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))

72[vii] be met with in the above mentioned Preface of Pappus; where he
tells us that in the ſix Problems of Book I. there were “Sixteen
Epitagmas, or general Caſes, five Determinations; and of theſe,
four were Maxima, and one a minimum: That the maxima are at the
ſecond Epitagma of the ſecond Problem, at the third of the fourth,
the third of the fifth, and the third of the ſixth; but that the minimum
was at the third Epitagma of the third problem. ” It moreover ſeem- ed reaſonable to me, that theſe Problems wherein the feweſt points
are given, would be antecedent to thoſe wherein there were more;
and of theſe wherein the number of given points are the ſame, that
thoſe would be prior to the others, wherein there was a given ex-
ternal line concerned: and laſtly, that when the number of given
points were two, the ſecond Caſe, or Epitagma, would naturally
be when the required point O is ſought between the two given
ones.

Now the three new Problems, together with the three firſt of
Snellius, making exactly ſixteen Epitagmas, viz. one in the firſt,
and three in each of the others; it ſeemed highly probable, that
theſe compoſed the firſt book. Alſo that the Problem, wherein
only one point was given, would be the firſt; and it ſeemed eaſy
to aſſign the ſecond, becauſe it is the only one wherein the limita-
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