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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 626, page id 1815201908:0683
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AYPERBOLIA
PROPOSITIOICLZZZII
Aex hypertola aliam exhibere aequalem cuius asomproci darum
Ctcat dde ta
Conotuibe cumonstratte.
1. dC
131.
Perele-
CAbid.
ETE ADC hyperbolae alympeori F D, DF: angulus dacus V Y a oportententii-
berc hyperbolam, aequalem datae AB C, cuius asympeoci, darum angulum V l’a
Contineane. Sic prime dacus angulus V L a minor angylo si DF, lyperboIx ABC
axis ponacur DB, ex ad illum ordinacim A C, percingens ad asymprocos in R ec fi.
Super fi. B seomentum describatur, circuli coninens angulum equalem V P a: qui
cum minorponarur atisulo P, D F, cader bscomencum delcripcum supra D, 2dc0.
que Ci aequidistans A C legmencu circulioccurrer in puticto quodam C: rungan-
cur isieur (B. CB. FF; actaq; per B concingenci BI, aequidistances ponantur
T. KIOcCUrenceS ABC trpertiola in N, axi DB in, M, rectae TTC in O: hanE.
quc M lincis aequales OP, OO: dico P, 1, . esle ad hyperbolam, aequalem
ABC, cuius asympeori E G. C F dacum obcinent anculum. cum enim ED, F F, IB.
exc. aequidistene, ve rectangulum DM B est c ad rectangulum DM B, SCCOYFC.
etangulum est ad rectangulum, CO I: sed Ve DM B ad DMB, SIC MN quadracum
adquadratum MINid est OP quadrarui ad quadeacu O Pigitur reC OTrectagulum
ad rectangulum GOT, Ec quadrarum OP ad quadrarum OP, huc OO quadrari
d1. 9. 12. Ex ad quacracu OO: punctaigitur dP FO Tune 2d tispotbola enius aBmproci, OF C P.
5. huius.
26. ht
quam in c P concingic Z R. quia vero G) D, OR RH aequidictane, cecta  L AB
aequales lunc: unde e criansula contingentium CIL. XDB, aequalia Cunc: quare e
(17+. hu. hyperbole  IC, AB C F aequales: angulus aurem F G F dato V T a per constru-
ationem estaegualis, dare igitur hyperbolae, ec.
Sic iam angulus dacus S F V, maior angulo F D D; Producaturque S F in a an-
SIs. huius. Gulusigitur VTa minor est angulo H DE; per constructionem isicur primxe par-
tisshuius, extibeatur hyperbola equalis AB C cuius asmproth atigilum obcineane
VTa. Svilla PFO ex asympcori D Ct C F. Produeaneur DC In Y. d F O in inh.
nicum: C Y aurem aqualis sC YZ iuneta Z Y HOCCHFEaE F C in X. Iguoniamipicue
C
T aequalessunE, d ParalleIX, rex quoque (xP, Z V aguialessune de paral
lelas, _ quia Z K in L bistecta eAt
 tique in Y biRecta CxIC: pohtissigieue
L, Parallelis 2B. Halie LLQuadratis aquali rectan gula Bdy _ Bcoy: CrUnED, Xa
h1. 9. 1. 15. adhhyxerbolam quam in L Comgit ZX. dhmpeocisune Y G, OFr constituen-
ces ansulum aequalem aaco. LV. Quia vero rethneula concindentium ZIG, Z ZC
equalia sunE, hyperbola quoque dP a aguasis e Ryperbolae P YO id est pet EoN
Aructionem, hyperbole AB C: dara ixirur hyperbole, et c. Quod erac faciendurs ul
PRC
penta.
enris.
1
6. huin
e e e oe 5areo e e ena33eat e