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

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155131 ALCO eſt _MINIMA_ circumſcripta datæ Ellipſi ABCO, per terminos ap-
plicatæ AC, cum dato tranſuerſo DE: immo ipſa ALCN vnica eſt, his con-
ditionibus circumſcriptibilis. Quod faciendum, & demonſtrandum erat.

SCHOLIVM.

SIquæratur, qua nam ratione in prop. 82. ad finem, dicatur _licet minor fue-_
_rit eadem ALCN_ in hac verò, _licet maior fuerit eadem ALCN_ (perinde ac
ſi, per terminos A, C, cum diametro æquali ipſi LN alia in ea deſcribi poſſit
Ellipſis minor ALCN, in hac verò alia maior ALCN) vtrunq; noshaud te-
merè dixiſſe ex ſequéti Theoremate manifeſtum fiet, à quo habebitur quam-
libet aliam Ellipſim per A, C, adſcriptam, cum tranſuerſo ęquali ipſi LN, ſed
cuius ſegmenta ab applicata AC abſciſſa, ſint magis inæqualia quàm ſint ſe-
gmenta NF, FL, minorem eſſe ipſa ALCN; & è contra, eam quę cum ſegmentis
minus inæqualibus, quàm ſint NF, FL, eadem ALCN maiorem eſſe.

THEOR. XL. PROP. LXXXV.

Ellipſium, perterminos communis applicatæ ſimul adſcripta-
rum, & quarum tranſuerſa latera ſint æqualia, MINIMA eſt ea,
cuius communis ordinatim ducta ſit diameter coniugata: aliarum
verò illa, cuius ſegmenta diametri ſunt minùs inæqualia, minor eſt
ea, cuius diametri ſegmenta ſunt magis inæqualia.

SInt duę Ellipſes ABCD, AECF, per terminos eiuſdem applicatæ AC
ſimul adſcriptæ, & quarum tranſuerſa BD, EF ſint æqualia, ſitq; AGC
coniugata diameter Ellipſis ABCD, ſiue G eius centrum. Dico primùm
hanc minorem eſſe altera AECF, ſiue eſſe _MINIMAM_, & c.

Etenim, cum ſit DB æqualis EF, & DB

122[Figure 122] bifariam ſecta in G, erit EF in pũcto Ginæ-
qualiter ſecta, vnde rectangulum BGD ma-
ius erit rectangulo EGF, cum ſit 1160. h. _MVM_; ideoque rectangulum BGD ad qua-
dratum AG, ſiue tranſuerſum BD ad 2221. pri-
mi conic. ctum Ellipſis ABCD, maiorem habebit ra-
tionem quàm rectangulum EGF ad idem
quadratum AG, ſiue quàm 33ibidem. EF ad rectum Ellipſis AECF: ſed tranſuerſa
BD, EF ſunt æqualia, ergo rectũ Ellipſis AB
CD, minus erit recto AECF: ſi igitur Ellipſis
huiuſmodi Ellipſes (cum ſint ęqualiter incli-
natæ) concipiantur eſſe per eundem verticem ſimul adſcriptæ, ita vt tranſ-
uerſæ diametri ſimul congruant, ipſa ABCD, cuius rectum minus eſt, inſcri-
pta erit, ſiue minor AECF, cuius rectum maius eſt, & ſic minor 442. Co-
roll. 19. h. alia, cuius diametri ſegmenta ſint inæqualia: quare ABCD erit _MINI-_
_MA_, & c.

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