Apollonius

, of Perga, a city in Pamphilia, was a celebrated geometrician who flourished in the reign of Ptolemy Euergetes, about 240 years before Christ; being about 60 years after Euclid, and 30 years later than Archimedes. He studied a long time in Alexandria under the disciples of Euclid; and afterwards he composed several curious and ingenious geometrical works, of which only his books of Conic Sections are now extant, and even these not perfect. For it appears from the author’s dedicatory epistle to Eudemus, a geometrician in Pergamus, that this work consisted of eight books; only seven of which however have come down to us.

From the collections of Pappus, and the commentaries of Eutocius, it appears that Apollonius was the author of various pieces in geometry, on account of which he acquired the title of the Great Geometrician. His Conies was the principal of them. Some have thought that Apollonius appropriated the writings and discoveries of Archimedes; Heraclins, who wrote the life of Archimedes, affirms it; though Eutocius endeavours to refute him. Although it should be allowed a groundless supposition, that Archimedes was the first who wrote upon Conies, notwithstanding his treatise on Conies was greatly esteemed; yet it is highly probable that Apollonius would avail himself of the writings of that author, as well as others who had gone before him; and, upon the whole, he is allowed | the honour of explaining a difficult subject better than had been done before; having made several improvements both in Archimedes’s problems, and in Euclid. His work upon Conies was doubtless the most perfect of the kind among the ancients, and in some respects among the moderns also. Before Apollonius, it had been customary, as we are informed by Eutocius, for the writers on Conies to require three different sorts of cones to cut the three different sections from, viz. the parabola from a right angled cone, the ellipse from an acute, and the hyperbola from an obtuse cone; because they always supposed the sections made by a plane cutting the cones to be perpendicular to the side of them: but Apollonius cut his sections all from any one cone, by only varying the inclination or position of the cutting plane; an improvement that has been followed by all other authors since his time. But that Aiv chimedes was acquainted with the same manner of cutting any cone, is sufficiently proved, against Eutocius, Pappus, and others, by Guido Ubaldus, in the beginning of his commentary on the second book of Archimedes’s Equiponderants, published at Pisa in 1588.

The first four books of Apollonius’s Conies only have come down to us in their original Greek language; but the next three, the fifth, sixth, and seventh, in an Arabic version; and the eighth not at all. These have been commented upon, translated, and published by various authors. Pappus, in his Mathematical Collections, has left some account of his various works, with notes and lemmas upon, them, and particularly on the Conies. And Eutocius wrote a regular elaborate commentary on the propositions of several of the books, of the Conies.

The first four books were badly translated by Joan. Baptista Memmius. But a better translation of these in Latin was made by Commandine, and published at Bononia in 1566. Vossius mentions an edition of the Conies in 1650; the fifth, sixth, and seventh books being recovered by Golius. Claude Richard, professor of mathematics in the imperial college of his order at Madrid, in the year 1632, explained, in his public lectures, the first four books of Apollonius, which were printed at Antwerp in 1655, in folio. And the grand duke Ferdinand the second, and his brother prince Leopold de Medicis, employed a professor of the Oriental languages at Rome to translate the fifth, sixth, and seventh books into Latin. These were published at | Florence in 1661, by Borelli, with his own notes, who also maintains that these books are the genuine production of Apollonius, by many strong authorities, against Mydorgius and others, who suspected that these three books were not the real production of Apollonius.

As to the eighth book, some mention is made of it in a book of Golius’s, where he had written that it had not been translated into Arabic, because it was wanting in the Greek copies, from whence the Arabians translated the others. But the learned Mersenne, in the preface to Apollonius’s Conies, printed in his Synopsis of the mathematics, quotes the Arabic philosopher Aben Nedin for a work of his about the year 400 of Mahomet, in which is part of that eio-hth book, and who asserts that all the books of Apollonius are extant in his language, and even more than are enumerated by Pappus; and Vossius says he has read the same; De Scientiis Mathematicis, p. 55. A neat edition of the first four books in Latin was published by Dr. Barrow, at London 1675, in 4to. A magnificent edition of all the eight books, was published in folio, by Dr. Halley, at Oxford in 1710; together with the lemmas of Pappus, and the commentaries of Eutocius. The first four int Greek and Latin, but the latter four in Latin only, the eighth book being restored by himself.

The other writings of Apollonius, mentioned by Pappus, are, l.The Section of a Ratio, or Proportional Sections, two books. 2. The Section of a Space, in two books. 3. Determinate Section, in two books. 4. The Tangencies, in two books. 5. The Inclinations, in two books. 6. The Plane Loci, in two books. The contents of all these are mentioned by Pappus, and many lemmas are delivered relative to them; but none, or very little of these books themselves, have descended down to the moderns. From the account, however, that has been given of their contents, many restorations have been made of these works, by the modern mathematicians, as follow: viz. Vieta. Apollonius Gallus. The Tangencies, Paris, 1600, in 4to. Snellius, Apollonius Batavus. Determinate Section. Lugd. 1601, 4to. Snellius, Sectio Rationis & Spatii. 1607. Ghetaldus, Apollonius Redivivus. The Inclinations. Venice, 1607, 4to. Ghetaldus, Supplement to the Apollonius Redivivus. Tangencies, 1607. Ghetaldus, Apollonius Redivivus, lib. 2, 1613. Alex. Andersons Supplem. Apol, Redivivi. Inclin, Paris, 1612, 4to. Alex. | Anderson, Pro Zetctico Apolloniani problematis a se jam pridem editio in Supplemento Apollonii Redivivi. Paris, 1615, 4to. Scbooten, Loca Plana restituta. Lug. Bat. 1656. Fermat, Loca Plana, 2 lib. Tolos. 1679, folio. Halley, Apol. de Sectione Itationis libri duo ex Arabico ms. Latine versi duo restituti. Oxon. 1706, 8vo. Simson, Loca Plana, libri duo. Glasg. 1749, 4 to. Simson, Sectio Detenninat. Glasg. 1776, 4to. Horsley, Apol. Inclinat. libri duo. Oxon. 1770, 4to. Lawson, The Tangencies, "in two books, Lond. 1771, 4to. Lawson, Determinate Section, two books. Lond. 1772, 4to. Wales, Determinate Section, two books. Lond. 1772, 4to. Burrow, The Inclinations. Lond. 1779, 4to. ¹