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

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22543

Sit verò A B C D in ſecunda figura Ellipſis, cuius axis maior B D, mi-
nor A C, centrum E, & punctum intra datum ſit F. Oportet per F re-
ctas in ſectione applicare quales inuenire propoſuimus.

Sit per F maiori axi B D ordinatim ducta G F H, minori verò ſit I F L.
Dico rectangulum G F H eſſe _MINIMVM, MAXIMVM_ verò I F L.

Sit quælibet alia per F ap-

187[Figure 187] plicata M F N, & portionis
M O N ſit vertex O, atque ex
axium verticibus A, B, vti e-
tiam ex O agantur contingen-
tes A P, B Q, P O Q, quæ ſi-
mul occurrent in R, P, Q. 1158. pri-
mih. Erit ergo rectangulum G F H
ad I F L, vt quadratum B 2216. tertij
conic. ad quadratum A R, ſed eſt
contingens B R, minor A 3387 primi
huius. ſiue quadratum B R minus quadrato A R, ergo, & rectangulum G F H
minus erit rectangulo I F L.

Præterea rectangulum G F H ad M F N eſt vt quadratum B Q ad qua-
dratum O Q, ſed eſt contingens B Q minor contingente O Q, ſiue 44ibidem. dratum B Q minus quadrato O Q, ergo rectangulum G F H minus eſt re-
ctangulo M F N, & hoc ſemper vbicunque cadat applicata M F N: qua-
re rectangulum G F H eſt _MINIMVM_ quæſitum.

Demùm cum rectangulum I F L ad N F M, ſit vt quadratum A P 5516. tertij
huius. quadratum QP, ſitque contingens A P maior contingente Q P erit 6687. primi
huius. dratum A P maius quadrato Q P, ergo rectangulum quoque I F L maius
erit rectangulo N F M, & hoc ſemper vbicunque ſit ducta N F M inter
applicatas I F L, G F H quare rectangulum I F L eſt _MAXIMVM_ quæſi-
tum. Quod vltimò inuenire propoſitum fuit.

DEFINITIONES.

PLANVM ACVMINATVM REGVLARE, vel ACVMINATVM
tantùm voco omnem figuram planam, circa diametrum, in alteram par-
tem deficientem, & cuius perimeter ſit in eaſdem partes cauus.

Hoc eſt figura plana A B C,

188[Figure 188] in qua omnes rectæ lineæ A
C, E F, G H, & c. à figurę pe-
rimetro terminatæ, ac inter ſe
æquidiſtantes, à quadam re-
cta B D bifariam ſecentur, &
in alteram partem, vt puta ad
B, continuò decreſcant, do-
nec abeant in punctum B, ſit-
que earum perimeter A G B H C ad eaſdem partes cauus vocetur

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