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.
[5.] EXTRACT from PAPPUS’s Preſace to his Seventh Book in Dr. HALLEY’s Tranſlation. DE TACTIONIBUS II.
[6.] Synopsis of the PROBLEMS.
[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 .
[26.] LEMMA IV.
[27.] LEMMA V.
[28.] PROBLEM XIII.
[29.] PROBLEM XIV.
[30.] SUPPLEMENT. PROBLEM I.
< >
page |< < ((v)) of 161 > >|
9(v)
EXTRACT from PAPPUS’s Preſace to his Seventh Book
in
Dr. HALLEY’s Tranſlation.
DE TACTIONIBUS II.
HIS ordine ſubnexi ſunt libri duo DE Tactionibus, in
quibus
plures ineſſe propoſitiones videntur;
ſed & ex
his
unam etiam faciemus, ad hunc modum ſe habentem.
E
punctis
rectis &
circulis, quibuſcunque tribus poſitione
datis
, circulum ducere per ſingula data puncta, qui, ſi fieri
poſſit
, contingat etiam datas lineas.
Ex hac autem ob mul-
titudinem
in Hypotheſibus datorum, tam ſimilium quam diſſi-
milium
GENERUM, fiunt neceſſario decem propoſitiones di-
verſæ
;
quia ex tribus diſſimilibus generibus fiunt diverſæ
triades
inordinatæ numero decem.
Data etenim eſſe poſſunt
vel
tria puncta;
vel tres rectæ; vel duo puncta & recta; vel
duæ
rectæ &
punctum; vel duo puncta & circulus; vel duo
circuli
&
punctum; vel duo circuli & recta; vel punctum,
recta
&
circulus; vel duæ rectæ & circulus; vel tres circuli.
Horum duo quidem prima problemata oſtenduntur in libro
quarto
primorum Elementorum.
Nam per tria data puncta,
quæ
non ſint in linea recta, circulum ducere, idem eſt ac
circa
datum triangulum circumſcribere.
Problema autem in
tribus
datis rectis non parallelis, ſed inter ſe occurrentibus,
idem
eſt ac dato triangulo circulum inſcribere.
Caſus vero
duarum
rectarum parallelarum cum tertiâ occurrente,

Text layer

  • Dictionary

Text normalization

  • Original
  • Regularized
  • Normalized

Search


  • Exact
  • All forms
  • Fulltext index
  • Morphological index