A History of Greek Mathematics and Astronomy

Page 20

The main results obtained are (1) that the diameter of the sun is between 18 and 20 times the diameter of the moon, (2) that the diameter of the moon is between 2/45ths and 1/30th of the distance of the centre of the moon from our eye, and (3) that the diameter of the sun is between 19/3rds and 43/6ths of the diameter of the earth. The book contains a good deal of arithmetical calculation.

Archimedes was born about 287 B. C. and was killed at the sack of Syracuse by Marcellus's army in 212 B. C. The stories about him are well known, how he said 'Give me a place to stand on, and I will move the earth' (πα βω και κινω ταν γαν {pa bô kai kinô tan gan}); how, having thought of the solution of the problem of the crown when in the bath, he ran home naked shouting ἑυρηκα, ἑυρηκα {heurêka, heurêka}; and how, the capture of Syracuse having found him intent on a figure drawn on the ground, he said to a Roman soldier who came up, 'Stand away, fellow, from my diagram.' Of his work few people know more than that he invented a tubular screw which is still used for pumping water, and that for a long time he foiled the attacks of the Romans on Syracuse by the mechanical devices and engines which he used against them. But he thought meanly of these things, and his real interest was in pure mathematical speculation; he caused to be engraved on his tomb a representation of a cylinder circumscribing a sphere, with the ratio 3/2 which the cylinder bears to the sphere: from which we infer that he regarded this as his greatest discovery.

Archimedes's works are all original, and are perfect models of mathematical exposition; their wide range will be seen from the list of those which survive: On the Sphere and Cylinder I, II, Measurement of a Circle, On Conoids and Spheroids, On Spirals, On Plane Equilibriums I, II, the Sandreckoner, Quadrature of the Parabola, On Floating Bodies I, II, and lastly the Method (only discovered in 1906). The difficult Cattle-Problem is also attributed to him, and a Liber Assumptorum which has reached us through the Arabic, but which cannot be his in its present form, although some of the propositions in it (notably that about the 'Salinon', salt-cellar, and others about circles inscribed in the αρβηλος {arbêlos}, shoemaker's knife) are quite likely to be of Archimedean origin. Among lost works were the Catoptrica, On Sphere-making, and investigations into polyhedra, including thirteen semi-regular solids, the discovery of which is attributed by Pappus to Archimedes.

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T. L. Heath
A History of Greek Mathematics and Astronomy

Learned Freeware

T. L. Heath A History of Greek Mathematics and Astronomy

Learned Freeware

T. L. Heath
A History of Greek Mathematics and Astronomy