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Besides other works on astronomy and chronology, Eratosthenes wrote a Geographica in three books, in which he first gave a history of geography up to date and then passed on to mathematical geography, the spherical shape of the earth, &c., &c. Apollonius of Perga was with justice called by his contemporaries the 'Great Geometer', on the strength of his great treatise, the Conics.
Nor, though I bragged perpetually of my shorthand, of my literature, of my indispensable share in Rawdon's business, did Parload lay stress on the conics and calculus he "mugged" in the organized science school.
I sat down to warm my hands and my half-frozen face, and when I felt comfortable I said, "Do you read conic sections, young gentleman?" His bonnet was off now, and I saw his broad, compact forehead and his massive temples. He looked capable of reading anything. He replied, quite simply: "Oh, yes! I read geometrical conics." "And did you teach yourself?" "Yes.
Dionysodorus gave a solution by means of conics of the auxiliary cubic equation to which Archimedes reduced this problem; he also found the solid content of a tore or anchor-ring. Zenodorus was the author of a treatise on Isometric figures, the problem in which was to compare the content of different figures, plane or solid, having equal contours or surfaces respectively.
Although Euclid knew that an ellipse could be otherwise produced, e. g. as an oblique section of a right cylinder, there is no doubt that he produced all three conics from right cones like his predecessors.
These equations represent, in Cartesian co-ordinates, and with rectangular axes, the conics by the intersection of which two and two Menaechmus solved the problem; in the case of the rectangular hyperbola it was the asymptote-property which he used. We pass to Euclid's times.
Almamoun, by a liberal reward, sought to engage in his service a famous mathematician of Constantinople; and Ibn Korrah enriched the stores of his country in this department with translations of Archimedes and the conics of Apollonius.
I have visited it twice, and I know." "I am glad to learn that you have been up the Congo," replied Randolph Rover. "Perhaps during your leisure hours on the trip you will not mind giving me such information as conics to your mind." "I will tell you all I know willingly," answered Captain Cambion.
The second greatest contribution of the Greeks was the statics and the conics of which Archimedes was the chief creator in the third century B.C. In his work he gave the first sketch of an infinitesimal calculus and in his own way performed an integration. The third invaluable construction was the trigonometry by which Hipparchus for the first time made a scientific astronomy possible.
Normals are treated, not in connexion with tangents, but as minimum or maximum straight lines drawn to the curves from different points or classes of points. Certain propositions of great difficulty enable us to deduce quite easily the Cartesian equations to the evolutes of the three conics. He was also a master of the theory of epicycles and eccentrics.
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