PREFACE.

Commandinus — Some Works of Archimedes in Latin. Venice 1558, folio.

Wallis — Archimedes’ The Sand Reckoner and Measurement of a Circle. Oxford 1678, 8vo. — Works III, p. 509 ff.

Sturm — Archimedes’ Incomparable Books of Art, translated and explained. Nuremberg 1670, folio.

Barrow — Works of Archimedes illustrated and demonstrated by a new method. London 1675, 4to.

Hauber — Archimedes’ On the Sphere and Cylinder and On the Measurement of a Circle, translated with notes. Tübingen 1798, 8vo.

Gutenäcker — Archimedes’ Measurement of a Circle, Greek and German. Würzburg 1828, 8vo.

Nizze — Archimedes’ Extant Works, translated and explained. Stralsund 1824, 4to.

Jena Critic (Jen.) — A learned unknown man, who proposed a critique of the Torelli edition in the Jenaer Litteraturzeitung 1795, No. 172—73, pp. 610—23.

Wurm — Fr. Wurm’s critique of the Gutenäcker edition, Jahn’s Jahrbücher XIV, pp. 175—85.

I have proposed some emendations myself in Quaest. Arch. short for Quaestiones Archimedeae chapter VII and in the edition of The Sand Reckoner appended to that book, some of which I have now rejected, while most I have accepted. I have attempted to correct certain matters in Eutocius in the Neue Jahrbücher für Philologie und Pädagogik, Supplement volume XI, pp. 375—83.

In the Latin translation, which I have written entirely on my own, I have followed this principle above all: that the meaning should appear sufficiently clear everywhere, and that the Archimedean form of expression and method of demonstration should be preserved as much as possible, yet in such a way that, where it could be done, I would express those things which Archimedes had explained in words by the signs which our modern mathematicians use. So that this might be achieved, I was sometimes forced to depart further from the usage of the Latin language, especially in the arrangement of words, and to speak in a style that is less Latin, lest the interpretation be either obscure or deviate too much from the Greek words. In the interpretation of many words, I have followed Hultsch; for instance, with him as a guide, instead of the Greek διπλάσιος double etc., followed by the genitive, I have said: "twice as large as," etc. (Hultsch: Pappus I, p. 59, note 1); but where this form of expression was less suitable, for example for the Greek διπλασίονα λόγον ἔχειν to have a double ratio, I have written: "to have a double ratio to," and similar things (cf. Livy XXXIV, 19, 4; Columella I, 8, 8; Pliny, Natural History XIX, 9; Quintilian II, 3, 3).