Usage examples for Geometers

Famous quotes with Geometers

• Who are the inventors of Tlön? The plural is inevitable, because the hypothesis of a lone inventor — an infinite Leibniz laboring away darkly and modestly — has been unanimously discounted. It is conjectured that this brave new world is the work of a secret society of astronomers, biologists, engineers, metaphysicians, poets, chemists, algebraists, moralists, painters, geometers... directed by an obscure man of genius. Individuals mastering these diverse disciplines are abundant, but not so those capable of inventiveness and less so those capable of subordinating that inventiveness to a rigorous and systematic plan.

  Jorge Luis Borges
• Descartesmade the final break with the Greek tradition of admitting only the first, second, and third powersin geometry. After Descartes, geometers freely used powers higher than the thirdrecognizing that representability as figures in Euclidean space for all of the terms in an equation is irrelevant to the geometrical interpretation of the analysis.

  René Descartes
• The great Cartesian invention had its roots in those famous problems of antiquity which originated in the days of Plato. In endeavoring to solve the problems of the trisection of an angle, of the duplication of the cube and of the squaring of the circle, the ruler and compass having failed them, the Greek geometers sought new curves. They stumbled on the ...There we find the nucleus of the method which Descartes later erected into a principle. Thus Apollonius referred the parabola to its axis and principal tangent, and showed that the semichord was the mean propotional between the latus rectum and the height of the segment. Today we express this relation by = L, calling the height the (y) and the semichord the (x); the being... L. ...the Greeks named these curves and many others... ... Thus the ellipse was the of a point the sum of the distances of which from two fixed points was constant. Such a description was a of the curve...

  Tobias Dantzig
• "While then for a long time everyone was at a loss, Hippocrates of Chios was the first to observe that, if between two straight lines of which the greater is double of the less it were discovered how to find two mean proportionals in continued proportion, the cube would be doubled; and thus he turned the difficulty in the original problem into another difficulty no less than the former. Afterwards, they say, some Delians attempting, in accordance with an oracle, to double one of the altars fell into the same difficulty. And they sent and begged the geometers who were with Plato in the Academy to find for them the required solution. And while they set themselves energetically to work and sought to find two means between two given straight lines, Archytas of Tarentum is said to have discovered them by means of half-cylinders, and Eudoxus by means of the so-called curved lines. It is, however, characteristic of them all that they indeed gave demonstrations, but were unable to make the actual construction or to reach the point of practical application, except to a small extent Menaechmus and that with difficulty."

  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 (= Eucl. XII., 2) 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 , 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

Related words & questions

Related words: geometric solids, polyhedra, equilateral triangle, isosceles triangle, trapezoid

Related questions:

What are geometers?

What is a polyhedra?

What is a geometric solid?

subjective psychology

Objective psychology is the antonym for subjective psychology. While the latter refers to theories and concepts that rely on individual views and experiences, objective psychology ...