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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 802, page id 1815201908:0859
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2
DYCTVS PLANL
Demonstratio.
MP, XqUaEUE P C ba AuE C M LV. Quod erac demonaran dUM.
Voniam N MO rectangulaaqualla sunc rectangulis ONLP, VE MN ad MO
LAC MP ad MO, d diuidendo ve MN ad NO, sic MP ad PQ: rectangu
laixICuE MN P Q, aequalia sunc rectangulIs NO PM, _ NO planum ductum in
PROPOSITIO CLIX.
irculum ABC COICS AE HI A, B, C PaNCtis lInCX ETeS AD, DF
SE C; _ AD, C E quidem aequidictances (INC, D E vero ad illas nor-
malis, ponatur aurem d P. D linex aeguidistans FC3 Faciens DFG F re.
ctangulum hancque proporrionales FD, AD, FID; ICEM E. B, L C, F. H:
_ pec HI, B, IE puncta, parabola describatur.
Dico L. M planum ductum in DIL, corpus proferre aequale illi quod
exlurgit ex NO plano ducto in alcirudinemr L. I:
monst
VCantUE quOLIS AAMeTO RECtX LONTMF parallele ad DF. Ouoniam FD,
AD. ETDDrOPOrrionAleSSUnE, ec HTOBR parabOla _ AN B C circuluS, re-
Etangula OLI aequalia uncrectangulis N F. M ve ex libro de parabola Facile colli-
SicuF quarCVE LO ad L N, GC LM ad LI, _ convercendo ve L N ad OH, EC
ET ad TNT, rectangula igicur E NFN I aequalia sunc rectangulis ON L L. er∞OON
A6. huins. Balis dueta in . alcicudinem L. L aequalem illi producie magnicudinem que exlurgie
ex ductu C N plani in planuem MI. Ouod crac demonstrandum.
Propolicio quoque rera cAE F C linca ip(i D P. xquidistans circulum concins aes
_ prortus eadem demonstrario eAt.
PROPOSITIO CLZ.
TEmicirculo AB C circum lerivcum hC re Ctanoulum ADE C RDF.
quidem semicirculum conringar in B: hanrque proportionales F. D,
F D, BD, LD: X per L. d A parabola deseribaturhabens verricem in A.
Dico F.K planum duccum in alcicudinem FC aquari FHI ducto
in 11C.
Demona