The doctrine of ratios and proportion is introduced by **Euclid** as a part of his system of geometry ; and the student seldom fails to remark, that in the treatises on algebra, the same subject is presented under a considerably different form; though he is usually quite unable to determine wherein the essential difference consists; and would probably find but few teachers who could precisely point out the distinction to him.

— Rev. Baden Powell,

I claim that many patterns of Nature are so irregular and fragmented, that, compared with **Euclid** a term used in this work to denote all of standard geometry Nature exhibits not simply a higher degree but an altogether different level of complexity ... The existence of these patterns challenges us to study these forms that **Euclid** leaves aside as being "formless," to investigate the morphology of the "amorphous."

— As quoted in a review of

Detection is, orought to be, an exact science, and should be treated in the
same cold and unemotional manner.You have attempted to
tinge it with romanticism, which produces much the
same effect as if you worked a love- story oran
elopement into the fifth proposition of **Euclid**.

— 1890 The Sign of Four, ch.1.

**Euclid** alone Has looked on
Beauty bare. Fortunate they Who, though once only
and then but far away, Have heard her
massive sandal set on stone.

— 1923 Harp-Weaver and Other Poems,'Sonnet 22: Euclid alone has looked on Beauty bare'.

**Euclid** alone has looked on Beauty bare.Let all who prate of Beauty hold their peace,And lay them prone upon the earth and ceaseTo ponder on themselves, the while they stareAt nothing.

— Sonnet XXII from

**Euclid** … manages to obtain a rigorous proof without ever dealing with infinity, by reducing the problem [of the infinitude of primes] to the study of finite numbers. This is exactly what contemporary mathematical analysis does.

— 2.4, "Discrete Mathematics and the Notion of Infinity", p. 45

How little inventiveness there is in man, Grave copier of copies, I give thanks For a new relish, careless to inquire My pleasure's pedigree, if so it please, Nobly, I mean, nor renegade to art. The Grecian gluts me with its perfectness, Unanswerable as **Euclid** , self-contained, The one thing finished in this hasty world, Forever finished, though the barbarous pit, Fanatical on hearsay, stamp and shout As if a miracle could be encored.

—

**Euclid** 's manner of exposition, progressing relentlessly from the data to the unknown and from the hypothesis to the conclusion, is perfect for checking the argument in detail but far from being perfect for making understandable the main line of the argument.

— p. 70 (How to Solve It (1945))

On an attentive examination of the methods adopted by modern elementary writers, in laying down the first principles of ratios and proportion, and especially in commenting upon **Euclid**, I long since experienced a conviction of the extremely unsatisfactory nature of most of their views; and this chiefly, as appearing to me to involve inadequate ideas of **Euclid**'s real principle in treating of proportionals in his 5th book, and of the nature of the quantities which form the subject of investigation.

— Rev. Baden Powell,

I claim that many patterns of Nature are so irregular and fragmented, that, compared with **Euclid** a term used in this work to denote all of standard geometry Nature exhibits not simply a higher degree but an altogether different level of complexity ... The existence of these patterns challenges us to study these forms that **Euclid** leaves aside as being "formless," to investigate the morphology of the "amorphous."

— Benoît Mandelbrot As quoted in a review of

The Greeks elaborated several theories of vision. According to the Pythagoreans , Democritus , and others vision is caused by the projection of particles from the object seen, into the pupil of the eye. On the other hand Empedocles , the Platonists , and **Euclid** held the strange doctrine of ocular beams, according to which the eye itself sends out something which causes sight as soon as it meets something else emanated by the object.

— Florian Cajori,

**Euclid** alone has looked on Beauty bare.

— Edna St. Vincent Millay, Sonnet