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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
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ete
let
di
D.
OVADRATVRA CFRCVLI
Schema
ommune.
10.
eROPOSITIO XXXVII
rEper recta AB corntantur quadraca ABC, B AD, quorum dia-
PsonalesLC,OD aCMpCi Parabolis AE C, AFC, Q BGD,
BHID quarum verrices sine A ex B, in linca AB altumantur qua cumque
IE, NIE, ponancurq per l, L, N, IE puncta Parallela laceri AD OcCurren-
tes diagonalibus in punctis P, O. T, V, parabolis aurem in punctis F, R,
E, O, S,C, X, HI, compleantur deinde rectagula FIL, R NH; IL. S, NIC;
iceMP IL, ONIE; ILT, NK V, denique EIL, IL. Z; ONK, NRFI.
Dico parallelexipedum luper FIL. Se IL S, ad parallelepipedum Cuper
RNK, NIE C duplicaram habere rarionem eius quam parallelepipedum
(WveF PLL, IL T, haber ad parallelepipedum (uper ONK, NKV.
Demonstratio.
Vm enim aparalle lexipeda super FTL, TF. S, Super PIL, TF. F, supet aTY, a Per
in5.
TEx sinc proporcionalia; icem cum proporcionalia sine parallelexipeda loper ut
RNK, NK G, TUPCF O NK, NTRV, TUPCE ONTK, NRZ, _ cum liae dux series vI-
cimahabeant aequalia, scilicer parallelepipedum luper coTI, IL. a, _ (UPEF BNYK,
NKZ, pacec bprimum parallelexipedum rnius seriei ad primum alcerius seriei esse B Por 9.
in duplicaca racione sccundi ad secundum. Ouod erar demonstrandum.
PROPOSITIO XZXVIII
Ildem politis:
LDicoparallelepipedum Tuper PIL, IL T, ad parallelepipedum (uper
ONK, NKV, duplicatam habere rationem eius quam parallelipipedum
super EIL, IL. X habet ad paralle lepipedum (uper O NK, N I HI.
Demonstratio.
vuins.
R Vrtus enim paralle lepipeda super PIL, IL Y, SUPEFP IF, IFZ, Super CTL, cPer 30.
TE x sunc proporrionalia, icem proporrionalia sunc paralle lexipeda luper O NK, hurus.
NRV, CUPCE ONTK, PTRFI, SUPCF ON R; NVRE, a vicima veriulque scrici LuINE X-
qualia, isicur dicerum primum paralle lepipedum prime seriei est ad primum secundE huius.
seriei, re secundum ad secundum. Duod erar demonstrandum.
CCC 2
Sche-