Ancient Philosophers.
Thales was the first we know of who predicted eclipses. He pointed out the advantages that must arise from a due observation of the little bear or polar star; and taught that the earth was round, and the ecliptic in an oblique position.
Pytheas also, by accurate observations at Marseilles, more than 300 years before Christ, determined the obliquity of the ecliptic, by means of the solstitial shadow of the sun upon a dial. He found the height of the gnomon was to the length of the shadow as 600 to 2131⁄8; whence he concluded, that the obliquity of the ecliptic was 23° 49′. When Gassendi was at Marseilles with the celebrated Peiresc, he reiterated the experiment, and found it very just.
Thales went to the Egyptians to be instructed in geometry, and himself instructed them in that science. He showed them how to measure the pyramids by the length of their shades, and to determine the measure of inaccessible heights and distances, by the proportion of the sides of a triangle. He demonstrated the various properties of the circle; he discovered, respecting the isosceles triangle, that the angles at its base were equal; and he was the first who found, that in right lines cutting one another, the opposite angles are equal.
Anaximander, the successor of Thales, was the inventor of the armillary sphere, and of sun-horologes, or dials; he was likewise the first who drew a geographical map.
Pythagoras was the first who gave sure and fundamental precepts in music. Struck by the difference of sounds which issued from the hammers of a forge, but came into unison at the fourth, and fifth, and eighth percussions, he conjectured that this must proceed from the difference of weight in the hammers; he weighed them, and found he had conjectured right. Upon this he wound up some musical strings, in number equal to the hammers, and of a length proportioned to their weight; and found, that at the same intervals, they corresponded with the hammers in sound. Upon this principle he devised the monochord; an instrument of one string, capable of determining the various relations of sound. He also made many fine discoveries in geometry.
Plato by his studies in mathematics was enabled to devise the analytic method, or that geometric analysis, which enables us to find the truth we are in quest of, out of the proposition itself which we want to resolve. He it was who at length solved the famous problem, respecting the duplication of the cube. To him also is ascribed the solution of the problem concerning the trisection of an angle; and the discovery of conic sections.
Hipparchus discovered the elements of plane and spherical trigonometry.
Diophantes, who lived 360 years before Jesus Christ, was the inventor of algebra. It was from this science that the ancients drew those long and difficult demonstrations which we meet with in their works. They are presumed to have aimed at concealing a method which furnished them with so many beautiful and difficult demonstrations; and to have preferred the proving of their propositions by reasonings ad absurdum, rather than hazard the disclosure of the means by which they arrived more directly at the result of what they demonstrated. We meet with strong traces of algebra in the 13th book of Euclid. From the time of Diophantes, algebra made but small progress, till that of Vietus, who restored and perfected it, and was the first who marked the known quantities by the letters of the alphabet. Descartes afterwards applied it to geometry.
Aristarchus was the first who suggested a method of measuring the distance of the sun from the earth, by means of the half section of the moon’s disk, or that phasis of it wherein it appears to us when it is in its quadratures.