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nomenon Genuina Rationes Investigantur et Exponuntur; 4to, 1669, London. We are informed in the preface that Mr. Isaac Newton revised the copy, suggested several corrections, and made some additions of his own. An account of this book may be found in the Philosophical Transactions, No. 75, p. 2258, for September, 1671.
4. Lectiones Geometrica 13, in quibus Præsertim Generalia Linearum Curvarum Symptomata Declarantur, 4to. 1670, London. An account of this book is inserted in the abovementioned Transaction, p. 2260; with an addition of some Corollaries, communicated by the author belonging to the second problem of his Third Appendix to the Twelfth Lecture. These lectures were first printed separately from the former upon optics; but afterwards, in the years 1672 and 1674, were published with them, though without the Corollaries just mentioned; whence it is probable they were not reprinted, but had only a new title-page prefixed.
5. Archimedis Opera, Apollonii Conicorum Libri Quatuor; Theodosii Sparica, Methodo novo illustrata, et succincte demonstrata, 4to, 1675, London. In the preface to this book,
we are told, that the Lemmata of Archimedes contained in it, now appear in Latin from two translations; the one by the learned John Gravius, published in 1659, with some animadversions by Mr. Samuel Foster, professor of astronomy at Gresham College; the other by Abraham Ecchellensis, published at Florence, with notes by the celebrated mathematician Alphonsus Borellus. An account of this work may be seen in the Philosophical Transactions, No. 114, p. 314, May, 1675. And the copy of all the books of Archimedes published in it, except the second book, De Equiponderantibus, the two books De Insidentibus Humido, the Lemmata, and the book, De Arena Numero, written in Dr. Barrow's own hand, in one octavo volume, and the four books of Apollonius in another volume in quarto, are reposited in the royal society.
His posthumous works in Latin were the following:
1. Lectio in quâ Theoremata Archimedis de Sphæra et Cylindro, per Methodum Indivisibilium investigata, ac breviter demonstrata exhibentur, 12mo. 1678, London. This book, however, was written in English; but so:ne time after the author's death, was translated
into Latin, and subjoined to the editions of Euclid's Elementa and Data.
2. Mathematica Lectiones Habite in Scholis Publicis Academia Cantabrigiensis, 1664-5-6, London, 1683, 8vo. These were a part of his Lucasian Lectures; to which the editor, Mr. Wells, has prefixed the author's Oratio Præfatoria, delivered at the opening of them.
3. His English works, which are also posthumous, were published in 1685, in three volumes folio, by Dr. Tillotson, then dean, and afterwards archbishop of Canterbury. There' were several subsequent editions, of which the last was in 1741. I shall not pretend to give a particular account of these works, which consist for the most part of sermons, but only observe, that for the learning and good sense which pervade them, they have preserved their repute even to modern times.
4. There is a fourth volume however of Barrow's works, printed after the foregoing, in 1687, folio, London. The contents of this volume are partly in Latin and partly in English. The title is, Isaaci Barrow, S.S.T. Professoris Opuscula, viz. Determinationes, Conciones ad Clerum Poemata, &c. volumen quartum. The Dissertatiuncula de Sestertio, p.356,
was reprinted the same year in the Philosophical Transactions, No. 190, p. 383.
5. There are two letters written by Dr. Barrow to Mr. Willoughby, printed in the Philosophical Letters between Mr. Ray and his correspondents, p. 360, 362, upon the following subjects. The former, dated March 26, 1662, contains "the method whereby Mons. Robervell was said to have demonstrated the equality of a spiral line with a parabola." In this letter he signifies his intention of reading lectures upon Archimedes' De Equiponderantibus; whether he afterwards put this design in execution is uncertain. In the latter, dated October 5, 1665, he approves Mr. Willoughby's "Discourse, inferring the Solidity of the Sphere from the Surface, by comparing the Concentrical Surfaces of the Sphere, with the Parallel Arches of the Cone," and informs him of his own method of doing it.
In addition to the foregoing works, there are several curious papers of Dr. Barrow, written. in his own hand, and communicated by William Jones, esq. to the author of the Lives of the Professors of Gresham College.
1. A Latin volume in quarto, in which are contained, 1. Compendium pro Tangentibus.
2. Equationum Constructio per Conicas Sectiones. 3. Equationum Constructio Geome trica. 4. Additamenta' de Curvis. These tracts appear to have been written before his Geometrical Lectures.
2. Theorema Generale ad Lineis Curvis Tangentes, et Curvarum Figurarum Areas, per Motum Determinandas.
3. Letters to Mr. John Collins, upon va rious mathematical subjects; viz. 1. Concerning Parabolical Conoids; without date. 2. Rectifying a Mistake of Mr. Collins, concerning the Parallel Sections of the Cubical Parabolical Conoid; without date. 3. Rules to compute the Portions of a Sphere or Spheroid. Sept. 5, 1664.
4. A Character of Mengólus's Elementa Geometria Speciosa, with whom he is displeased for his affectation of new definitions, and uncouth terms. Nov. 12, 1664.
5. He thanks him for a catalogue of mathematical books, which he sent him; gives a character of Alsted's Admiranda Mathematica, which he thinks a work of no great importance. Nov. 29, 1664.
6. Concerning a parallel to the Axis. Jan. 9, 1665.
Parabolical Conoid cut