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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 648, page id 1815201908:0705
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d
HT Y P E R BOL A.
PROPOSITIO CCXAII
DALaSolam ABC sCCEF AB, d POHEIS DM ari paralleliS quX OcCUF-
Lranc paladea  L. C; ponancut L, BC parallela. diametris. hays
tandem media propocoates et LV, M, lcilicet DF.
Dico B F C essc ad candem hyperVraI.
LV
Demonstratio.
DEE PUNCCA PP ducan-
cur parallela EI ips
B A, quxe lincam BC du-
clam ex B parallelam axi
lecentin C, O. Aancq; in.
TeF IO, C F medix pro-
porcionales FIG. crichrc
Parabola prourlib. depa-
culane Tabola 275. demonstracui
eAtrigitur ve quadracum
OHI ad CFI, quadrarum.
ica est BC line2 ad lincam
igicurre ADB eCcangulum ad receangulum ADB, ica est B C linea ad lineam
BC. hoc eADE. recca ad reCram D R: sed vE DF ad D E, ITA rECTanGUIUM F. DM
ad F. DMI recrangulum; igitur BD A reccangulum est ad reccangulum BD A, vE
eAt F. DM reccanigulum ad reccangulum F DMI. eA aurem F. DMI reccangulo xqua
le quadearum DF, exipla construccionesigieur vE BD A ad BD A, rcctangulum,
ita est quadrarum DF ad D F quadratum. Ouare ligyec BFC ese hyperbolam
cuius diamerer AB est cransuerta. Duod oporcuit demonstrare.
TKOFOSTFIO CEKXIV.
IEparabole ABC axis BD ad quem
Dordinarim sic Consticura AC, cui (IF
aequidistans F F, ductilque CI parallelis
ad axem, hanc rectangulis HIC laequalia
Quadrata OK.
DicoKEK eNe ad candem hyperbola.
Demonstratio.
ETanc CK lineis aequales GF, _ AF X.
qualis FV; Donacurque VM aequidistans
AC. Ouoniam rectangulis FT C I Xqualia lune
quadraca GK, hoc estrectangula LGK, _
quadrarum GT. aquatur 2 rectangulis HOI
ex GTII simul lumpris; e idem quadracum
CT hoc elt rectangula MI C+ I XqUenEuE qua-
dracis OK, de rectangulis MKI id cA M L G
isicur rectangula ML I, hoc CA LIK, aqua.
lia luncrectangulis OIFI. eA aurem FII, linea
ad lineam FIL. veb rectangulum ATC ad AIC.
rectangulum, igicur eriam M R I rectangulum
est ad rectangulum MRI VE AIC, rectan-
culum ad rectangulum ATC; puncta c erga
KK sunc ad hyperbolam. Ouod Fuic demon-
Aramdum.
PRO.
EBCOD ASAES iCASI
BG. sed quadrato F C aquale CM LB E recrangulum, hoc est L. F. G, hoC est A DB.
47.D0
con
versa 36.
Buins.