Viviani, Vincenzo - De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei

Viviani, Vincenzo, De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei

Table of contents

[21.] COROLL.

[22.] MONITVM.

[23.] PROBL. I. PROP. II.

[24.] ALITER.

[25.] ALITER.

[26.] MONITVM.

[27.] LEMMAI. PROP. III.

[28.] PROBL. II. PROP. IV.

[29.] MONITVM.

[30.] PROBL. III. PROP. V.

[31.] PROBL. IV. PROP. VI.

[32.] PROBL. V. PROP. VII.

[33.] MONITVM.

[34.] THEOR. II. PROP. VIII.

[35.] MONITVM.

[36.] LEMMA II. PROP. IX.

[37.] THEOR. III. PROP. X.

[38.] COROLL. I.

[39.] COROLL. II.

[40.] MONITVM.

[41.] THEOR. IV. PROP. XI.

[42.] COROLL.

[43.] MONITVM.

[44.] LEMMA III. PROP. XII.

[45.] ALITER idem breuiùs.

[46.] ITER VM aliter breuiùs, ſed negatiuè.

[47.] COROLL.

[48.] THEOR. V. PROP. XIII.

[49.] COROLL. I.

[50.] COROLL. II.

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Itaque, quoniam rectangulum BKC ad quadratum AK eſt vt LF ad FH
per conſtrutionem, vel vt XN ad NH, & quadratum AK ad rectangulum
AKC eſt vt AK ad KC, vel HG ad GC, vel HN ad NS, ergo ex æqualire-
ctangulum BKC ad rectangulum AKC, ſiue recta BK ad KA, ſiue BG ad
GF, vel RN ad NF, eſt vt XN ad NS, ac propterea rectangulum ſub extre-
mis RN, NS, hoc eſt quadratum MN æquale rectangulo ſub medijs XN, NF:
_linea igitur MN poteſt ſpatium XF, & c._ vt ibi vſque ad finem.

Quo tandem ad 13. primi poſt ea verba _ergo rectangulum PMR æquale eſt_
_LM quadrato_ legatur ſic.

Cumque ſit rectangulum BKC ad quadratum AK ita HE ad ED ex con-
ſtrutione, vel XM ad MD, & vt quadratum AK ad rectangulum AKC ita
AK ad KC, vel DG ad GC, vel vt DM ad MR, erit ex æquo rectangulum
BKC ad rectangulum AKC, vel BK ad KA, ſiue BG ad GE, vel PM ad ME
vt XM ad MR, quare rectangulum ſub extremis PM, MR, vel quadratum
ML æquatur rectangulo XME ſub medijs. _Liuea igitur LM poteſt ſpatinm_
_MO & c._ vſque ad finem.

Sed iam ad propoſitas Apollonĳ propoſitiones accedamus, quas ſimul ſequenti
Theoremate amplectemur, itemque ſine compoſita proportione demonſtrabimus.

THEOR. I. PROP. I.

Si conus plano per axem fecetur, fecetur autem & altero plano
baſi coni non æquidiſtante, quorum communis ſectio conueniat,
11Prop. 11.
12. 13.
primi co-
nic. vel cum vnotantum, vel cum vtroque latere trianguli per axem vl-
tra, vel infra ſui ipſius verticem, planum verò, in quo eſt baſis co-
ni, & ſecans planum, conueniant ſecundum rectam lineam, quæ ſit
perpendicularis, vel ad baſim trianguli per axem, vel ad eam, quæ
indirectum ipſi conſtituitur, & fiat, vt rectangulum ſegmentorum
diametri ſectionis inter latera, & baſim trianguli per axem interce-
ptorum, ad rectangulum ſegmentorum baſis, ita ſectionis diameter
ad aliam: recta linea, quę à ſectione coni ducitur æquidiſtans com-
muni ſectioni plani ſecantis, & baſis coni vſque ad ſectionis diame-
trum, poterit rectangulum adiacens lineæ quarto loco inuentæ, la-
titudinem habens lineam, quæ ex diametro abſcinditur inter ipſam,
& verticem ſectionis interiectam (ſi tamen ſectionis diameter ęqui-
diſtet alterutri laterum triãguli per axem) ſed ipſum excedet (ſi cum
vtroque latere vltra verticẽ conueniat) vel ab eo deficiet, (ſi ijſdem
lateribus infra verticem occurrat) rectangulo ſimili ſimiliterque po-
ſito ei, quod continetur prædicto diametri ſegmento, & quarta in-
uenta, iuxta quam poſſunt, quæ ad diametrum applicantur.

SIt conus, cuius vertex A, baſis circulus BC, & ſecetur plano per axem,
quod ſectionem faciat triangulum B A C, ſecetur autem &

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