13-i 



CONIC SECTIONS. 



Catalogue 

 ©f works 

 »n conic 



ections. 



In explaining the nature and properties of geome- 

 trical figures, it becomes a question how they are to be 

 defined. A figure may be defined from any one of its 

 properties, which distinguishes it from all other figures 

 of a different kind ; but that o\ight to be chosen which 

 is simple, 'which shews how the figure may be readily 

 constructed, and which naturally leads to its other pro- 

 perties. The ancients defined the class of curves we 

 are about to consider, by supposing a cone to be cut by 

 * plane ; and their example has been followed by seve- 

 ral modern writers, who have, upon this principle, 

 composed elaborate and valuable treatises. As the doc- 

 trine of solids is, however, a more intricate branch of 

 geometry than that of plane figures, other modern wri- 

 ters, of whom Dr Wallis was the first, have thought 

 it better to define the curves, by shewing how they 

 may be described on a plane, without any refei'ence to 

 a cone ; and treatises not less valuable, and (in our opi- 

 nion) in some respects more simple, have been written 

 on this plan. We propose to follow this second me- 

 thod, believing it to be the best adapted to our work. 



If our system of Geometry were written, we should 

 'refer to it as often as we had occasion to quote a propo- 

 sition in the elements of geometry; as, however, from 

 our mode of publication, that article is not yet ready, 

 we shall, in the mean time, refer to the propositions in 

 Euclid's Elements of Geometry, as contained in Mr Pro- 

 fessor Playfair's edition: and in our article Geometry 

 give a table shewing to what proposition, there, each of 

 Euclid's corresponds. 



We shall conclude this Introduction with a catalogue 

 of some of the more curious and valuable works on this 

 branch of geometry. 



Among the works of Archimedes which have been 

 preserved, there is a treatise, On the Quadrature of the 

 Parabola, and another On Conoids and Spheroids. See 

 Barrow's edition, London, 1675 ; or Torelli's edition in 

 Greek and Latin, Oxford, 1792 ; or Peyrard's French 

 translation of Archimedes' works, Paris, 1808. 



Apollonii Pergcei Conicorum libri octo, et Sereni An- 

 tissensis de Sectione Cyllnclri et Coni libri duo. This is 

 Dr Halley's edition. The first four books, together 

 with the Lemmata of Pappus, and the commentaries of 

 Eutocius, have been published from Greek manuscripts, 

 accompanied with a Latin translation; the 5th, 6th, 

 and 7th books, which also contain the Lemmata, have 

 been translated from Arabic into Latin ; the eighth has 

 been restored by Dr Halley. The books of Serenus are 

 in Greek and Latin. 



Collectiones Mathematical Pappi Alerandrini, lib. vii. 

 Bononia?, 1660. Hei*e some account of Apollonius' Co- 

 nies, and the Lemmata, is given. 



Emend atio et Restitutio Conicorum Apollonii Pergcei, 

 authore Francisco Maurolyco. Colonias, 1675. 



Apollonii Pergwi Conicorum lib. v. vi. vii. Paraphrasle 

 Abalpliato Asphahnensi ex Arabico in Latinum per Abra- 

 ham Ecchellensem Maronitam redditi, cum notis J. Al- 

 fonsi Borelli. Florentini, 1661. 



Apollonii Pcrg. Con. Sect. Lib. v. vi. vii. in Grecia 

 deperdita, jam vero ex Arabico MS. ante quadringenlos 

 annos elaborala opera subitanea Latinitate donati a Chris- 

 tiano Ravio. Upsal, I669. 



De Maximis et Minimis, Geomelrica Divinatione in 

 Quinlum Conicorum Apollonii Pergcei adhuc desidera- 

 tum, autore Vincentio Viviani. Florence, 1659. 



De Locis Solidis, Secunda Divinatio Geometrica in 



Juinque libros injuria temporum umissos Arisicei Senioris 

 •.eometrge. Aut. Vin. Viviani, &c. Ojaus C'ofiicoruvi, 



continens Elemenla Tracialuum ejusdem Viviani. 

 rence, 1701. 



