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))

138[ii]

N. B. Between each of the Data a full ſtop is placed. Moreover, m and n are
ſometimes uſed for different ſegments than thoſe of B by P, but then it is ſignified in
words: - the ſame alſo is to be obſeved of P.

Obſerve likewiſe, for the more ready finding any propoſed Problem in the Synop-
ſis, that the data are ranged in the ſame order as the Symbols here recited; viz.
all data whereof V is one are placed firſt; next thoſe where B is given, either ſim-
ply by itſelf, or combined with any other datum; next P, & c.

Moreover, when in the references you find this mark*, it ſignifies that ſuch Authors
have only conſtructed the Problem partially, and not generally as propoſed in the Synop-
ſis, e. g. for a right-angled triangle, when it is propoſed for a triangle in general;
and again, for a line biſecting another, when it is propoſed to cut it ſo that the ſeg-
ments may be in any given ratio.

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