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

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20220

COROLL.

HInc, data ratione maioris inæqualitatis, hoc eſt D E, ad E H, &
differentia A C inter duo s terminos ignotos A G, G C, qui de-
beant eſſe in data ratione, eruitur quomodo reperiantur ipſi termini A G,
G C. Facta enim fuit vt D H differentia primorum, ad H E minorem ter-
minum, ita data differentia A C, ad aliam C G, & reperti ſunt quæſiti
termini A G, G C, Nam ſtatim oſtenſum fuit eſſe A G ad G C, vt D E
ad E H.

THEOR. XII. PROP. XVII.

Si fuerit in angulo rectilineo quælibet applicata, à qua hinc
inde ab eius termino æqualia ſegmenta ſint abſciſſa, & per v-
num diuiſionis punctum deſcribatur Hyperbole, cuius aſympto-
ti ſint latera dati anguli, ipſa per alterum punctum neceſſariò
tranſibit.

SIt in angulo A B C applicata quæcunque A C, quæ inæqualiter ſece-
tur in D, & ſumatur C E æqualis A D. Dico ſi per punctum D de-
ſcribatur Hyperbole, cuius aſymptoti ſint B A, B C, ipſam omnino tran-
ſire per E.

Quod huiuſmodi Hyper-

162[Figure 162] bole tranſiens per D, alibi
ſecet applicatam A C, pa-
tet. Nam ſi eam continge-
ret in D, eſſet A C æquali-
ter ſecta in D: quod 113. ſecun-
di conic. contra hypoteſim. Secet er-
go in F; & erit F C 228. ibid. lis A D, ſed eſt quoque E
C eidem A D ęqualis, qua-
re F C, E C ęquales erunt;
hoc eſt punctum F congruet
cum ipſo E; quare Hyper-
bole D F, quæ in angulo aſymptotali A B C deſcribitur per D, omnino
tranſit per E. Quod erat demonſtrandum.

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121	97
122	98
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125	101
126	102
127	103
128	104
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130	106
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