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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 789, page id 1815201908:0846
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1
in
e
Demonstratio.
actaca F A hoc  sCC
diS F BF vna cum quacati
rectangula xqualia u Guacacts
AL. xqualta eteUr lunC G+ AD rC.
etangula, rectansulis LL. Va C
rectangulis B AC. rectangusis au-
cem G AD aequalia lunc rectan-
suta CrAR, CADR; rectangula
iBICUE C AR, C AD R aequalia lune
ductum in BFb et equale DL ducoi a 
LF A F a aqualia sunc rectansu
BA
id estrectangulis B A C. irem G A L
rectangulis FBF, B AC: ablatis igitur xqualibus ex hypothehrectangulis B AC
GAK manec rectangulum F B I aequale rectangulo DR C A. erxo planum F B
eROPOSITIO CZXXI.
b 46. hiunius.
Tameeri dux A C, BD Pemicirculi A B C ad angulos insistant rectOSi
Dico F F. planum ductum in planum F. C, corpus proterre xquale illi
quodbalim haber criansulum AB D _ alcicudinem BD.
NE RLMLCHE. PaTaIC-
IX ad A C, aGAHEUT PEF B dC A
contingences qua convenianein
O; Pohrisque NFI Parallelis
AC, tiane proporcionales NTI
FI, C I, icem NB, F I, R T: CruHE
CARB, DL B parabOIX. SCCC-
cur deinde BD bitariam in 9
Ponaturque OP xequidictans AC, occurrens parabolis in R Y, Semicirculis aurem
in S e V, ducacurque recta AB, quae circulo F F, _E FCCtX MM occurrit in
eodem puncto S, ve Facile demonstrabicur quoniam AKB patabola CR, 1 pFOpOF- d67. Pa
cionales sunclinex PO. F S, P Y: eAt aurem PO in S bilocta, recta isitur PS in Y
3c
quoq: bilecta elti _ S L dimidia est iphuSS P, hoC estS O. quia vero P C, SO, R 9, 299. pa.
proporrionales Tunt, _ 59 dimidia P O: recta quoque R O dimidia eAt S 9, FX - rab.
qualesigirursuneT S, R O quoniam aurem L I cAt ad RO, ve DIB rectangulum
ad rectangulum D OB id cA AMT B ad AS B rectangulum, _ VE AN B rectanou-
lum ad rectangulum ASB ECFM K linca ad lineam Y S, crieve F I ad R G. SICMR C47 parabu
ad FS, id est R 9. Xequaeles ioicur (unclinCx LI, RM, vicerius cum F C in Idiui-
(a Ecbitariam ex non bitariam in F quadraca F Pequalia sunc recrangulis F R G, Vna
cum quadraris FI, id est (quia NT, F I, P I Cunc conrinuxe) una cum N I rectangulis
id Cst (quia F I, RMIxquantur) rectansulis NTKM. Scd F L quadrara quoque xqua
lia Cunc rectangulis NFK, (quod NI, FI, RI. sinc proporcionalis) rectangula igieur
NTIK Equalia sumr rectangulis F F G, _ NIKM. rectangula aurem NIK aequalia
quoque sunc rectangnlis NTMs NTTMK, igitHE NTMT, NIMR ceccangula equa-
lia sunc reccangulis N IMR, F P C. dempeo ergo communi NIMT K, reldua N IM,
FFC recransula aqualia sonc: planum igicur F P duetum in B Ct XQUaEUTML
criangulo, ducco in. quadratum N Lidest in alcicudinem BD.
htrhh
Diunctaque AB, describatur super B D ve diamerro circulus B F. D.
Demonstratio.
Veancur saelcunque lu
 i  . te  es i t ue u t e t  e s ta t e  e   ete  ti et    e t  t t e   e   elt