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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 810, page id 1815201908:0867
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DYCxYS PL A NB
eR OPOSITIO CLXXVII
810
AVper A B D E rectanguli vno larere BD, descriprus sic BC D semi-
circulus, ducacur aurem cora illa Agura in se:
Oporrer exhibere magnicudinem a qa a BCCb4.
Cm ee alcicudinem daFat.
Constructio ex demonstratio
Aca licaleitudo BL, in directum polica cum A B: pertecto aurem rectangulo
299. D DBCCRM Loctangula aequalia hane quadraris LR, coltac BM D ellC 2 PaF2.
bolam. Deinde quadeacis FTK aequalia hane rectangula P R NT, pacec ex elemeneis
NN cAelinea eca. densguc rectangulis subdupla HlR ee rectis R traequalia
Aanc rectansula L K, N O: constac ex illis qua in libro de ellipit demonstrani, pun-
eta O0 ee adellipum. Dicoiritur corpus ex ductu OM bali coonica in BF alci-
cndinem dacam aquari FIL ducto in sc. HII ductum in (c lunc HI L quadrarai Scd HT I
quadraca aequalia lunr quadracis HIK _ RI, ina cum reccangulis IIKI bissum-
pcis: quadratis HIK aurem aequancur ex construct. recrangula L RN, _ IK quadra-
eis aequalia sune rectangula LK M per constructionem; recrangulis icem TIKL
bis sumpeis id est receangulis subduplis FTR _ recris RI, aequaneuE recrangul2
TRNO, igicur HI duccum in se, id cst quadraca FI L aequalia sunc recrangulisL. R N
id est KM ducco in alticudinem K L, _ rectangulis L K N id cA N K in alcicudi-
nem LR, rna cum recrangulis L KNO, id est NO ducro in alcicudinem L R,
id est HYY ducco in sc, aquatur OM ducro in alcicudinem daram BF SIHC LK,
exhibuimusigitur corpus, ecc. Duod cracfaciendum.
Lvercicem in C: de Case Guidemraxem habear C A, parabola ve-
rO C F. C axem C D. Iunganturaurem CC puncca.
Dico lB planum auccum in canguu LA MuCut A C. MI LB,
aequari magnicudini que balim habet P. F. e alcirudinem AB.
PROPOSITTO CLZAVIII
Ectangulo A B in scrivEx Cine parabolX dux C F. C, C IE C habentes
car.
Demon.