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

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[41.] PROBLEM V.
[42.] PROBLEM VI.
[43.] PROBLEM VII.
[44.] LEMMA I.
[45.] LEMMA II.
[46.] LEMMA III.
[47.] LEMMA IV.
[48.] LEMMA V.
[49.] PROBLEM VIII.
[50.] PROBLEM IX.
[51.] PROBLEM X.
[52.] PROBLEM XI.
[53.] PROBLEM XII.
[54.] PROBLEM XIII.
[55.] PROBLEM XIV.
[56.] PROBLEM XV.
[57.] Synopſis of the PROBLEMS.
[58.] THE TWO BOOKS OF APOLLONIUS PERGÆUS, CONCERNING DETERMINATE SECTION, As they have been Reſtored by WILLEBRORDUS SNELLIUS. By JOHN LAWSON, B. D. Rector of Swanſcombe, Kent. TO WHICH ARE ADDED, THE SAME TWO BOOKS, BY WILLIAM WALES, BEING AN ENTIRE NEW WORK. 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. MDCC LXXII.
[59.] ADVERTISEMENT.
[60.] EXTRACT from PAPPUS's Preface to his Seventh Book in Dr. HALLEY's Tranſlation. DE SECTIONE DETERMINATA II.
[61.] THE PREFACE.
[62.] PROBLEMS CONCERNING DETERMINATE SECTION. PROBLEM I.
[63.] LEMMA I.
[64.] LEMMA II.
[65.] LEMMA III.
[66.] PROBLEM II.
[67.] LEMMA IV.
[68.] LEMMA V.
[69.] PROBLEM III.
[70.] PROBLEM IV.
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page |< < ([iii]) of 161 > >|
68[iii]
DE SECTIONE DETERMINATA II.
HIS ſubjiciuntur libri duo de Sectione Determinatâ,
quas
etiam ad modum præcedentium unam pro-
poſitionem
dicere liceat, ſed disjunctam:
quæ hujuſ-
modi
eſt.
Datam rectam infinitam in uno puncto ſe-
care
, ita, ut è rectis interceptis inter illud &
puncta
in
illâ data, vel quadratum ex unâ, vel rectangulum
ex
duabus interceptis, datam habeat rationem, vel ad
contentum
ſub aliâ unâ interceptâ &
datá quâdum;
vel etiam ad contentum ſub duabus aliis interceptis:
idque
ad quam partem velis punctorum datorum.

Hujus
autem, quaſi bis disjunctæ, &
intricatos Dio-
riſmos
habentis, per plura neceſſario facta eſt demon-
ſtratio
.
Hanc autem dedit Apollonius communi methodo
tentamen
faciens, ac ſolis rectis lineis uſus, ad exemplum
ſecundi
libri Elementorum primorum Euclidis:
ac rur- ſus idem demonſtravit ingenioſe quidem, & magis ad
inſtitutionem
accomodate, per ſemicirculos.
Habet
1

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