3515LIBER I.
tinget figuram, ABC, contingatin ſitu ipſius, FG, &
in pun-
cto, A, igitur, A, erit vertex figuræ, ABC, reſpectu ipſius, B
11A. Def. 1. C, à nobis inuentus, qui in huius Problematis priori parte inue-
niendus proponebatur.
cto, A, igitur, A, erit vertex figuræ, ABC, reſpectu ipſius, B
11A. Def. 1. C, à nobis inuentus, qui in huius Problematis priori parte inue-
niendus proponebatur.
Sit nunc figura ſolida, ſiue ſolidum, ADE, in quo reſpectu
plani, BECD, ſit vertex inueniendus, ſumpto igitur exrra pla-
num figuræ, vtcumque puncto, N, per ipſum agatur planum, K
HVX, ipſi, BECD, æquidiſtans, quod vel continget ſolidum,
BAC, vel non, ſi autem non contingat, moueatur accedendo,
22Poſtul. 2. velrecedendo, à plano, BECD, tandem igitur contingetipſum,
tangatin, A, puncto, igitur punctum, A, erit vertex ſolidi, AD
33A. Def. 2. E, reſpectu plani, BECD, qui inueniendus proponebatur.
plani, BECD, ſit vertex inueniendus, ſumpto igitur exrra pla-
num figuræ, vtcumque puncto, N, per ipſum agatur planum, K
HVX, ipſi, BECD, æquidiſtans, quod vel continget ſolidum,
BAC, vel non, ſi autem non contingat, moueatur accedendo,
22Poſtul. 2. velrecedendo, à plano, BECD, tandem igitur contingetipſum,
tangatin, A, puncto, igitur punctum, A, erit vertex ſolidi, AD
33A. Def. 2. E, reſpectu plani, BECD, qui inueniendus proponebatur.
COROLLARIVM.
_H_Inc manifeſtum eſt, ſi recta, BC, tangat planam figuram, AB
44_B. Def. 1._ C, quod ductæ erunt oppoſitę tangentes ipſius figuræ, ABC,
reſpectu datæ rectæ lineæ, quæ fuit vna ex eiſdem tangentibus, nem-
55_B. Def. 2._ pè, BC; & ita ſi figura, BDCE, tangit ſolidum, ADE, ducta erunt
oppoſita tangentia plana ſolidi, ADE, reſpectu plani, BECD, in
66_A. Def. 2._ quibus puncta contactuum erunt oppoſiti vertices earumdem figura-
rum, boc pacto inuenti: Siverò recta linea, BC, ſecaret figuran, A
BC, vel planum, BECD, ſecaret ſolidum, ADE, eodem pacto ex
alia parte lineæ, BC, vel plani, BDCE, inueniemus verticem, vn-
de inuenti erun@ propoſitæ figuræ planæ oppoſiti vertices, & ductæ op-
poſitæ tangentes reſpectu datæ lineæ BC; & in ſolido iuuenti erunt
oppoſiti vertices, & ducta oppoſita tangentia plana reſpectu dati
plani, BDCE, quæ cum tangunt in figuris planis, figuræ contactuum
77_C. Def. 2._ vocantur etiam oppoſitæ baſes, & earum ſingulæ baſes, & baſes li-
neares, ſi contactus fieret in lineis: binc ergo diſcimus inuenire op-
88_A. B. Def._
_1. & 2._ poſitos vertices figuræ planæ, vel ſolidæ cuiuſcumque, & eorum op-
poſita tangentia ducere reſpectu datæ in figura plana rectæ lineæ, &
dati plani par@ter in ſolida figura.
44_B. Def. 1._ C, quod ductæ erunt oppoſitę tangentes ipſius figuræ, ABC,
reſpectu datæ rectæ lineæ, quæ fuit vna ex eiſdem tangentibus, nem-
55_B. Def. 2._ pè, BC; & ita ſi figura, BDCE, tangit ſolidum, ADE, ducta erunt
oppoſita tangentia plana ſolidi, ADE, reſpectu plani, BECD, in
66_A. Def. 2._ quibus puncta contactuum erunt oppoſiti vertices earumdem figura-
rum, boc pacto inuenti: Siverò recta linea, BC, ſecaret figuran, A
BC, vel planum, BECD, ſecaret ſolidum, ADE, eodem pacto ex
alia parte lineæ, BC, vel plani, BDCE, inueniemus verticem, vn-
de inuenti erun@ propoſitæ figuræ planæ oppoſiti vertices, & ductæ op-
poſitæ tangentes reſpectu datæ lineæ BC; & in ſolido iuuenti erunt
oppoſiti vertices, & ducta oppoſita tangentia plana reſpectu dati
plani, BDCE, quæ cum tangunt in figuris planis, figuræ contactuum
77_C. Def. 2._ vocantur etiam oppoſitæ baſes, & earum ſingulæ baſes, & baſes li-
neares, ſi contactus fieret in lineis: binc ergo diſcimus inuenire op-
88_A. B. Def._
_1. & 2._ poſitos vertices figuræ planæ, vel ſolidæ cuiuſcumque, & eorum op-
poſita tangentia ducere reſpectu datæ in figura plana rectæ lineæ, &
dati plani par@ter in ſolida figura.
PROBLEMA II. PROPOS. II.
CVilibct figuræ planæ parallelogrammum circumſcri-
bere, cuius latera duabus datis rectis lineis, in pro-
poſitæ figuræ plano ſe ſecantibus, ſint parallela.
bere, cuius latera duabus datis rectis lineis, in pro-
poſitæ figuræ plano ſe ſecantibus, ſint parallela.
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