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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 588, page id 1815201908:0645
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1
XI Y PER BD L A.
PROPOSTTIO CXTII.
Dico illas abhyperbolam  a proporcionalirer dividi.
2206. h1 -
BiOS. h1-
CEX 109
huius.
d1oS. ha-
u5
10
1c
Demonstratio. I. CW
5
DOnanEuE AD, AF, RO, AT, e pertician-
curcriangula D N O, FOT. Cum DB, FF
proporcionales sine OTI IKs DB cst ad C II,
VE F F ad TR: quare tam segmenra Loonca-
na BD OTI; FFKI quam COnUEXABDNO,
FOT aequalia liinc: quia vero BD OHI e
FF KI seomenta aequantur, aequalia quoque
Concerianoulac ADC, A FI; limilicer quia
DNG, FOI seomenta aequalia sune, crianou-
la quoque sDNO, FOL aquanEuF. igituIE
DNC criangulum adcriangulum D A. C,svE
FOI criangulum ad criansulum F AI: sed
DNC criangulum est ad criangulum D AG
CVELNadL A, _ VE NIOAdMA, ICFOI
eriangulum est ad criangulum F AL: PFOPOT
cionalicer isitur in N ec O diuile lunc diame-
eri P. A, M A: quod erac demonstrandum.
eROBOSITIO CXIV
nie Demonstratio.
TInE AB, AC asympeori hyperbola DFI, posicises DB, FE, OH
lIE proportionalibus, quae alymproro A C aequidistene; iunganEUF
DC, F I; quibus diuilis in L. ee M bitariam, diametri potianeur AL, AM.
dividat diaerex F. FO, _ duCANEUE AC, BD.
Zperbolam ABC secenF dux parallela AB, C D quas bitariam
DiCO SEGMENEA COnVexA AC, D B cscincer le xequalia.
licto alstabcocto eica a liti
producaneur AB, C. D donccoC.
currane alempeoris in M, P, N, O
puinctis, ducaneurque F A, FC, BB,
E. D, item AL, C I, DK, BHI, P2.
Fallela asymprocis: Cxic ergO AM
ad CN, EVE CA AL 2d C L. sed ve
H AM ad C N, ica quoque eA BP
ISIEUT ETaPCZIA i ACVE, DBFTK incel le aqualia; se d eadem de caulacriam con
194. hu. Calla LeSHichea Khyperbolica AIL C, DR HL B aqualia lunri residua ipicur scomen-
X7
ad D
R. Igicur vE AT ad CT, ita cA BTT ad DR. sune
hy. C2 COnVexA AC, D B aequalia lunc. Ouod demonstrandum fuit.
es    
put
11II
i
PF
16
Si