the other also. 
Fig. 7 
Given the plane MN || plane PQ, and AB ± PQ. 
To prove AB _L MN. 
Proof. Through AB pass a plane intersecting PQ and MN 
in the lines BC and AF respectively; also through AB pass 
another plane intersecting PQ and MN in BD and AH, re- 
spectively. 
Then BC || AF, and BD || AH. 
But AB ± BC and BD. 
AB ± AF and AH. 
/. AB _L plane MN 
(Art. 531) 
(Art. 505) 
(Art. .123) 
(Art. 509) 
Q. E. D. 
It is a concise style; yes. But ask any schoolboy of your 
acquaintance whether Euclid does not suffer constantly from NEW ENGLAND ELEMENT IN EUCLID 
59 
leaving too much to the imagination. It is a style admirably 
suited to a couple of aviators on a falling airplane, or a 
subway passenger talking with a friend, but as a medium 
of normal social intercourse it leaves much to be desired. 
If Euclid were ever tempted to drop into poetry he would 
probably have said " Love || Truth," or 11 Man ± the Stars." 
And it all came about from the child Euclid's too intimate 
association with his grandmother. To realize what Com- 
plexes will do to a man's literary style we need only compare 
the above citation from Euclid with almost any passage from 
Mr. George Moore or Mr. James Branch Cabell's 11 Jurgen." 
In these men we find a mellifluousness, an easy grace, a 
rhythmic movement and a savoir faire, which testify plainly 
to the absence of all inhibiting complexes. CHAPTER XXVIII 
THE ASTERISK AND THE DOTTED LINE 
(A Missing Chapter in Euclid) 
Like nearly all literary and historical relics of the ancient 
world, the manuscript of Euclid's " Elements of Geometry " 
has come down to us in mutilated form. 
Euclid, as is well known, was passionately interested in all 
kinds of points - points in a circle; points outside of a circle; 
points in a straight line; points outside of a straight line, etc. 
He was just as passionately interested in lines - straight 
lines; curved lines; broken lines, etc.; all of them conveying 
a more or less obvious meaning. 
It seems odd, therefore, that Euclid should have omitted 
all consideration of what is unquestionably the most sexually 
significant of all points, namely, the Asterisk; and the most 
sexually significant of all lines, namely, the Dotted Line. 
To the recovery of these lost phenomena in Euclid, the 
present author devoted himself. The search involved pro- 
longed and exacting labor, but it was crowned with success. 
We are now in a better position to appreciate the full im- 
portance of Euclid the Elemental Amorist. 
There is little doubt that the potentialities of the asterisk 
and the dotted line were first drawn to Euclid's attention by 
the contemporary writers of fiction. In the remorseless 
studies of life and sex to which the realistic novelists of Kos 
and the adjacent islands devoted themselves, there constantly 
arose situations which could be more safely imagined than 
described. That is where the symbolic line of asterisks or 
dots came in handy. 
60 NEW ENGLAND ELEMENT IN EUCLID 
61 
Euclid was no doubt familiar with passages in the realistic 
fiction of his time which looked as follows: 
" It was only two hours since Fate, for its own purpose, 
had first introduced Glaucus to Sybilla. Now that the fes- 
tival lights were dying out and the moment had come to say 
farewell, he looked at her and said, ' Must you go? ' 
" The next morning dawned clear and crisply cold, with 
a lively breeze from the Phoenician coast." 
There were realistic novelists who preferred the asterisk 
to the dot, but the general effect was the same: 
" He looked at her and said ' Must you go? ' 
" The next morning dawned clear and crisply cold, with a 
lively breeze from the Phoenician coast." 
There was a third school which made use neither of the 
asterisk nor the dot, but of the double space, but still with 
the same effect: 
" He looked at her and said, ' Must you go? ' 
" The next morning dawned clear and crisply cold, with a 
lively breeze from the Phoenician coast." 
It was argued in behalf of the double-space school of 
realistic fiction that it involved a considerable saving in 
linotype composition; but it was not a conclusive argument. 
As a matter of fact, the most successful realists of Euclid's 
time confined themselves to no one fixed style. They made 
free use of the dotted line, the asterisk line, and the double 
space, as the occasion demanded and their fancy moved them. 
And both the occasion and the fancy operated with great 
frequency. 
Nevertheless, it is a tribute to the genius of the Greek 
mind, that the realistic novelists were not long permitted to 62 
EUCLID'S OUTLINE OF SEX 
monopolize the advantages of the dotted or the asterisk style. 
