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))

74[ix] miſtake muſt be admitted in this Author, or the fifth Problem is
wrong placed. I am not prepared farther to obviate theſe objec-
tions, and only mention them to ſhew that although I ſaw them
in their full force, I could by no means agree, that they are pow-
erful enough to overturn thoſe already advanced for what I have
11[Handwritten note 1]22[Handwritten note 2]done.

I come now to Book II, which if I am not much miſtaken, was
entirely employed about what Snellius makes his fourth Problem.
In this I am confirmed not only by the account which Pappus gives
in his Preface, but much more by the Lemmas of Apollonius
11[Handwritten note 1]22[Handwritten note 2] which he hath left us. For we there find that Lemma 21, where-
in is aſſigned the leaſt ratio which the rectangle contained by AO
and UO can bear to that contained by EO and IO, when O is ſought
between the two mean points of the four given ones, is ſaid to be
concerned in determining the μοναχὴ, or ſingle Caſe , of Problem 1. This Problem therefore of Apollonius contained only thoſe
Caſes of the general one, where O is ſought between the two mean
points. In like manner, we gather from Lemma 22, that his ſe-
cond Problem was concerned in determining the point O when ſought
between a mean point, and an extreme one. And laſtly, from
Lemma 24, that the third Problem of Book II. determined
the point O when required without all the given ones.
1

Text layer

Text normalization

Search