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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 646, page id 1815201908:0703
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HTY PF KDOL A
eR OPOSTSTO CCXH.
Erum praecedencem propoti
tione vniuerlalius placet pro:
ponere. Friangulo A BC inscriba.
tur quodliber parallelostamimum
DE F. Deinde ponatur guaeuis re-
cta linea ex puncto E, Scilicer EM,
a ductis C K quae aequidistentBF,
hac rectanoulis GFIl una cum qua-
draco, IIE aquale quadrarum G L.
Dico DL. L essc hyperbolam.
Demonstratio.
lac rectae F. F aequalis NY O que sic di-
uta in PP ve est divisa P F in punctis
FTF. hanc quoque rectangulis CFTIX-
qualia PO quadraca, cric NO9. para
bola: astumpea denique rectâ R S quX
aqualis sc CM, dividatur RS in TT,
ve es dinisa F F vel NO in punctis PP.
cruncrectis IK aqualesrcetX R Y cum
SIE FF ad F TT, VE CM ad SK; scd vE
F F 2d F FL, ica eAt ex Constr. S R ad R I
igicurS R est ad R Y, VE CM ad IR.
aequalesigicursunE R Z ∞ IK, cum SR.
CM aequales polieae sine, itaque rectis
PO hanc aquales TV; criam RLV
parabola eric, b cum sE R Y ad R F, ve
NP ad NP. tandem si hanc rectis RV
aequales V TX, cerir R X Xhyperbola.
ipitur rectangulum C tel hoc est quadracum T. V una cum quadraro IK, hoc est
R F producechyperbolam. sic itaque recta Y R lacuseransuersum hyperboleR XZ,
e AaCVE RS ad RY, ita E F ad E.Z. Dico rectas GT aequalesrectis T X cum
carum quadraca xqualia sine, eciam esse ad hrperbolam cuius diamerec D B, esséque
CT, CC ordinacim ad D B posicas. Fric enim ve YYR rectangulum ad cectan-
sulum XTR hoc est re quadracum Z P ad quadratum Z T, hoc est ve quadracum
CL ad C L, ica rectangulum Z HIE ad rectangulum Z HIF, hoc cst. Rincellig2
tur Da linea aequalislinca, L. C, rectangulum a CD, ad rectangulum a CF D. icagi
17. huins. D L. L d est hyperbola, _ linca C F ordinacim applicara ad DC. Flinc quadrata
aequalia recrangusis OFTI, ec quibuscum que quadraris LR producene hyperbo.
lam, modo quadtaca IK incer duas lincas C. P. MP quemcumque ariguloni con.
mencia parallela sine polica. Duodrniverlalicer placuir demonstrare.
PROPOSITIO CCXXI.
1s saeiita
abra  ece Qudam recta AB, ductis deinde paFallelis
SE tanc rectangulis C D P x qualia quadrata DF.
Dico B FF esse ad candem hyperbolam cuius AI B diameror elt.
Demon
ee ea