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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 580, page id 1815201908:0637
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8c
AZPER BO L A.
PROPOSITIOKCM.
cur alympcoris parallela AM, C. L: rellalum vero M A, C B communis
inrerlectio lEN, _ K communislectio linearum C L, HI.
Dico ANB, HIK C, criangula elle Mer se aqualia.
C
ADC
Scendimus in prioris pro.
posicionis demonstrarione
esse ON ad N B; VE M H
ad N A, adeoque eAe veOH ad
NMI, sC NB ad N A, _ob cat.
deeariOneM vE IR ad RL, lic
FIK ad C K: quia vero est ex posi-
tionere ti A hoc est C N adH B,
sic CF hoc est TK 2d KHL, _ vE
MN ad NA, ACL K ad K C, ixi-
cur ex aquo cAre NVB ad N A. lC
FTK ad KC; ivicur cum anguli, ad
N _ R, aquales SnC, XquaIIZ quo-
que sunc criangula AN B, HIK C.
Quod erat demonstrandum.
XCVII
11
Lpervolam A B C inter a lymptotos D F,
FC consticuram subrendac AC: ducti(q;
lineis AH, C F quae alympeoris aquidictent,
ee invicem decussene in l, agacur por ldiame.
tex LB:
Dico F B productam rectam AC bitariam
Demonstratio.
DA ad. RC, id est FF ad F C, aHC FF est ad
=D, id est XI ad K A: _ dividendo vEF Fad IF.
AICKTad TA: _ permucando vE R P ad TK, (IC C 199
IA: Similia igicur se ad candem diameerum polca sunt
parallelosratuma RF R, ATC, e F. I diameter bile-
cac diamecrum AC. Quodtuic demonstrandum.
PROPOSITIO, XCDILI
IIdem posiris. auC aCAF A(B aequidistans AD.
Duo,LCin continua essc analosia.
Demonstratio
Srmpcoristiyverbolae A B C, aquidistantes, de inter le proponio-
Lnales ponancurlinex AE, GB, C. F, HII. iuncti(q AB, C. H; ponan.
est (I 1EC
17
DF
D
dividere.
675. h1-
AniECCta CR, cum enim BprOPOEEIONALeS SINEF L, HTB, EC, _ PL reaX xque-
cur AD, linea quoquc AD, HLB, P. C in concinua lunc analoBia. uod erae
PAD.
demonttratelum.
e er s  et t u  es tit pet e e p e e tat e e  ute e etet ta pat    t e  t it  et   t e tit     t    t