Thomas Little Heath

“ Halley added in his edition (1710) a restoration of Book viii., in which he was guided by the fact that Pappus gives lemmas “to the seventh and eighth books” under that one heading, as well as by the statement of Apollonius himself that the use of the seventh book was illustrated by the problems solved in the eighth.
The degree of originality of the Conics can best be judged from Apollonius’ own prefaces. Books i.-iv. form an “elementary introduction,” i.e. contain the essential principles; the rest are specialized investigations in particular directions. ”

“ No blame attaches to the Roman general, Marcellus, since he had given orders to his men to spare the house and person of the sage; and in the midst of his triumph he lamented the death of so illustrious a person, directed an honourable burial to be given him, and befriended his surviving relatives. ”

“ It is clearly the form of the fundamental property (expressed in the terminology of the “application of areas”) which led him to call the curves for the first time by the names parabola, ellipse, hyperbola. ”

“ Alexander became at Rome one of the most celebrated medical men of his time; Olympius was deeply versed in Roman jurisprudence; and Metrodorus was one of the distinguished grammarians of the great Eastern capital. It is related of Anthemius that, having a quarrel with his next-door neighbour Zeno, he annoyed him in two ways. First, he made a number of leathern tubes the ends of which he contrived to fix among the joists and flooring of a fine upper-room in which Zeno entertained his friends, and then subjected it to a miniature earthquake by sending steam through the tubes. ”

“ Arenarius, or sand reckoner) , a small treatise, addressed to Gelo, the eldest son of Hiero, expounding, as applied to reckoning the number of grains of sand that could be contained in a sphere of the size of our “universe,” a system of naming large numbers according to “orders” and “periods” which would enable any number to be expressed up to that which we should write with 1 followed by 80,000 ciphers!
(9) A Collection of Lemmas, consisting of fifteen propositions in plane geometry. This has come down to us through a Latin version of an Arabic manuscript ”

“ Given two, three or four points on a straight line, to find another point on it such that its distances from the given points satisfy the condition that the square on one or the rectangle contained by two has to the square on the remaining one or the rectangle contained by the remaining two, or to the rectangle contained by the remaining one and another given straight line, a given ratio. ”

“ Praemittitur, &c., Opera et Studio Edmundi Halley (Oxoniae, 1706) , 4to; (5) a German translation of the Conics by H. Balsam (Berlin, 1861) ; (6) the definitive Greek text of Heiberg (Apollonii Pergaei quae Graece exstant Opera, Leipzig, 1891–1893) ; (7) T. L. Heath, Apollonius, Treatise on Conic Sections (Cambridge, 1896) ”

“ The second book is in nine propositions, eight of which deal with segments of spheres and include the problems of cutting a given sphere by a plane so that (a) the surfaces, (b) the volumes, of the segments are in a given ratio (Props. 3, 4) , and of constructing a segment of a sphere similar to one given segment and having (a) its volume, (b) its surface, equal to that of another (5, 6) .
(2) The Measurement of the Circle (Κύκλου μέτρησις) is a short book of three propositions, the main result being obtained in Prop. ”