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

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5838 rint æqualiter inclinatæ, ſi ſint per vertices ſimul adſcriptæ, inter ſe mutuò
congruant.

VIII.

CONI-SECTIONIS VEL CIRCVLI PORTIO, SIVE SEGMENTVM
vocetur ſuperficies à quadam ſectionis ordinatim ducta, & curua ſectionis,
aut circuli peripheria terminata. Et ipſa ordinata dicatur
BASIS PORTIONIS, SIVE SEGMENTI.

35[Figure 35]

IX.

MENSALIS CONI-SECTIONIS, VEL CIRCVLI
dicatur differentia duorum ſegmétorum eiuſdem coni-
ſectionis, quorum baſes ſint parallelæ.

Vt ſi ex coni-ſectione, vel circulo ABC abſcindan-
tur duæ portiones ABC, DBE, quarum baſes AC, DE
ſint parallelæ, ipſarum portionum differentia ADEC di-
catur menſalis, & ipſæ AC, DE baſes, & AD, CE late-
ra eiuſdem menſalis.

THEOR. XI. PROP. XIX.

Si fuerint duæ quæcunque coni-ſectiones æqualiter inclinatæ
per vertices ſimul adſcriptæ, ipſæ vel erunt in totum congruentes,
& eiuſdem nominis, vel in totum diſiunctæ, præter in vertice, hoc
eſt altera alteri inſcripta, vel in duobus tantùm punctis ſe mutuò ſe-
cabunt in ipſis tamen verticibus ſe contingentes.

SInt in præſenti ſchematiſmo duæ quæcunque coni-ſectiones ABC, DBE
11Schematif-
mus 1. & 2. æqualiter inclinatæ pereundem verticem B ſimul adſcriptę, quarum có-
munis diameter ſit BF: dico has ſectiones, vel eſſe in totum congruentes, vel
in totum diſiunctæ, vel in duobus tantùm punctis, ſe mutuò ſecantes.

Ducatur ex vertice B cuilibet in altera ſectionum ordinatim applicatæ æ-
quidiſtans BGH, quæ vtranq; ſectionem continget ſuper qua ſumatur 2232. primi
conic. rectum latus ſectionis ABC, & BG rectum ſectionis DBE, ipſarumque regu-
læ, ſectionis videlicet ABC, ſit HPL, & ſectionis DBE ſit GOI.

Iam, vel regulæ GOI, HPL ſibi mutuò congruunt, vel infra contingen-
tem BGH nunquam conueniunt, vel infra eandem ſe mutuò ſecant. Si pri-
mùm, vt in primis 4. figuris; dico ſectiones in totum ſimul congruere, & eiuſ-
dem nominis eſſe.

Sumpto enim in ſectione ABC quolibet puncto M, per ipſum ducatur ſe-
ctionum communis ordinatim applicata MNFOP, ſectionem ſecans DBE in
N, diametrum in F, regulam GI in O, NL in P. Et quoniam in 4. primis fi-
guris, in quibus regulæ ſunt congruentes latitudines FO, FP ſunt æquales,
& altitudo eadem BF erit rectangulum BFO ſiue quadratum NF in 33Coroll.
prop. 1. h. DBE, æquale rectangulo BFP ſiue quadrato MF in ſectione ABC, 44Coroll.
brop. 1. h.& ſemi-applicatæ NF, MF æquales erunt, hoc eſt ſectiones DBE, ABC con-
ueniunt ſimul in punctis N, & M, quæ ſunt extrema communium

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