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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 568, page id 1815201908:0625
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266. tnino.
mui
oid
59. BH
68
HY PE RBOL A.
Demonstratio.
InE AB C, DHF coniusacxe hyperbolx, ee punctum
Spsuocum in atrmptoro RI. ex quo polica linc ordi.
nacim TF, IA ad diamectos conusacas HIF, C B, d SC
BN lacus rectum cranlucrsi laceris CB. Dicove cA C B
ad BNI, siC FD quadracum esse ad quadratum A C: est
enim ve GB adBN, sicaquadracum CB ad quadracum
TTF: Ccd ve GB quadracum ad quadracum HTF, (IC F D
bquadrarum ad quadracum A C: igicur velinca eB ad
BN lincam, sC F D. quadrarum ad quadracum AC.
lerac demonstrandum. . Caniseo c cills d vet
 EIM
Corgaret
PROPOSITTO LXVTTTM I
 obeB et
et
135
E ABC hyperbola, cuius diamerer HB de ordinatim ad illam pot.
ta AC; heaurem B L. lacus rectum diameero TIB, Peruicts. LCl rivin
Dicorectan gulum HF B ad A F. quadracum.
camdem habero rarionem quam linea fI B 2d
BL; lacus sciliceceranluersum ad rectumsi ciup,
Demonstratio.
IL Et HB E
C1.  2S. S23:L et CrHBEVB BB CAESBItCEP
VAdlraco AF. aequale est rectansulumoTOK, isi.
OCuE FTE B rectangulum ad quadracum A F, es vE
FC quadracum ad quadracum AF: sed F et quadratu
eA ad quadracum a AF ve AIB cranluersum d laEUSEC
aum BT, rectangulum isieur HIE B ad AF. quadra
cum est ve HB linea ad lineam BL. Quod exac de
monstrandum.
1t I
ac.
eRODOSTTIO EXIX
1c1t
Unes diamerri coningarx lunc axibus proporrionales in quibuluis
Demonstratio.
experbolisconiugaris.
3aO 
ERIB L. XM: qu
BOHancuE ABC, DF. F opponca cccoes, quatu
ee alia queus allumatur diametrorum coniusacio FN,
Dico FN ad L. M eam proporcionem habere, qua
axis F B ad FTK. Posicisenim AC, TG ad axes HR
E B ordinacim; gux cum almproco in eodem puncto
conveniane; AaC F N adN R, vE F: B ad B Z: _C VEXH
ad FTX, AIC LM adNIT: _E PeT R _C F ordinarim
PONRNEUE R P, FO. isicur eric F X B rectangulum ad
rectangulum FRN, VE R X II rectangulum ad rc
Etangutum L lM, d permucando vE F ZB 2AK Z I
sC FR N ad L T N rectangulum: sed E YB, RXI
rectanoulac proporcionalia lune quadraris RB, FTK, 8
FN. LMI quadracis proparcionalia sune rectaneula
atata e L LB  Propocionalia lunc quadraris axium E B.
RF
GFII eAconiugaca; sinegucaxes carum R B, R H.
 e at i   e tite a  e ta tet s te te ete   t et e et ut et u  i e   i e ti   e i t e et  t e t e e  s te  te    e e te    e    . d  1