Apollonius <Pergaeus>; Lawson, John - The two books of Apollonius Pergaeus, concerning tangencies, as they have been restored by Franciscus Vieta and Marinus Ghetaldus : with a supplement to which is now added, a second supplement, being Mons. Fermat's Treatise on spherical tangencies

Apollonius <Pergaeus>; Lawson, John, The two books of Apollonius Pergaeus, concerning tangencies, as they have been restored by Franciscus Vieta and Marinus Ghetaldus : with a supplement to which is now added, a second supplement, being Mons. Fermat's Treatise on spherical tangencies

Table of contents

[Item 1.]

[2.] THE TWO BOOKS OF APOLLONIUS PERGÆUS, CONCERNING TANGENCIES, As they have been Reſtored by FRANCISCUSVIET A and MARINUSGHETALDUS. WITH A SUPPLEMENT.

[3.] THE SECOND EDITION. TO WHICH IS NOW ADDED, A SECOND SUPPLEMENT, BEING Monſ. FERMAT’S Treatiſe on Spherical Tangencies. LONDON: Printed by G. BIGG, Succeſſor to D. LEACH. And ſold by B. White, in Fleet-Street; L. Davis, in Holborne, J. Nourse, in the Strand; and T. Payne, near the Mews-Gate. MDCCLXXI.

[4.] PREFACE.

Page: 7 ((iii))

[5.] EXTRACT from PAPPUS’s Preſace to his Seventh Book in Dr. HALLEY’s Tranſlation. DE TACTIONIBUS II.

[6.] Synopsis of the PROBLEMS.

Page: 11 ((vii))

[7.] PROBLEMS CONCERNING TANGENCIES. PROBLEM I.

[8.] PROBLEM II.

[9.] PROBLEM III.

[10.] The GENERAL Solution.

[11.] PROBLEM IV.

[12.] PROBLEM V.

[13.] The general Solution.

[14.] PROBLEM VI.

[15.] The general Solution.

[16.] PROBLEM VII.

[17.] LEMMA I.

[18.] PROBLEM VIII.

[19.] Mr. Simpſon conſtructs the Problem thus.

[20.] PROBLEM IX.

[21.] LEMMA II.

[22.] LEMMA III.

[23.] PROBLEM X.

[24.] PROBLEM XI.

[25.] PROBLEM XII .

Page: 22 ((10))

[26.] LEMMA IV.

Page: 23 ((11))

[27.] LEMMA V.

Page: 23 ((11))

[28.] PROBLEM XIII.

Page: 23 ((11))

[29.] PROBLEM XIV.

Page: 24 ((12))

[30.] SUPPLEMENT. PROBLEM I.

Page: 26 ((14))

7(iii)

OF the twelve Analytical Treatiſes recited by Pappus in
his Preface to the 7th Book of his Mathematical Col-
lections, we have very little of the Originals remaining, viz.
only Euclid’s Data, and part of Apollonius’s Conics. The
loſs of the reſt is very much to be lamented by all Lovers of
the Mathematics. “ Valde quidem dolendum eſt quod re-
liqui tractatus Veterum Analytici, a Pappo memorati,
aut perierint, aut nondum lucem conſpexerint. Nam
minime dubito quin eorum nonnulli, Arabicè ſaltem
verſi, alicubi terrarum lateant, pulvere magis quam tene-
bris ſuis involuti. ” Dr. Halley’s Preface to his Apol-
LONIUS DE Sectione Rationis et Spatii.

Some ingenious men have attempted, from the account of
them given by Pappus, to reſtore ſome of theſe loſt Trea-
tiſes. Snellius has endeavoured to give us the Books De
Sectione Rationis, De Sectione Spatii, and De Sec-
TIONE Determinata. Fermat and Schooten have laboured
in the Treatiſe De Locis Planis; and Marinus Ghetaldus
in that De Inclinationibus. But thoſe who have ſuc-
ceeded beſt, and done the moſt this way, are two

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