Thomas Little Heath Quotes

35 Sourced Quotes

The trisection of an angle was effected by means of a curve discovered by Hippias of Elis, the sophist, a contemporary of Hippocrates as well as of Democritus and Socrates. The curve was called the quadratrix because it also served (in the hands, as we are told, of Dinostratus, brother of Menæchmus, and of Nicomedes) for squaring the circle. It was theoretically constructed as the locus of the point of intersection of two straight lines moving at uniform speeds and in the same time, one motion being angular and the other rectilinear.

Thomas Little Heath
The actual writers of Elements of whom we hear were the following. Leon, a little younger than Eudoxus, was the author of a collection of propositions more numerous and more serviceable than those collected by Hippocrates. Theudius of Magnesia, a contemporary of Menæchmus and Dinostratus, "put together the elements admirably, making many partial or limited propositions more general". Theudius's book was no doubt the geometrical text-book of the Academy and that used by Aristotle.

Thomas Little Heath
Once the first principles are disposed of, the body of doctrine contained in the recent textbooks of elementary geometry does not, and from the nature of the case cannot, show any substantial differences from that set forth in the Elements.

Thomas Little Heath
For the mathematician the important consideration is that the foundations of mathematics and a great portion of its content are Greek. The Greeks laid down the first principles, invented the methods ab initio, and fixed the terminology. Mathematics in short is a Greek science, whatever new developments modern analysis has brought or may bring.

Thomas Little Heath
An edition is... still wanted which shall, while in some places adhering... to the original text, at the same time be so entirely remodeled by the aid of accepted modern notation as to be thoroughly readable by any competent mathematician, and this want it is the object of the present work to supply.

Thomas Little Heath
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
The Pythagoreans discovered the existence of incommensurable lines, or of irrationals. This was, doubtless, first discovered with reference to the diagonal of a square...

Thomas Little Heath
The problem of doubling the cube was henceforth tried exclusively in the form of the problem of the two mean proportionals.

Thomas Little Heath
Almost the whole of Greek science and philosophy begins with Thales.

Thomas Little Heath
It is... the author's confident hope that this book will give a fresh interest to the story of Greek mathematics in the eyes both of mathematicians and of classical scholars.

Thomas Little Heath