Full text: Viviani, Vincenzio: De maximis et minimis, geometrica divinatio

fas portiones eſſe Acuminata Proportionalia.

Repertis enim earum diametris B G, E H, diuidantur ipſæ proportio-
naliter in I, L, applicenturque M I N, O L P. Cum ſit ergo G I ad I B,
vt H L ad L E, erit componendo G B ad B I, hoc eſt quadratum A C ad M N, vt H E ad E L, ſiue vt quadratum D F ad O P, ideoque & ap-
plicata A C ad M N, vt applicata D F ad O P. Quare, ex ſecunda præ-
cedentium definitionum, ipſæ portiones A B C, D E F erunt Acuminata
Proportionalia. Quod primò, & c.

266.1.

20. pri-
mi conic.

Præterea ſint A B C, D E
F duæ portiones eiuſdem, vel
diuerſarum Hyperbolarum, vt
in ſecunda figura, vel Elli-
pſium, aut circulorum, vt in
tertia, quarum baſes A C, D
F, & diametrorum ſegmenta
in ipſis intercepta ſint B G, E
H, quæ vſque ad ſectionum
centra Q, R producantur, & ſit vt G B ad BQ, ita H E ad
E R. Dico item has portio-
nes A B C, D E F eſſe inter ſe
Acuminata Proportionalia.

266.1.

0228-01

Nam diuiſis diametris B G,
E H proportionaliter in I, L,
per I, L applicentur M I N,
O L P, & productis ſemi-dia-
metris B Q, E R ſumantur eis
æquales Q S, R T, ita vt S B,
T E ſint ſectionum diametri.

Iam cum ſit G B ad B Q vt
H E ad E R, erit conuerten-
do, & ſumptis antecedentium duplis S B ad B G, vt T E ad E H, ſuntq; S B, T E bifariam ſectæ in Q, R, & partes adiectæ, in ſecunda figura,
vel demptæ in tertia B G, E H proportionaliter diuiſæ ſunt in I, L, ergo
rectangulum S G B ad S I B, ſiue quadratum A C, ad M N, erit vt re- ctangulum T H E, ad T L E, vel vt quadratum D F ad O P, nempe ap- plicata A C ad M N erit vt applicata D F ad O P, & permutando A C
ad D F, vt M N ad O P, & hoc ſemper de quibuslibet applicatis per
pnncta diametrorum B G, E H ipſas proportionaliter ſecantia, quare, ex
definitione ſecunda, ipſæ portiones A B C, D E F erunt Acuminata pro-
portionalia. Quod vltimò demonſtrandum erat.

266.1.

21. primi
conic.
35. h.
21. primi
conic.

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