Quotes about Euclid

75 Sourced Quotes

The history of Alexandrian mathematics begins with the Elements of Euclid and closes with the Algebra of Diophantus, both of which are founded on the discoveries of several preceding centuries.

James Gow (scholar)

[Relativist] Rel. There is a well-known proposition of Euclid which states that "Any two sides of a triangle are together greater than the third side." Can either of you tell me whether nowadays there is good reason to believe that this proposition is true?
[Pure Mathematician] Math. For my part, I am quite unable to say whether the proposition is true or not. I can deduce it by trustworthy reasoning from certain other propositions or axioms, which are supposed to be still more elementary. If these axioms are true, the proposition is true; if the axioms are not true, the proposition is not true universally. Whether the axioms are true or not I cannot say, and it is outside my province to consider.

Arthur Eddington

I taught myself decimals, equations, the square, cube, and biquadrate roots. I got some knowledge of logarithms, and some of algebra. I readily got through a small schoolbook of geometry; and having an odd volume, the first, of Williamson's ' Euclid,' I attacked it vigorously and perseveringly. Williamson's is by no means the best book on the subject, yet I am still of opinion that it is the best book I could have had for the purpose of teaching myself.

Comparatively few of the propositions and proofs in the Elements are his [Euclid's] own discoveries. In fact, the proof of the "Theorem of Pythagoras" is the only one directly ascribed to him.

The ideal of strictly scientific method in mathematics which I have tried to realise here, and which perhaps might be named after Euclid I should like to describe in the following way... The novelty of this book does not lie in the content of the theorems but in the development of the proofs and the foundations on which they are based... With this book I accomplish an object which I had in view in my Begriffsschrift of 1879 and which I announced in my Grundlagen der Arithmetik. I am here trying to prove the opinion on the concept of number that I expressed in the book last mentioned.

A bird's-eye view of centralised and disempowered societies will reveal a strictly rectilinear network of streets, farms, and property boundaries. It is as though we have patterned the earth to suit our survey instruments rather than to serve human or environmental needs. We cannot perhaps blame Euclid for this, but we can blame his followers. The straight-line patterns that result prevent most sensible landscape planning strategies and result in neither an aesthetically nor functionally satisfactory landscape or stretscape. Once established, then entered into a body of law, such inane (or insane) patterning is stubbornly defended. But it is created by, and can be dismantled by, people.

Discontinuity of its linguistic and logical terms is for the conscious analytical intellect psychologically and logically prior to notions of continuity.... This functional priority... may not have been reflected in the history of the development of reason in all human communities.... But it is relevant for the West that the Pythagoreans, with their discrete integers and point patterns, came before Euclid, with his continuous metrical geometry, and that physical atomism as a speculative philosophy preceded by some two thousand years the conception of a continuous physical medium with properties of its own.

Lancelot Law Whyte

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.

The oldest definition of Analysis as opposed to Synthesis is that appended to Euclid XIII. 5. It was possibly framed by Eudoxus. It states that "Analysis is the obtaining of the thing sought by assuming it and so reasoning up to an admitted truth: synthesis is the obtaining of the thing sought by reasoning up to the inference and proof of it." In other words, the synthetic proof proceeds by shewing that certain admitted truths involve the proposed new truth: the analytic proof proceeds by shewing that the proposed new truth involves certain admitted truths.

James Gow (scholar)

The idea that theorems follow from the postulates does not correspond to simple observation. If the Pythagorean theorem were found to not follow from the postulates, we would again search for a way to alter the postulates until it was true. Euclid's postulates came from the Pythagorean theorem, not the other way around.

Richard Hamming

[The books of Euclid pass on to us] something admirable and very necessary to see and to read, namely the order in the method of writing on mathematics in that aforementioned time of the wise age.

I would say, if you like, that the party is like an out-moded mathematics...that is to say, the mathematics of Euclid. We need to invent a non-Euclidian mathematics with respect to political discipline.

I expect that mathematicians have classified such fuzzy logics. Certainly they have been much used by physicists. But is there not something to be said for the approach of Euclid? Even now that we know that Euclidean geometry is (in some sense) not quite true? Is it not good to know what follows from what, even if it is not necessarily FAPP? Suppose for example that quantum mechanics were found to resist precise formulation. Suppose that when formulation beyond FAPP was attempted, we find an unmovable finger obstinately pointing outside the subject, to the mind of the observor, to the Hindu scriptures, to God, or even only Gravitation? Would that not be very, very interesting?

John Stewart Bell

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.

Edna St. Vincent Millay

Hippocrates himself is an example of the concurrent study of the two departments. On the one hand, he was the first of the Greeks who is known to have compiled a book of Elements. This book, we may be sure, contained in particular the most important propositions about the circle included in Euclid, Book III. But a much more important proposition is attributed to Hippocrates; he is said to have been the first to prove that circles are to one another as the squares on their diameters with the deduction that similar segments of circles are to one another as the squares on their bases. These propositions were used by him in his tract on the squaring of lunes, which was intended to lead up to the squaring of the circle. The latter problem is one which must have exercised practical geometers from time immemorial. Anaxagoras for instance is said to have worked at the problem while in prison.

Thomas Little Heath