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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 614, page id 1815201908:0671
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1
624
parabola as
sunt allarura.
a24. Buit
1. a
rabola
1u5.
HZDERDOLA.
Scholion.
Dracedentibus proposirionibus quae pa-
rabolam habent admixtam secantem
hyperbolicam lineam, 2 sus sum ordinarie
asemptoris hyperbolarum quae angulum
rectum contineant; non quod propositio.
nes oniversales non sint, es excludi de-
beani aliae hyperbolae, quarum asymproti
contractiorem, aut diductiorem recto, an-
culum constituunt, sed hoc eo consilio fa-
ctum est. ut commodior ratio iniretur ex-
planandi ficuras es scemata, imo vi con-
structiones ac demonstrationes propositionum minus essent impedicae: facilius enim est axem
o accommodare quam aliam quamlibet diametrum, quae diversa semperre-
perbolam in F. _ L, ConaML MCL a(y mpEOTOS AB, AC conti-
nences angulum rectum, demirrancur aucem ex D puncto incerlectionis
parabolarum alyisploris aequidistantes DB, DC, E G, FIBL R.
Demonstratio.
St enim ratio CM ad FIF, a id est
LATTad A C duplicaca bFIF ad LR,
sive CD: quare sesmentum MCHF.
duplum est sCGMENCI FTP, R L PeF 129.
huius. Amilicer quia rario D C ad PC,
id eAtKEL ad FG,c duplicaTA CA AC
ad A C, id est d F C 2d C M: Cegmen.
cum RBOF duplum est segtend
nuni F, C TTF 5 XQUALIA MIHE SEBIEHCA RL HF et
periri deberet, quoties asympio anau durarent. Interim quorsum haec materia vereat.
facile collici potest: invento namque puncto D intersectionis parabola cum hyperbola haberetur
ona e mediis duabus, quae postulari possent inter BP. C C nimirum DF; cum ostensum sit
rationem CC ad D F, duplicatam esse rationis quam habet DF ad BF: ac proinde ratio.
nem CC ad BF., triplicatam esse BP. ad D F. quod si quis procedendo per rectas AB,
BFT, TTF LR, RL, LM. M N, exc. terminum hujus progressionis assienare valeret, pro.
blema quod de duabus mediis proponitur expediret, ut paret remaccuratius consideranti. In-
rerim proprietates alias prosequemur qua non leue ad illud problema soluendum, subsidium
ROPOSIFIO, CFXTLI
Ferumi AB, AC sine axes parabolarum AE D, A F D secancium hy-
DicOOMI, GE, LIF, LK cAc quaruorin concinua analogia.
Plicata es F C ad M O: igicur ratio R L a LG, duplicaca cst KI ad TIF. etg0
racio K L. ac. P. Hl, cadem eAt cum cacione F. Hadt CP; Xt C F ad C M. Duoctue
demonstrandum.
ExY7Z. F C+ GML:VHdC CVER L. ad FII, ita B C ad CM: sed racio L R ad F G, Idu.
paio
R
IS oAS