How to use Geometers in a sentence
The ancient Egyptians were famed as " geometers," and as early as the days of Rameses II.
Having determined the difference of latitude between Alexandria and Syene which he erroneously believed to lie on the same meridian, and obtained the distance of those places from each other from the surveys made by Egyptian geometers, he concluded that a degree of the meridan measured 700 stadia.'
The harmony between arithmetical and geometrical measurement, which was disturbed by the Greek geometers on the discovery of irrational numbers, is restored by an unlimited supply of the causes of disturbance.
It is probable that the algebra of the Egyptians was of a most rudimentary nature, for otherwise we should expect to find traces of it in the works of the Greek geometers, of whom Thales of Miletus (640-546 B.C.) was the first.
The quadratrix of Dinostratus was well known to the ancient Greek geometers, and is mentioned by Proclus, who ascribes the invention of the curve to a contemporary of Socrates, probably Hippias of Elis.Advertisement
The third volume includes, however, some theological treatises, and the first part of it is occupied with editions of treatises on harmonics and other works of Greek geometers, some of them first editions from the MSS., and in general with Latin versions and notes (Ptolemy, Porphyrius, Briennius, Archimedes, Eutocius, Aristarchus and Pappus).
Simson's contributions to mathematical knowledge took the form of critical editions and commentaries on the works of the ancient geometers.
Leibnitz, the Bernoullis, Roger Cotes and others - and so assiduously was it studied that it was sometimes named the "Helen of Geometers."
After being educated at Dusseldorf and at the universities of Bonn, Heidelberg and Berlin he went in 1823 to Paris, where he came under the influence of the great school of French geometers, whose founder, Gaspard Monge, was only recently dead.
The Greek geometers invented other curves; in particular, the conchoid, which is the locus of a point such that its distance from a given line, measured along the line drawn through it to a fixed point, is constant; and the cissoid, which is the locus of a point such that its distance from a fixed point is always equal to the intercept (on the line through the fixed point) between a circle passing through the fixed point and the tangent to the circle at the point opposite to the fixed point.Advertisement
The Greek geometers were perfectly familiar with the property of an ellipse which in the Cartesian notation is x 2 /a 2 +y 2 /b 2 =1, the equation of the curve; but it was as one of a number of properties, and in no wise selected out of the others for the characteristic property of the curve.
The invention of the conic sections is to be assigned to the school of geometers founded by Plato at Athens about the 4th century B.C. Under the guidance and inspiration of this philosopher much attention was given to the geometry of solids, and it is probable that while investigating the cone, Menaechrnus, an associate of Plato, pupil of Eudoxus, and brother of Dinostratus (the inventor of the quadratrix), discovered and investigated the various curves made by truncating a cone.
This work, the earliest published in Christian Europe, treats the conic sections in relation to the original cone, the procedure differing from that of the Greek geometers.
Desargues has a special claim to fame on account of his beautiful theorem on the involution of a quadrangle inscribed in a conic. Pascal discovered a striking property of a hexagon inscribed in a conic (the hexagrammum mysticum); from this theorem Pascal is said to have deduced over 400 corollaries, including most of the results obtained by earlier geometers.
Despite the large number of species, including lots of geometers, the only interesting species were orange footman and marbled brown.Advertisement
Here and there particular curves, for example, had been obliged to yield the secret of their tangent; but the ancient geometers apparently had no consciousness of the general bearings of the methods which they so successfully applied.
It dashes at once into the middle of the subjects with the examination of a problem which had baffled the ancients, and seems as if it were tossed at the heads of the French geometers as a challenge.