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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 627, page id 1815201908:0684
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BC
idec
et
attuI
et
1
Et Y P ER BO LA.
PROPOSITIO CLZAAMI
Aram AB divilam in C denuo secare im D, verectangulum BDC
quadraro relidui AD sc xquale.
Constructio e demonstratio.
 RIGAEUE A F vecum B A D, anoulum
lemirectum constieuat, e ex L dimi
dio CB, linCx PONaNCUE E O, F HI anons
los lemirectos exhibences cum A F lincas,  0t
ex deleripra sichyperbola LC B, inter 2F 101
Ermptocos FC, FFI habens axem AF :L . 5
sieque B punctum incerlectionis rectam
A Fn productae cum hyperbola DCF: de
missaisicur perpendicularis ex F. ad AB,
exhribebic punctum D quaelicum, cum
enim assymproci HIF, PC angulum For.
mene rectum ex constructione, rectanou-
lum + BDC aequale cAt quadrato D R
quia vero dnsulus D A F semirectus cH, d AD F Rctus, religuus A F D dimidio
recti, adcoque e angulo F AD aequalis est _ F. D quadracum axquale quadraco
AD: unde d rectangulum BD C, AD quadraco aequaeur. Fecimusisirur, ec. quod
pecebatur.
e
ee r
121 1.. CIIE R O P OSIFIO CLXXXIV
acam AB sectam in C parciriin D. Verectangulum BDC ad AD,
quadrarum dacam obrincar rarionem quadrari F. ad F quadrarum.
iat
Lu Constructio es demonstratio.
lIr
nalis B C veracio quadrari C C ad G FI,
hocest CB ad HF, eadem sic cum proporrio-
he F, ad F. pertecto deinde parallelogrammo
ductilque GK, CT. descripea Bonaeur hyper-
bola InCeF alZMPEOTOS C K, G L, HabENSVEFEI-
cem C. ex puncto deinde A duCATUIE AM, vE
cum D A recta Temirectum angulum FOrMCE,
Occurrens perimerro sectionis in MI: _ POnatuE
MD Parallela FTI. Dicopunctum D esse quod
guarieur: est enim rectangulum BD C’ad qua-
dracum DM ve CB, quadracum ad TII qua-
dratum per ea que praemitimus. Sed quadraro
DM aequale est D A quadrato, igitur rectan
sulum BDC ad D A. quadtacum cam haber
racionem quam CB ad FTT quadracum, hoc
cA quadcacum E, ad P, quadcacum. quod prx.
Randum tuic.
luita CB Bitariam in O ponatur orthogo.
t
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