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

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[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.
[71.] DETERMINATE SECTION. BOOK I. PROBLEM I. (Fig. 1.)
[72.] PROBLEM II. (Fig. 2 and 3.)
[73.] PROBLEM III. (Fig. 4. and 5.)
[74.] PROBLEM IV. (Fig. 6. 7. and 8.)
[75.] PROBLEM V. (Fig. 9. 10. 11. 12. 13. 14. 15. 16.)
[76.] PROBLEM VI. (Fig. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26.)
[77.] THE END OF BOOK I.
[78.] DETERMINATE SECTION. BOOK II. LEMMA I.
[79.] LEMMA II.
[80.] LEMMA III.
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page |< < ([iii]) of 161 > >|
68[iii]
EXTRACT from PAPPUS's Preface to his Seventh Book
in Dr. HALLEY's Tranſlation.
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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