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

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

Table of contents

[91.] PROBL. XVI. PROP. XXXI.

[92.] THEOR. XIII. PROP. XXXII.

[93.] THEOR. IV. PROP. XXXIII.

[94.] MONITVM.

[95.] THEOR. XV. PROP. XXXIV.

[96.] THEOR. XVI. PROP. XXXV.

[97.] THEOR. XVII. PROP. XXXVI.

[98.] COROLL.

[99.] THEOR. XIII. PROP. XXXVII.

[100.] THEOR. XIX. PROP. XXXVIII.

[101.] LEMMA IV. PROP. XXXIX.

[102.] THEOR. XX. PROP. XXXX.

[103.] COROLL.

[104.] THEOR. XXI. PROP. XXXXI.

[105.] COROLL.

[106.] THEOR. XXII. PROP. XXXXII.

[107.] ALITER.

[108.] COROLL. I.

[109.] COROLL. II.

[110.] LEMMA V. PROP. XXXXIII.

[111.] THEOR. XXIII. PROP. XXXXIV.

[112.] COROLL.

[113.] Quod ſuperiùs promiſimus oſtendetur ſic.

[114.] THEOR. XXIV. PROP. XXXXV.

[115.] COROLL.

[116.] LEMMA VI. PROP. XXXXVI.

[117.] THEOR. XXV. PROP. XXXXVII.

[118.] ALITER.

[119.] COROLL. I.

[120.] COROLL. II.

9470

THEOR. XXI. PROP. XXXXI.

Similes Hyperbolæ per eundem verticem ſimul adſcriptæ, ſunt
inter ſe nunquam coeuntes, & ſemper magis recedentes, ſed ad in-
teruallum nunquam perueniunt æquale cuidam dato interuallo.

SInt duæ ſimiles Hyperbolæ ABC, DBE per eundem verticem B ſimul
adſcriptæ, & Hyperbolæ ABC maiora ſint latera, tranſuerſum nempe
FB, rectũ autem BG; & DBE minora ſint, tranſuerſum HB, rectum verò BI.
Patet primùm has ſectiones eſſe inter ſe nunquam coeuntes; cum enim DBE
alteri ABC ſit inſcripta, ipſæ, licet in infinitum producantur, 115. Co-
roll. 19. h.conuenient.

Dico ampliùs, eaſdem in-

64[Figure 64] ter ſe longiùs ſemper recede-
re. Applicatis enim in alte-
ra ſectionum, nempe in in-
ſcripta, duabus vbicunque
rectis MN, LD, fiat vt BH ad
BF, ita BM ad BQ, & BL ad
BR, & per Q, R, applicentur
in circumſcripta Hyperbola
rectæ QS, RA; & cum dia-
metrorum ſegmẽta BM, BQ,
BL, BR ſint tranſuerſis BH,
B F proportionalia, 2238. h. quoque applicatæ MN, QS;
LD, RA ijſdẽ lateribus pro-
portionales, quare M N ad
QS erit vt LD ad RA; cum-
que ſit vt tota BL ad totam BR, ita pars BM ad partem BQ, erit & reliqua
ML ad reliquam QR, vt tota BL ad totam BR, vel vt BH ad BF, vel vt MN
ad QS, & vt LD ad RA, vt nuper oſtendimus; quare iunctis rectis DN, AS
in menſalibus DM, AQ, erunt ipsæ DN, AS inter ſe parallelæ. Iam 3339. h. ductis MN, LD vſque ad circumſcriptam ſectionem ABC, in P, & O, ſi iun-
gatur PO, hæc omninò ſecabit iunctam AS, vel intra ipſam ſectionem; (ſi
nempe vnius iunctarum ſectioni occurſus, alterius occurſibus contineatur)
vel extra (ſi nullius occurſus, alterius occurſibus amplectatur) ſed AS 4425. ſe-
cundi co-
nic ducta ad partes verticis tota cadit extra ſectionem in SK, & punctum P eſt in ipſa ſectione, quare punctum P eſt inter parallelas lineas ASK, DN, ſed
5510. pri-
mi. conic. producta PO conuenit cum altera parallelarum AS, vt modò monitum fuit;
taliſq; occurſus eſt omnino ad partes O infra applicatam PN, cum punctum
S cadat infra P (nam ex ipſa conſtructione applicata QS eſt infra applicatam
MP) quare eadem OP producta conueniet quoque cum altera æquidiſtan-
tium DN, ad oppoſitas tamen partes, vtputa ſupra ipſam applicatam PN,
vnde intercepta applicata OD, maior erit intercepta PN vertici B

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