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

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9874 interceptæ applicatarum portiones à contingente AE magis remouentur eò
ſunt minores, vnde tales ſectiones ad ſe propiùs accedunt. Sed quod de
congruentibus, ſiue æqualibus parabolis hactenus expoſuimus, & iam olim
demonſtrauimus (dum Aſymptoton doctrina promoueri poſſe animaduer-
timus) maximos poſtea Geometras, Torricellium nempe, ac Gregorium à
S. Vincentio aliter quoque oſtendiſſe reperimus, quorum edita opera ad
vberiorem de hac re eruditionem conſulere ſuademus.

Dico tandem has con-

67[Figure 67] gruentes Parabolas ad in-
teruallum ſimul peruenire
minus quocunque dato in-
teruallo 1 2. Fiat enim vt
1 2 ad AE, ita AE ad 2 3
quæ ipſi 1 2 indirectum po-
natur, & tota 1 3 bifariam
ſecetur in 4, & per B appli-
cetur BK ęqualis 1 4; aga-
turque KI parallela ad BX,
& per I recta IDS contingẽti
BK æquidiſtans, erit ergo
IX æqualis KB, ſiue 4 1;
eſtque IX dimidium IS, &
4 1 dimidium 1 3; quare
IS, 1 3 ſunt æquales; ſed
factum eſt rectangulum 1 2 3 æquale quadrato AE, & rectangulum IDS
oſtenſum eſt æquale eidem quadrato AE, ergo rectangula IDS, 1 2 3 in-
ter ſe ſunt æqualia; ſed rectæ IS, 1 3, ſunt æquales, quare ſegmentum ID
æquatur dato interuallo 1 2; interceptæ verò infra ID ſunt minores ipſa
intercepta ID, quapropter huiuſmodi congruentes Parabolę ad interuallum
perueniunt minus dato interuallo 1 2. Quod erat vltimò demonſtrandum.

COROLL. I.

EXhac patet, in congruentibus Parabolis per diuerſos vertices ſimul ad-
ſcriptis, omnes, inter eas, interceptas lineas communi diametro ęqui-
diſtanter ductas, eſſe inter ſe æquales, quales ſunt EB, DN, & c.

COROLL. II.

PAtet quoque, ex penultima parte huius, rectangula ſegmentorum ap-
plicatarum vtranque Parabolen ſecantium omnia inter ſe æqualia eſſe,
qualia ſunt rectangula LMY, IDS, & c.

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