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** '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))

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,

Closely related to the problem of the parallel postulate is the problem of whether physical space is infinite. **Euclid** assumes in Postulate 2 that a straight-line segment can be extended as far as necessary; he uses this fact, but only to find a larger finite length for example in Book I, Propositions 11, 16, and 20. For these proofs Heron gave new proofs that avoided extending the lines, in order to meet the objection of anyone who would deny that the space was available for the extension.

— Morris Kline,

Jaisingh collected and studied all the available astronomical works...Several European works were translated into Sanskrit under his orders, particularly **Euclid** ’s elements, with a treatise on plane and spherical trigonometry ; and on the construction and use of logarithms ...and also a treatise on conical sections...maps and globes of the Ferenghis were obtained from Surat .

— G.R. Kaye, on the efforts made by Jai Singh to set up the Astronomical Observatory in Jaipur, in p.213

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,

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,

It is a remarkable fact in the history of geometry , that the Elements of **Euclid**, written two thousand years ago, are still regarded by many as the best introduction to the mathematical sciences.

— Florian Cajori,

The term 'axiom' was used by Proclus , but not by **Euclid**. He speaks, instead, of 'common notions' common either to all men or to all sciences.

— 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,

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

— Edna St. Vincent Millay, Sonnet