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

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10278 tercepta applicatarum ſegmenta metitum, licet ſemper magis, ac magis de-
creſcat, eſſe tamen non minus interuallo 1 3, quod iuxta eaſdem æquidi-
ſtantes ordinatim ſectionibus applicatas, inter vtranque aſymptoton cadit.
Nam per ea, quæ infra demonſtrabimus, interuallum 2 1, maius eſt inter-
uallo 1 3. Pariter 4 5, eſt maius 6 7, communique addito 5 6, erit inter-
uallum 4 6, maius interuallo 5 7, ſiue 1 3, & hoc ſemper vbicunque ſu-
matur harum ſectionum interuallum infra applicatam 2 1 3. Quare hy-
perbolæ congruentes per diuerſos vertices ſimul adſcriptæ, licèt ſemper ma-
gis accedentes, ad interuallum nunquam perueniunt æquale cuidam dato
interuallo. Quod erat vltimò, & c.

COROLL.

EX his conſtat, congruentium Hyperbolarum non per eundem verticem
ſimul adſcriptarum aſymptotos eſſe inter ſe æquidiſtantes, & aſympto-
ton inſcriptæ ſecare Hyperbolen circumſcriptam.

Quod ſuperiùs promiſimus oſtendetur ſic.

SInt duæ congruentes Hyperbolæ KBC, DEF, per diuerſos vertices B, E
ſimul adſcriptæ, & circumſcriptæ KBC ſit centrum G, & aſymptotos
GI, inſcriptæ verò ſit centrum H, & aſymptotos HM, quæ ipſi GI æquidi-
ſtabit, per præcedens Coroll. ſitque applicata quæcunque IL vtranque
aſymptoton, & Hyperbolen ſecans in I, A, K, D, communemque diame-
trum in L: dico interceptum applicatę ſegmentum AD inſcriptæ Hyperbolę
DEF, maius eſſe intercepto eiuſdem applicatæ ſegmento IK inter aſympto-
ton, & circumſcriptam.

Ducta enim IM parallela ad GHO, & per

70[Figure 70] Mapplicata MNO, erunt IH, IO parallelo-
gramma, ac ideò tàm GH, quàm LO ipſi IM
æquales erunt, & inter ſe; quare addita com-
muni HL, erit GL æqualis HO, ſed eſt GB
æqualis HE, (cum ſint ſemi-tranſuerſa late-
ra congruentium Hyperbolarum) vnde reli-
qua BL, reliquæ EO æqualis erit, & ob id
ſemi-applicata LK ſemi-applicatę ON ęqua-
lis, ſed eſt tota LI æqualis totæ OM (cum ſint
oppoſitæ in parallelogrammo IO) ergo reli-
quæ KI, NM æquales erunt, ſed eſt 1110. h. maior NM, quare & eadem DA erit maior
KI. Quod erat, & c.

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