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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 902, page id 1815201908:0959
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902
PRODORTIONALLTATES
eROPOSTETO LXI.
CaCMaOrario AB aetationem C B, veratio P F ad rationem C FI.
Droracene L elle adracionem Hl. D, veratio BFolt ad ra-
58. tuiuo
c38. Bt
Demonstratio
Voniam racio AB est ad rationem CD.
sEracio R F eA ad rarionem GTI, erie
permurando racio AB ad racionem R F, vE
Pacio C D ad racionem GFI. ergo a bracio
AF CA ad r2
em BF, veracio C C ad
rationem D II. Sed ratio C C es ad racio-
nem D FI vecratiO FT D ad rarionem CC.
cOHCM CC.
ergo ratio AF est adrationem BF, ve racio HF D ad rarionem OC: vnde permu-
cando ratio A F est ad rationem FYD, veracio BF ad racionem GC. Quod erat de-
OnArAH duM. LIANC GUIOQUE PCT PTXCEdeNTEM COAVETEES. OI
P R OP OSITIO LXII.
Imiles ponancurrariones AB, d C.D, et inter AB, CD ponantur
E. de F.
Dico rationem AF este ad CF racionem, ve racio F D ad racio-
Hem L.B.
monsra
FF
I
FTaC VE F ad C, SC F
adC, crie d ve A all
Cracio A C da 12
AC, B tioneM CF, LCMITM
Aac ve D ad F; AC  de
F: Cxic vE P 20 113 lc
racio FD ad raciollem
FB. Detuee Guontam
eAtretadC. SCF. dll
muc. B ad B. HF. dd fl. led exhrpochelire A, CA adC, Sic B adD. Cr∞OH, Cl an
F CA ad FT. Ouoniamigitur cAve AadC, SicF ad HI, e licur paulo anre octendi,
ve C ad BsicF ad P, erir ex xequa, ledracione perrurbara re Aad C: HIC L ad fI, hoc
est quemadmodum ancea demonstraui, veracio A P elt ad rarionem C F, GC critra-
ei0 F: D adrationem F B. Ouoderat demonstrandum.
LR OP OSITIO LXIII
eritpermuT. VE Fad F, sic C ad E: irem quoniam est veB adF, sic D ad YI, erix per
ut turtumlmchtalionesAB. Ll.  canalicut quauoenat.
Dicorationem L. A eNe adracionem EC, VELaEIO L. B Ct al lac
NCM LL.
Desoi.