The writers of clean, wholesome fiction for the home quickly 
adapted the device to their own use. 
They began tentatively with a few dots or asterisks in the 
manner made familiar in our own time by Mr. H. G. Wells; 
as when he writes: 
" Mr. Hengist picked up his paper. ... It was the Morn- 
ing Post. ... He began to operate on his breakfast egg . . . 
thoughtfully ..." 
From this it was not a very long step to the full exploi- 
tation of the dotted and starred line. Greek best-sellers 
of the clean, wholesome type, began to show on every page 
passages like the following: 
" Leuconoe smiled as she glanced at the vegetable pedler 
kneeling over his basket. 
" I have seen better garlic in the market at three pounds 
to the drachma," she said. " Much more convincing garlic." 
" The vegetable seller looked up at Leuconoe. 
" Five minutes later Leuconoe in the kitchen was rinsing 
the garlic in cold water and singing to herself." 
It is my firm belief that what the romantic school of Kos 
fiction achieved, our own writers of the clean and wholesome 
school will soon be practicing. As for instance: 
" She looked up at him and smiled, with the tea-cup poised 
over the tray. 
" Will it be lemon or cream? " she said. 
" Five minutes later he asked for a third cup." 
But, it may be asked, What has all this to do with Euclid? 
The answer is, A great deal. Euclid did not go in for fiction, 
but he did go in for geometry. And when his preoccupation 
with the Eternal Triangle began to manifest itself, the dotted 
line played a prominent part. To prove that two triangles The Asterisk NEW ENGLAND ELEMENT IN EUCLID 
63 
are equal if three sides of the one are equal respectively to 
three sides of the other, Euclid was continually drawing 
figures like the following: 
PROPOSITION 6 
Fig. 8 
Or take Proposition 12 in Book I. A novelist would have 
described the situation somewhat as follows: 
" Right Triangle ABC looked at Right Triangle A'B'C' 
and A'B'C' at ABC. They knew that they were equal to 
each other in respect to their hypotenuses and one of the 
short sides. But "were they equal to each other in all re- 
spects? They wondered. 
" Yes, they were congruent in every respect." 
Euclid, employing his own idiom, stated the same funda- 
mental sex-truth in the following manner: EUCLID'S OUTLINE OF SEX 
64 
PROPOSITION 12 
Pig. 9 
Later mathematicians have developed the possibilities of 
the dotted line. I need only recall to my readers the familiar 
friend of their youth, the Binomial Theorem: 
(X 4- Y)12 = X12 + 12 xny 4- 66 x10y2 
12 x y11 4- y12 
Among the mathematicians the dotted line is known as the 
Line of Infinite Suggestion. BIBLIOGRAPHY BIBLIOGRAPHY 
Maxwell, Dream-Factors in the Fordney Tariff (New York, 
1922). 
Pizzicati, The Nightmare in Futurist Art (Napoli, 1921). 
Williams, Sex-Elements in the Ferromanganese Industry 
(Pittsburgh, 1920). 
Dubost, La Nevropathie du parallelogramme (Paris, 1913). 
Grove, How to Bisexualize an Angle (Annals of Academy of 
Science, Mathematical Sexion, 1922). 
Jones, The Labor-Day Complex at Grand Central Station 
(New York, annually). 
Jells, H. B. An Outline of Hysteria; original fortnightly serial 
edition, London, 1920; 2 vol. edition, New York, 1921; 1 
vol. edition, New York, 1921; 4 vol. edition, New York, 
1923; condensed edition. New York, 1922; expanded 
edition, New York, 1922; wide-margin edition, New 
York, 1922; uncut-edges edition, New York, 1922; Fox- 
Paramount film edition, with special titles, Hollywood, 
1923; Sonorola edition, with record cabinet, New Jersey, 
1922; Slampico edition, with foot-pump or electric at- 
tachment, New York, 1920; Radiophone WZQ edition, 
1340 metres, New York, passim; New Republic edition, 
New York, 1921; Snappy Stories edition, New York, 
1922; Incompletely-read edition, at various second-hand 
book stores. 
Smith, The Mirrors of Matteawan (New York, 1923). 
67 68 
EUCLID'S OUTLINE OF SEX 
Horlick, Musical Comedy and the Unconscious (New York, 
annually). 
Zumpft, Die Mutterliebe und Schneider sr echnungen (Mater- 
nal Love and Tailors' Bills, Erlangen, 1921). 
Drinkhard, Typical Cases from Canada and Cuba (Publi- 
cations of the Federal Warehouse Association, New 
York, 1922). 
THE END