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))

13

PROBLEMS
CONCERNING
TANGENCIES.

PROBLEM I.

THROUGH two given points A and B to deſcribe a circle whoſe radius
ſhall be equal to a given line Z.

Limitation. 2 Z muſt not be leſs than the diſtance of the points A and B.

Construction. With the centers A and B, and diſtance Z, deſcribe two
arcs cutting or touching one another in the point E, ( which they will neceſſarily
do by the Limitation ) and E will be the center of the circle required.

PROBLEM II.

Having two right lines AB CD given in poſition, it is required to draw 2
circle, whoſe Radius ſhall be equal to the given line Z, which ſhall alſo touch
both the given lines.

Case 1ſt. Suppoſe AB and CD to be parallel.

Limitation. 2Z muſt be equal to the diſtance of the parallels, and the
conſtruction is evident.

Case 2d. Suppoſe AB and CD to be inclined to each other, let them be
produced till they meet in E, and let the angle BED be biſected by EH, and
through E draw EF perpendicular to ED, and equal to the given line Z; through
F draw FG parallel to EH, meeting ED in G, and through G draw GH paral-
lel to EF. I ſay that the circle deſcribed with H center, and HG radius,
touches the two given lines: it touches CD, becauſe EFGH is a

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