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

hoc eſt portiones A B C, S O R eſſe æqualium baſium, ſed H O I maior eſt
S O R, totum parte, ergo, & A B C, quæ ipſi H O I eſt æqualis, erit maior eadem S O R, & hoc ſemper, & c. vnde portio A B C eſt _MAXIMA_ portio-
num æqualium baſium. Quod primò erat, & c.

289.1.

47. h.
45. h.
0250-01

Pręterea, cũ in tertia figura, quæ ex K ducitur interiorem Ellipſim F D G
contingens ſit _MAXIMA_ eandem Ellipſim contingentium, ipſa erit omni- no maior A C; quare eidem axi applicata, quæ ipſi A C ſit æqualis, mino-
rem axim ſecabit inter L, & K, & ſit ea T V X. Si ergo concipiatur per V
deſcripta Ellipſis, datis A B C, F D G ſimilis, & concentrica, recta T V X
hanc Ellipſim continget, eritque _MAXIMA_ eandem Ellipſim contingen- tium, quapropter portiones, quarum baſes ſint æquales baſi T V X, hanc
mediam Ellipſim omnino ſecabunt, ac ideo maiores erunt portione T L X,
cum portiones ab ijſdem contingentibus abſciſſæ ſint omnes portioni TLX æquales. Quare portio T L X eſt _MINIMA_ portionum æqualium baſium,
ex eadem Ellipſi A B C abſciſſarum. Quod erat vltimò demonſtrandum.

289.1.

47. h.
ibidem.
45. h.

290. COROLL.

EX his conſtat _MINIMAM_ portionum ſemi-Ellipſi maiorum, quarum
baſes ſint ęquales eam eſſe, cuius diameter ſit ſegmentum maioris axis,
_MAXIMAM_ verò, cuius diameter ſit ſegmentum minoris.

Nam in tertia figura, cum portionum A B C, S O R, T L X, & c. ſemi-El-
lipſi minorum, & ſuper æqualibus baſibus, ipſa A B C ſit _MAXIMA_, & TLX
_MINIMA_, ac ipſæ ſint portiones eiuſdem terminatæ magnitudinis, ſiue Elli-
pſis eiuſdem A B C N, patet reliquarum portionum ſemi-Ellipſi maiorum
A N C, S N R, X M T, & c. quæ item ſunt ſuper æquales baſes A C, S R,
T X, portionem A N C eſſe _MAXIMAM_, & X M T _MINIMAM_.

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