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

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146122 cadat inter I, & B; tunc enim m portione IBF, per punctum E, Ellipſis alteri
GEHD ſimilis inſcribi nũquam poterit, qualis ſemper inſcribi poteſt m triã-
gulis IBF, MBL, & c. primæ figuræ; quod omne, vel leuiter intuenti ſatis
patebit) illę omnino his minores erunt, cum verticibus ſint propiores; & ob
id, quæ ad oppoſitas partes ibi inſcribuntur, erunt quidem _MAXIMAE_
quæſitæ.

THEOR. XXXVII. PROP. LXXVII.

MAXIMI circuli m Parabolæ inſcripti, & à vertice ſucceſſiuè ſe
mutuò contingentes, ſunt inter ſe in ratione quadratorũ, diſparium
numerorum ab vnitate incipientium.

SIt Parabole ABC, cuius axis BH, vertex B; & _MAXIMI_ circuli m e@ in-
ſcripti, & à vertice ſucceſſiuè ſe mutuò contingentes ſint, quorum dia-
metri BE, EF, FG, GH, & c. contactus veròſint, primi vertex B, ſecundi
punctum L, ter@ij O, quarti R, & c. dico huiuſmodi circulos, eſſe inter ſe, vt
quadrata numerorum diſparium ab vnitate incipientium, nempe 1. 9. 25.
49. & c.

Ducantur, tum ex diametrorum terminis E, F, G; tum ex contactibus L,
O, R ordinatæ EI, FN, GQ, LM, OP, RS.

Iam cum circulus BE ſit _MAXIMVS_ in-

112[Figure 112] ſcriptibilium per verticẽ B, erit BE 111. Co-
roll. 20. h. lis recto lateri Parabolę, ſed EI eſt 22Coroll.
I. h. proportionalis inter EB, & rectum latus,
hoc eſt inter æquales lineas, quare EI æ-
qualis erit ipſi EB, quæ concipiatur, vt
vnum; eſtque EI æqualis EM, ergo 332. Co-
roll. 75. h. eſt vt 1, & tota BM, vt 2; ſed eſt vt BE 441. Co-
roll. 13. h. BM, ita BM ad BF, vel vt 1 ad 2, ita 2, ad
4; erit ergo BF, 4: eſtque BM, 2; quare
552. Co-
roll. 75 h. FM, ſiue FN, ſiue FP erit pariter 2; 66ibidem. detota BP erit 6; eſtque BF ad BP, vel vt
771. Co-
roll. 13. h. 4 ad 6, ita BP ad BG, & vt 4 ad 6, ita 6 ad 9, vnde BG erit 9, ſed eſt BP, 6, ergo GP,
ſiue GQ, vel GS erit 3; quare tota BS, erit
12, ſed vt BG ad BS, vel vt 9 ad 12, ita BS
ad BH, & vt 9 ad 12, ita 12 ad 16, quare
BH, erit 16. Siergo dum BE eſt, vt I, BF
eſt 4, BG, 9, & BH, 16; ipſa BE cum ea-
rum differentijs EF, FG, GH, erunt, vt
ſunt numeri 1, 3, 5, 7, qui ſunt numeri im-
pares ab vnitate incipientes, ſed circuli
ſunt, vt quadrata ſuorum diametrorum,
ipſæque BF, EF, FG, GH ſunt inſcripto-
rum circulorum diametri, quare hi

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