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

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22038 vt quadratum D C ad C F, & per con-
uerſionem rationis, quadratum A B ad

181[Figure 181] rectangulum G B E, vt quadratum C D
ad rectangulum H D F, & conuertendo,
rectangulum G B E ad quadratum A B,
vt rectangulum H D F ad quadratum C
D, & quadratum A B ad B I, eſt vt qua-
dratum C D ad D L, ob triangulorum
I A B, L C D ſimilitudinem; quare ex
æquo rectangulum G B E ad quadratum
B I, erit vt rectangulum H D F ad quadra-
tum D L. Quod erat, & c.

LEMMA VIII. PROP. XXIX.

Si quatuor magnitudinum eiuſdem generis, prima A ad ſe-
cundam B maiorem habuerit rationem, quàm tertia C ad quar-
tam D E, ſitque prima minor tertia, erit ſecunda minor quar-
ta.

FIat, vt A ad B, ita C ad D F, & cum
A ad B habeat maiorem rationem,

182[Figure 182] quàm C ad D E, habebit quoque C ad D
F maiorem quàm ad D E, vnde D F erit
minor D E, & eſt A ad B, vt C ad D F,
erit permutando A ad C, vt B ad D F,
eſtque A minor C, ergo B erit minor D
F, & D F oſtenſa eſt minor D E, quare B
eò ampliùs erit minor D E. Quod erat, & c.

THEOR. XIX. PROP. XXX.

Rectorum laterum in Hyperbola, cuius axis tranſuerſus non
ſit minor eius recto latere, MINIMVM eſt rectum axis.

ESto Hyperbole A B C, cuius centrum D, axis tranſnerſus E B, qui
primò ſit minor recto B F. Dico rectum B F eſſe rectorum laterum
_MINIMVM._

Sit quæcunque alia tranſuerſa diameter G D A, in ſectione producta
ad I, cuius rectum ſit A K ex A contingenter applicatum, & axi occur-
rens in H; & ſit B I æquidiſtans A H, quæ ad diametrum G A I erit or-
dinatim ducta, atque ex I ſit I L ipſi D I perpendicularis, ex A verò A
M axi applicata, cui ex vertice B ſit parallela, vel contingens B O, ſe-
cans A H in P, iunganturque A B, O H.

Iam cum rectangulum D M H ad quadratum M A, ſit vt E B ad B 1125. pri-
miconic. ſitque E B maior B F, erit rectangulum D M H maius quadrato M

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118	94
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