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

**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.

—

To avoid any assertion about the infinitude of the straight line, **Euclid** says a line segment (he uses the word "line" in this sense) can be extended as far as necessary. Unwillingness to involve the infinitely large is seen also in **Euclid**'s statement of the parallel axiom. Instead of considering two lines that extend to infinity and giving a direct condition or assumption under which parallel lines might exist, his parallel axiom gives a condition under which two lines will meet at some finite point.

— Morris Kline,

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,

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,