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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 54, page id 898203430:0082
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VINCENTH YINTANI PROLOCIS,
X X
Triangulum denique TTZ. T eiusdem altirudinis P. B cum triangulo A sympto-
tal, e cujus semibases BFI, BZ aequales sunt lateribus EF, FL, Viraque
VErique, dicatur ASTMPTOTALF CIRCVMAVOIVM.
PROPOSTFIO XAMIII
N FTyperbola. Ouodrata ramorum ab orieine in cer
tro sunt inter se et rectancula sermentorum axis in-
ter ordinatas ex ramorum terminis, C9 terminos MO.
duli ex Asempeoto interceptorum. Centrum vero MIO.
duli cum centro datae LEyperbola concruit,
GTE Hyperbola ABC, cuius axis BD, verECX B, CeNrUM F, axis
transuersus BZ, triangulum Aymprorale F P. I. de circumauctum.
AIYmPEOTALC RF P, MOdutuS VeTO Cx AImPTOTIS R F, F F SIE L N, e
praeter minimum ramum P. B ex centro sic ad Ayperbolam A B C alius
quicunque FaIUS F A. DicO quadrALA FaIOTUM L. A, L B, _EC. esse in-
ter se ve rectingula NDL, NBL.
DuCatUT ex A ordinata ad
AXeM, quae iunctaS F R, F B
ac productas secet in 9. T3
AlymPTOtOS in C, R; Sectio.
nem in C, 2Zem in D, e
F H M determinantem Modu.
lum in S.
Tam, GuUm sIE extensa B R
aequalis segmentO A(YmPTOtOS
P F Cex Moduli incentione
exic quadratum BR aequale qua-
drato PF, sive quadraris simus
EB, BF, _ dempro commu
ni quadrato BF religuum re
Ctangulum RFP equale CxiEre.
liguo quadrato FB. Pari ratione (ob singulorum laterum proxorrionalin
tatem) demonstrabitur rectangulum OC I aequale quadrato LD.
Insuper rectangulum C7 AK aequatE 2 quadrato FB; Si his igieur ad
datur, vel ab ipsis suberahatur, prouc opus fueric, rectangulum ASR,
erit rectangulum CSK aequale quadrato semiordinatae AD; sed rectan
Cuum OCT aequale nuper octensum est guadrato F D, ergo rectangu
sum DCT cum rectansulo CSK, live rnicum OST aequale eAt duobus
simul quadratis AD, DE, vel rnico quadraco rami E. A.
Ec quoniam racio rectungulorum SY, R LP componitur ex racione
10. secun
ai C01