ARITHMETIC OF SINES, CONIC SECTIONS, CURVES, DIAL LING, EPICYCLOID, and other branches of mathematics that are to follow the present article ; also the biographical ac counts of mathematicians contained in our work. We shall now give a select catalogue of the principal works which have been written on geometry, particularly those which exhibit the progress of its improvement. Such as relate to conics have been already enumerated in CONIC SECTIONS, and those that treat of TRIGONOMETRY will be indicated in that article.
On the history of geometry, consult Montucla, Hiatoire de illathematiques, (2d edit.) Bossut's General History of Mathematics in French, of which there is an English trans lation, and Dr Hutton's Dictionary, (2d edit. 1815.) Euclid, The Elements of Geometry. Of this there are very many editions; the first is that of Ratdolt, 1482. There is an elegant Greek and Latin edition of his works by Dr Gregory, Oxford 1703. Perhaps the most valuable is that of Peyrard, in Greek, Latin, and French, of which the first six books are now published. Dr Barrow's edition of all the books, and the Data, and Dr Horsley's of the first 12, from the Latin versions of Commandine and Gregory, and the Data, are valuable. Simson's edition of the first six, and the llth and 12th books, and the Data; and Playfair's edi tion, the first six, (the same as Simson's) and three addi tional books en solids, are most commonly used.
Euclid's Porisms have been restored by Dr Simson in his Opera Reliqua, 1776.
Archimedes ; the best editions are Torelli's in Greek and Latin, Oxford, 1792 ; and Peyrard's French translation, Paris, 1808. The first edition of the Greek text was that of Venatorius, in 1544.
Apollonius ; the writings that have been recovered of this celebrated geometer are : 1. The Section of a Ratio; and, 2. The Section of a Space. These have been restored by Snellius, 1607; and by Dr Halley, 1706.
3. Determinate Section ; Snellius restored these in his Apollonius Batavus, 1601. There is an English transla
tion by Lawson, to which is added a new restoration by Wales, 1772. Simson has restored this work in his Ope ra Reliqua, 1776; and Gianinni, an Italian geometer, in 1773.
4 Tangencies ; Vieta restored this in his Attollonius Gallus, 1600. Some additions were made by Ghetaldus, and others by Alexander Anderson, in 1612. The labours of Vieta and Ghetaldus have been given in English by Law son, 1771.
5. The Plane Loci; these have been restored by Schoo ten, 1656; and Fermat, 1679 ; but the best restoration is that of Dr Simson, 1749.
6. The Inclinations ; these were restored by Ghetaldus, in his Apollonius Redivivus, 1607 : To this there is a Sup plement by Anderson, 1612. There is also a restoration by Dr Horsley, 1770 ; and another by Reuben Burrow, 1779.
Theodosius and Menelaus : These were published by Maurolicus in 1558, and Burrow gave Theodosius in 1675. There is also an Oxford edition by Hunter, in 1707.
Proclus, Commentarlorum in librum Li bri iv. Latine vertit F. Baroccius, 1560. Proclus has also been given in English by Taylor, 1788.
Eratosthenes, Geometria, E.g'c. cunt afloat. 1672.
Veterurn Mathematicoritm Athenzei, Bitonis, Apollodori, Heronis, Philonis, et alioruni, Opera Gr. et Lat. 1693. Lucas de Burgo, Sumizza de A•ithnzetica, Geometria, &c.
Albert Durer, Institutiones Geonzarice, 1532.
Buteo, De Quadratura Circuli. 1559.
Ramus, .4rithmeticx, lib. ii. Geonietrice, lib. xxvi. 1580. Vieta, Opera Mathematica, 1589.
Vieta, Variorum. de reb math. responsorunz, lib. viii. 1596. Lucas Valerius, De centro Gravitatis Solidorunz, 1604. Metius, Arithmet. et Geomet. pract. 1611.
Anderson, Supplementurn Apollonii Redivivi, 1612.
ArrizzAeryza Pro Zetetico Apolloniani p•oblema as a se jam pridenz edito in Sup. Apol. Red. 1615.
- Theorenzata Ka00Azzol-qa A. Fr. Vieta Fonte racensi excogitata, Sic. 1615.
Anderson, Vindicicc Archinzalis, Sic. 1616.
Exer. Mathcnzat. 8cC. 1619.
Kepler, Nova S'terconzetria, Sc. 1618.