LIBER I.
tinget figuram, ABC, contingatin ſitu ipſius, FG, & in pun-
cto, A, igitur, A, erit vertex figuræ, ABC, reſpectu ipſius, B
C, à nobis inuentus, qui in huius Problematis priori parte inue-
niendus proponebatur.
51.1.
A. Def, 1.
Poſtul. 1.
A. Def. 1.
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,
velrecedendo, à plano, BECD, tandem igitur contingetipſum,
tangatin, A, puncto, igitur punctum, A, erit vertex ſolidi, AD
E, reſpectu plani, BECD, qui inueniendus proponebatur.
51.1.
Poſtul. 2.
A. Def. 2.
52.
COROLLARIVM.
_H_Inc manifeſtum eſt, ſi recta, BC, tangat planam figuram, AB
C, quod ductæ erunt oppoſitę tangentes ipſius figuræ, ABC,
reſpectu datæ rectæ lineæ, quæ fuit vna ex eiſdem tangentibus, nem-
pè, BC; & ita ſi figura, BDCE, tangit ſolidum, ADE, ducta erunt
oppoſita tangentia plana ſolidi, ADE, reſpectu plani, BECD, in
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
vocantur etiam oppoſitæ baſes, & earum ſingulæ baſes, & baſes li-
neares, ſi contactus fieret in lineis: binc ergo diſcimus inuenire op-
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.
52.1.
_B. Def. 1._
_B. Def. 2._
_A. Def. 2._
_C. Def. 2._
_A. B. Def._
_1. & 2._
53.
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.
