Thomas Little Heath

“ A Latin version of the complete work, with ancient scholia and figures, was given by Joseph Auria (Rome, 1591, 4to) . Pappus has given a pretty full commentary on the first book of this work of Theodosius. His work περὶ οἰκήσεων (On Habitations) also was published by Auria (Rome, 1588) . It gives an account of how, for every inhabitant of the earth from the equator to the pole, the starry firmament presents itself in the course of a year. ”

“ It is in this book that Hero proves the expression for the area of a triangle in terms of its sides. The Pneumatica in two books is also extant in Greek as is also the Automatopoietica. In the former will be found such things as siphons, “Hero’s fountain,” “penny-in-the-slot” machines, a fire-engine, a water-organ, and arrangements employing the force of steam. Pappus quotes from three books of Mechanics and from a work called Barulcus, both by Hero. The three books on Mechanics survive in an Arabic translation which, however, bears a title “On the lifting of heavy objects.” ”

“ If about two fixed points P, Q we make turn two straight lines meeting on a given straight line L, and if one of them cut off a segment AM from a fixed straight line AX, given in position, we can determine another fixed straight line BY, and a point B fixed on it, such that the segment BM' made by the second moving line on this second fixed line measured from B has a given ratio λ to the first segment AM. The rest of the enunciation's given by Pappus are incomplete, and he merely says that he gives thirty-eight lemmas for the three books of porisms ”

“ Playfair remarked that the careful investigation of all possible particular cases of a proposition would show that (1) under certain conditions a problem becomes impossible; (2) under certain other conditions, indeterminate or capable of an infinite number of solutions. These cases could be enunciated separately, were in a manner intermediate between theorems and problems, and were called “porisms.” ”

“ A locus (says Simson) is a species of porism. Then follows a Latin translation of Pappus's note on the porisms, and the propositions which form the bulk of the treatise. These are Pappus's thirty-eight lemmas relating to the porisms, ten cases of the proposition concerning four straight lines, twenty-nine porisms, two problems in illustration and some preliminary lemmas. ”

“ The Mechanics was first published by Carra de Vaux in the Journal asiatique (ix. série, ii., 1893) . In 1899 began the publication in Teubner’s series of Heronis Alexandrini opera quae supersunt omnia. Vol. i. and Supplement (by W. Schmidt) contains the Pneumatica and Automata, the fragment on Water Clocks, the De ingeniis spiritualibus of Philon of Byzantium and extracts on Pneumatics by Vitruvius. ”

“ Akin to the geometrical works is that On the Dioptra, a remarkable book on land-surveying, so called from the instrument described in it, which was used for the same purposes as the modern theodolite. ”

“ Theodosii Tripolitae, Sphaericorum, libri iii.; Euclidis, Data, Optica, Catoptrica, ac Phaenomena; Theodosii Tripolitae, De Hobitationibus et Noctibus ac Diebus, libri ii.; Autolyci Pitanaei, De Sphaera Mota, et libri ii. ”