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

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21432 _NIMA_ verò in hoc caſn, tum in quarta, tum in quinta figura eſt 119. huius
ad num. 4. G D; niſi punctum G cadat in ipſo D; tunc enim _MINIMA_ abit in pun-
ctum.

8. At, ſi, vt in ſexta figura, quando interuallum G B minus eſt dimidio
B E, punctum G cadat inter B, & E, tunc ſi concipiatur D eſſe Ellipſis
verticem, reliquum interuallum D G, vel erit non minus, vel minus di-
midio B F, quo in caſu duæ _MAXIMAE_ reperientur ad partem periphe-
riæ A D C: eadem conſtructione, & demonſtratione, ac ad num. 6. & 7.
huius, & reliqua G B erit _MINIMA_, & c.

9. Si denique datum pun-
ctum G fuerit inter ſemi-

176[Figure 176] axes, aut extra ſectioné,
vt in ſeptima figura; vel
intra, vt in octaua; vel in
ipſa ſectione, vt in nona.
Iungatur E G, quæ hinc
inde producatur, & fiat,
vt tranſuerſum D B ad re-
ctum B F, ita E H ad 22Coroll.
16. h. G, ac ita G I ad I E, &
ex H, I, ducantur H L,
minori axi A C, & I L
maiori D B parallelę, quę
ſimul occurrent in L, &
in angulo H L I per pun-
ctum E (quod eſt cen-
trum Ellipſis) deſcriba-
tur Hyperbole M G 334. ſecun-
diconic. N, quæ neceſſariò 4417. h. ſibit per G (cum ſegmen-
ta G H, E I rectæ H I ap-
plicatæ in angulo aſym-
ptotali H L I, ſint ęqua-
lia,) & in duobus tantùm
punctis M, N, Ellipſis
peripheriam ſecabit. 5518. h. co has interſectiones da-
re puncta quæſita: hoc
eſt iunctam G N in ſepti-
ma, octaua, & nona fi-
gura eſſe _MAXIMAM_, &
G M _MINIMAM_, in ſe-
ptima, & octaua figura, tantùm, quoniam in nona ipſa _MINIMA_ abit in
punctum.

Quò autem ad _MINIMAM_ oſtendendam. Ducatur ex M, Ellipſim
contingens M P maiori axi occurrens in P; appliceturque M Q.

6625. primi
conic.

Et quoniam in angulo aſymptotali H L I ſumptum eſt punctum Q, ex-

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