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

236. 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.

237. 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-
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 eſt contra hypoteſim. Secet er-
go in F; & erit F C ęqua- 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.

237.1.

0202-01
3. ſecun-
di conic.
8. ibid.

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