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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1053, page id 1815201908:1110
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S P H AE R OAD E 5.
des eam Habete laltonem quam habet
parabola AFB F. ad spacium parabo:
licum AGBF..
Demonscratio.
Scentum est 2 quod AGBF ductum in
alcicudinem BF aquetur AIIBE, du-
Eto in sc. praerere a demonstratum est b AIBF
in se ductum aequari AF BF ducto in BP, cst
aurem B P alcicudo communis. Igicur AHIBB
ductum insc ad AIB F; ductum in sC, cA ve
Parabola AGBF ad spacium parabolicum
AF B F. C0d sicue sehabCE A FIB F ductum
in (c ad AIBF in se ductum, ica Ce haber
sphaeroides ABCD ad conum AIBCD,
ccum quadraca IIR ad quadrata TK, can-
dem racionem obcineane quam circuli radio-
rum TIK ad circulos radiorum TK. IgicuE
sphaeroides ABCD ad inscripeum conum
cam habecracionem quam parabola AC BF. ad spacium parabolicum AF B F.
eROPOSITIO CXXXIV
VECCEUT (PHETOIAICS TLCLIOHC ad ARCIM FCCLA ExTIBeMCe CICUIOM IODeI
L quo vebali in scribatur conus parti spheroideos ABC D; polioque
Peraxem planO AB N, Bonaneur AMI, N M parallelae axibuS AR, R N e
Parabole inscribaneur AH N, AIE D parallelOgramMiS ARN; ALD,
quarum vertices (INE N, de A.
Dicoparcem (pharoideos ADC B, ad conum inlcripeum rarionem
habere compolicam exratione qua haber superticies parabolica F HI AL.
ad luverticiem parabolicam DR A L, _ CX
racione quam habet alcicudo AM ad alei-
cudinem DL.
Demonstratio.
baSIM AHLFL, _ aMem AMI. Similicer
Cuperficies criangularis ATDI in sC ductapyra-
midem exhibebic aequalem s magnicudini cuius
balis est spacium parabolicum AKDL, e alciru-
do T P. Sedha magnicudines HaBCnE PRTIONE CO.
Policah ex racione ba seos parabolice AFIFL ad
varabolica ARD L, _ ex alcicudine M A ad S A,
sive OP adTP. Proo corpora illis aequalia, ni-
mirum ACDE ductum in sC, et AID L un se
Dico conum inscriptum ad spheroi-
Veatur guauis OF quae aequidistet AM
ostensum elt d proporcionales esse lincas OP
OP, FIP. imilicer (I ex D puncto pOnatuF D S
quae sic parallela NMt; demonstracum cAcTP.
IP. X P esse proportionales, GLarC AODL Cu-
perticies in se ducta aeguarur E lolido quod Habet
a Collisitur
e
a
le dicb
C Pater est
discur
ta-
29. Ap
cs
Ibia
h 13. Baiu
ductu