Apollonius Cattus, a work on Conies in German, by 

 Benjamin Bramer, printed 1634. 



Claudii Mydorgii Patricii Parisini Prodromi Catop- 

 tricorum e£ Dioptricorum .- Sive Conicorum Operis ad 

 abdila radii refiexii et refracli mysteria prcevii et facem 

 praferentis. Libri iv. priores Parisiis, 1641. 



Erancisci a Schootcn Leydensis de organica ennicarum 

 seclionutn in piano descriptione. Lugd. Batavor. 1646. 



.?. Gregorii a Sto. Vincentio Opus Geomelricum Qua- 

 drature Circuit et Sectionum Coni decern libris compre- 

 hensum. Antwerpiae, 1647. 



Johannis Wallisii De Sectionibus Conicis nova mei\o- 

 do expositis traclatus. Oxonii, 1655. 



Joannis De Witt Elementa Curvarum Linearv.m per 

 Frattcisum Schooten edifa cum Cartesii Geomciria. Am- 

 sterdami, 1659 et 166l. 



Euclidus Audactus et Methodicus Mathematicaque U- 

 nioer salts. Authori Guarino Angustae, Taurin. 1671. 



Nouvelle methode en geometrie pour les sections lies su- 

 perficies coniqucs et cylindriques qui out pour base, des 

 circles, on des parabolcs, des ellipses et des hyperboles ; 

 par Ph. de la Hire. Paris, 1673. 



Nouveaux elemens des sections coniques, &c. par M. de 

 la Hire. Paris, 1679. 



Sectiones conicce in ix. libr. distributee, &c. Aut. Phil, 

 de la Hire. Paris, 1685. 



Sectionum conicarum elementa jiova methodo demon- 

 strata. Autore Jacobo Milnes. Oxonia 1 , 1702. 



Traite Analytiques des sections coniques it de leur 

 usage, &c. Ouvrage Posthume de M. le Marquis de 

 l'Hospital. Paris, 1707. 



Compendio delle Sczzioni Coniche d'Apollonio di P. 

 Guido Grando, Florent. 1722. 



Delle Sezzioni Coniche dedotte movamente in Piano did" 

 cerchio di Vincent Santini. Luca, 1722. 



Sectionum Conicarum elementa methodo facillime ds- 

 monsirata. Autore L. Trevegar, Cantabriga; 1731. 



A Treatise on Conic Sections, by R. Steel. Dublin, 

 1723. 



Elementa Sectionum Conicarum. Autore Nicolas de 

 Martino. Tomii II. Neapoli 1734. 



Elements of Conic Sections, in three books, by R. 

 Jack. Edinburgh, 1742. 



A' Mathematical Treatise, containing a system of Co- 

 nic Sections, &c. by J. Muller. London, 1736. 



Sectionum Conicarum Elementa. Autore Josepho 

 Boscovich. This treatise forms a part of his Elementa 

 Universe Matheseos. Roma?, 1754. 



De Sectionibus Conicis, traclatus geomeiricus, in quo 

 ex nalura ipsius Cono Sectionum qffecliones facillime de- 

 ducuntur methodo nova. Autore Hugene Hamilton. Dub- 

 lin, 1758. There is an English translation of this excel- 

 lent work. 



Sectionum Conicarum libri quinque. Auctore R. Sim- 

 eon. Edinburgh 1750. 



Antonii Rochii Conicarum Sectionum nova methodo 

 expositurum specimen de proporiionum cornpositione syn- 

 tagma. Patavii, 1756. 



Introduction aux Sections Coniques, par M. Mauduife 

 Paris, 1761. 



Sectionum Conicarum -Compendium. Autore D. Oc- 

 taviano Cametti. Venetiis, 1765. 



The Elements of the Conic Sections, in three booksj 

 by W. Emerson. London, 1767- 



The Elements of the Conic Sections, as preparatory 

 to the reading of Newton's Principia, by the Rev. §• 

 Vince. Cambridge., 178I. 



