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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[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.
[81.] LEMMA IV.
[82.] LEMMA V.
[83.] PROBLEM VII. (Fig. 32, 33, 34, &c.)
[84.] PROBLEM I. (Fig. 32 to 45.)
[85.] PROBLEM II. (Fig. 46 to 57.)
[86.] PROBLEM III.
[87.] THE END.
[88.] A SYNOPSIS OF ALL THE DATA FOR THE Conſtruction of Triangles, FROM WHICH GEOMETRICAL SOLUTIONS Have hitherto been in Print.
[89.] By JOHN LAWSON, B. D. Rector of Swanscombe, in KENT. ROCHESTER:
[90.] MDCCLXXIII. [Price One Shilling.]
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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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