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

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145121 rectangulum AKF ad rectangulum DKE, vt quadratum AK ad KD (ob la-
terum proportionalitatem) vel vt quadratum IO ad OE (ob triangulorum
AKD, IOE ſimilitudinem) vel vt rectangulum IOL ad EOM (ob homolo-
gorum laterum proportionalitatem) erit, ex æquali, rectangulum GKH,
vel quadratum GK ad rectangulum DKE, ſiue vt rectũ latus Ellipſis GEHD
ad eiuſdem tranſuerſum, vt rectangulum POQ, ſiue quadratum PO, ad re-
ctangulum EOM, vel vt rectum Ellipſis PMQE ad ipſius tranſuerſum: cum
ergo huiuſmodi Ellipſes habeant latera proportionalia, ſintque æqualiter
116. ſec.
defin. h. inclinatæ, erunt inter ſe ſimiles. Quod erat primò demonſtrandum.

111[Figure 111]

Præterea, cum ſit AD´ ad DK, vt IE ad EO, ſitque AD maior IE, 2232. vel
63. h. DK maior EO. Item, cum ſit FE ad EK, vt LM ad MO, ſitque FE maior
LM, erit EK maior MO, ergo integra tranſuerſa diameter DE, maior toto
tranſuerſo latere EM; ſed tranſuerſum DE ad tranſuerſum EM, eſt vt rectum
vnius ad rectum alterius, vt ſuperiùs demonſtrauimus, eſtq; tranſuerſum DE
maios EM, quare rectum recto maios erit, ſiue Ellipſis GEHD maiorum la-
terum, maior erit Ellipſi PMQE minorum laterum, quæ tùm in 335. Co-
roll. 19. h. tùm in ſectione, aut ſemi-Ellipſi, vel ſemi-circulo vertici B propior eſt.
Quod vltimò oſtendere propoſitum fuit.

SCHOLIVM.

SI ergo in figuris 29. & 30. Problematis, concipiantur methodo ſuperiùs
allata, per datum punctum inſcribi Ellipſes ad partes verticis, vel angu-
li, vel ſectionis, quæ ſimiles ſint alijs ad oppoſitas partes per idem punctum
inſcriptis (ſi tamen ſectionis, vel circuli portio, quæ ab applicata per datum
punctum terminatur, huius Ellipſis ſit capax, quod accidet, quando in ſe-
cunda præcedentium figurarum, diagonalis IL, quæ ex I ducitur diagonali
AF æquidiſtans, & occurrens ſectioni in L, punctum L pertingat ad B,

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