By Sir Thomas Heath
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Extra resources for A History of Greek Mathematics, Vol. 1: From Thales to Euclid
C. Cyrene, on the Libyan coast, was founded in the last third of the seventh century. , made settlements on the east coast of the Black Sea (Sinope was founded in 785); the first Greek settlements in Sicily were made from Euboea and Corinth soon after the middle of the eighth century (Syracuse 734). ), and many Greeks had settled in that country. The free communications thus existing with the whole of the known world enabled complete information to be collected with regard to the different conditions, customs and beliefs prevailing in the various countries and races; and, in particular, the Ionian Greeks had the inestimable advantage of being in contact, directly and indirectly, with two ancient civilizations, the Babylonian and the Egyptian.
Several of them are problems of dividing a number of apples or nuts among a certain number of persons; others deal with the weights of bowls, or of statues and their pedestals, and the like; as a rule, they involve the solution of simple equations with one unknown, or easy simultaneous equations with two unknowns; two are indeterminate equations of the first degree to be solved in positive integers. C. The cattle-problem attributed to Archimedes is of course a much more difficult problem, involving the solution of a ‘Pellian’ equation in numbers of altogether impracticable size.
34), but if the joining line is neither perpendicular to the plane of the circle nor equal to its radius, diameters with which it makes unequal angles will appear unequal (Prop. 35); if a visible object remains stationary, there exists a locus such that, if the eye is placed at any point on it, the object appears to be of the same size for every position of the eye (Prop. 38). (2) The second branch is Catoptric, or the theory of mirrors, exemplified by the Catoptrica of Heron, which contains, e.
A History of Greek Mathematics, Vol. 1: From Thales to Euclid by Sir Thomas Heath