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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 32, page id 1815201908:0089
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LIN F A R V M
ra, aequalia duobus laceribiis AC, AK; isicur criangulum NV AB, xqualc est crian.
sulo C AK, _ A F rectangulu, xquale rectangulo A P: eodem modo oltenditurre.
2
EtanguM C M, a GeaSLSBCCAIGCN CL. VIC HD Quadlratum, aequale est re-
ctancuns AL, CMlimul Cumpris. SeLLLCCa a perat quadracum AP, rC.
ctangulo BF, idCCSo ABH, dC M rectangulum, superac quadratum C F.
rectangulo BM, la CMccanslo CBL, id olt AB FTrectangulo; ioieur quadra-
cum AD, Superac quadraca AH, C F. rectangulo AB IT bis Sumpro. Ouod erar de-
monstrandum.
derorions
iniucundum tamen fore putaur, si Deramque Cosent su quo Pythacoras 47. primi Element.
hocloco demonsturem.
DRopositionem hanc, vii ex sequentem, licet demonstret Fuclides Zib. 2. prop. 12. Cx 13. non
eROPOSITIO XLV.
ST0ABCtriangulum orygo, d lacerum quadraTa AD, C F.
lineas C B, IF
EBC bis sumpro.
A F. DuCaTUEGNE ex A linca AC, Secans orchogonalicer in LI, e C,
Dico AD quadratum deficere a quadraris CF, AF, rectangulo
231. Zerrij.
Demonstratio
Vcatur ex C Li-
nea, lCCanSOF=
chogonaliterinL 8
R linCaS AB, FMI.
iungancurque pun-
CTa AL, CM, BD
BNV. delcripeo dein
(uper AC ve diame
cro, lemicirculo
AFTC, (GII EraNSI.
bicpeF = TIR R) de-
miccacur ex B, linca
BO, Cccans ortho-
gonaliterin OexP.
LInCaS AC, DII.
OUOnIA AM, L C
lincae aequidictane,
CFIE NAC crian
gulum, xequalc di
midio reccanguli
AK Codemqg; 1n0-
nem sint aequales, audico communi angulo B A C crunc anguli H A C, B ANquo-
que inter (C _GHALES, sUNE AuLE _ LaCCTA AMI, A C aequalia duobus laceribus AB,
APT, igitur ertangulum MI A C, aquale triangulo B AVF, _ A R recrangulum, aqua-
le rectangulo A P: dupro Mu crianguli B A RT. Eodem mOdO OCECNdICHIE RECFAN-
sulum CC, aequale cAe reclate ao P: quare AD. quaaratuM; aguase et re-
a cctalis clcaet
aequale dimidio recranguli C G. rursum cum anguli AX AB, C AN per constructio-
crangulis Cer HR. LedCeecatouu deticic a quadraco C F, reccangulollt
id est rectan sulo TTBC; X AR rectansulum, deticit a quadraro AL, rectarigu-
IOT F, id ele LCCaoulo AB C, id cM CCCLAHBMIO HLBC; IBITUE quadrarum AD.
u tu ti u u i u u pi u    u  u  p  u e  p i                   nmu