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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 811, page id 1815201908:0868
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IN P L. A N Y M
Demonstratio.
DLanum PF ductum in alcicudinem AB, id est lC-
atangula omnia FF AB, aequalia lune rectangulis
FF AF _C E F B, id eA B F ducto in AF S F F ducto
in EB: (Cd E F IN F R, XQUAEUT 2 A F iN FB: _C F F
in FB b aequale CA KB in F A. igicuE P F ductum
in alcicudinem AB, aequale AP in LB, _ KB in F A.
Ouod erat demonstrandum.
PROPOSIEIO CLXXIX
IE BC quaevis sectio conica; +
Dilliusque axis FC ad quem or- 7
dinatim polica sIE A D: act aque F
per L COntingenTCFHL, OCCUF- F
rant illi, crectae ex A ee D linex 
aguidistantes axi F G.
DicoB C planum ductumiin
alcicudinem. AD vna cum E B
ducto in se, aequari F C plano
ductointe.
s
3c
37CB LcctBIE 
51
29C1 15
Demonstratio.
a 105. hB
b +bid.
Vcancur quoruis AC, _ per C reCtx pONAnEUE C B R parallela AD, quadca-
cum AC caequale est rectangulis AD BC, A BDC; id est AD B C rectangu- c Prolo-
lorna cum quadeaco A B: est aurem quadrarum AC aequale quadraris AF, F C: mem lib. 1.
igieUE quadraCA A F, F. C. aequalia sunc quadrato AB, id est quadratis AF, F. B vn a ProP. 20.
cum rectangulo ADB; ablato igicur communi quadrato AF, manet rectangulum
AD B C vna cum quadraro F B, xequale quadraco F. C. igicur B C ductum in alciru-
dinem AD, vnd cum EB in CC ducto, aequatur plano E C ducto in sc. Quod erat
demonstrandum.
PROPOSITIO CLZZX.
VIc AB axis parabolx AC I, aequalis lateri reCtO: RaE AUTEM LUPEF AB
LD qUAdEAEUM AB, E. F, X per A e F parabola de ScribAFUT AOF, ae qua-
lis AC IBhabens verricem in F: FeutA VerO FB PTOdUICtA OCCUTTAEParA-
bolxe ACI in l.
OpOr.
S  ue   t es . 1 e pte i  e .  e e     e       t  e te  ti  e  1   s   t       u u   t.  et  a   l