By Sir Thomas Heath
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Extra resources for A History of Greek Mathematics, Vol. 1: From Thales to Euclid
C. (α) The quadratrix of Hippias (β) The spiral of Archimedes (γ) Solutions by Apollonius and Carpus (δ) Approximations to the value of π The trisection of any angle (α) Reduction to a certain νσις, solved by conics (β) The νσις equivalent to a cubic equation (γ) The conchoids of Nicomedes (δ) Another reduction to a νσις (Archimedes) () Direct solutions by means of conics (Pappus) The duplication of the cube, or the problem of the two mean proportionals (α) History of the problem (β) Archytas (γ) Eudoxus (δ) Menaechmus () The solution attributed to Plato (ζ) Eratosthenes (η) Nicomedes (θ) Apollonius, Heron, Philon of Byzantium (ι) Diocles and the cissoid (κ) Sporus and Pappus (λ) Approximation to a solution by plane methods only VIII.
32 Canonic is the theory of the musical intervals as expounded in works like Euclid’s κατατομὴ κανόνος, Division of the canon. 33 (1) The first is Optics proper, the business of which is to explain why things appear to be of different sizes or different shapes according to the way in which they are placed and the distances at which they are seen. Euclid’s Optics consists mainly of propositions of this kind; a circle seen edgewise looks like a straight line (Prop. 22), a cylinder seen by one eye appears less than half a cylinder (Prop.
In Plato’s curriculum for the education of statesmen the same subjects, with the addition of stereometry or solid geometry, appear, arithmetic first, then geometry, followed by solid geometry, astronomy, and lastly harmonics. The mention of stereometry as an independent subject is Plato’s own idea; it was, however, merely a formal addition to the curriculum, for of course solid problems had been investigated earlier, as a part of geometry, by the Pythagoreans, Democritus and others. Plato’s reason for the interpolation was partly logical.
A History of Greek Mathematics, Vol. 1: From Thales to Euclid by Sir Thomas Heath