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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 854, page id 1815201908:0911
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DY CTVS PLAN
Constructio ex demonstrario
DVeaturrecta B P. per cenerum circuli cui sic aequidistans A D; conveniens cum
contingence BN, in puncto NV. hanc aurem rectis A C, aequales recte C FM rC-
ctisaucem A I constiruancurxquales I F LI. divisis denique bitariam rectis M FI, tiane
iplarum dimidiis a quales recte RP. X R R, candem F. M tanc xequates L. O. Dico
imprimislincas OO, e L I, Fore parabolas. Dico insuper corpus ex duetu O L. su-
Perhcici in sciplam aequari magnicudini super bali PC consticurx, habenei alcicudi-
nem parem linex AC. Primam isicur parrem sic demonstro. Ostensum est lincas
CTe COrranslaras in rectas, qux a linea C. V incipiunc exhibere parabolas rireua-
los. insuper eriam demonstrauimus vircuales illas parabolas, s mediecas iltaru linca-
rum applicetur hinc inde ex punctis RR, carum medierares in punctis scili-
CCELI _ K R producere Formales ac verasparabolas I. K. oltendimus precercare-
Aas AC, hoc est G, OT adiunceas reccis R P, Formare eriam veram parabolam
OO; luncisicur verx parabolae 0O, ec I. K, lincviprimam isicur parcem Cutticien-
cer demonstravimus. R cctac ieaque secunda, Scilicec quod magnicudo habens balim
PC, e alticudinem AC, aequalis sic quancieaci quae resulcac ex duccu plani OL in (0
ducci: hoc aurem manifeltum hec hiac ratione. Ducacur ex quouis puncto Ci recra
COxequidictans AP. concingenci, ee simul ponacurrecca A i, eric icaque, re osten.
dimusa quadrarum AC a qualc recransulo  AC, hoces recransulo lub P C, de
 AC, polica est aurem ex constructione linea F MI, hoc est OF aqualis lincq AO.
Tgicur li hac CT parallela AP, OP. quadracum equale cA C, P Y. reccansulo. quam-
obrem per propolicionem quadragelimam quineam huius libri eric OC. planum in
se duccum producensmolem illi parem quam exhibet balis PG, ducra in alcicudi-
nem AC. Quoderir laciendum.
Corollarium.
Voniam demonstrario communis est non Colum segmenco AB C, veruim eriam
LAP. C, Tegmenco. Hlinc eoram superticiem PCi, ducram in alcicudinem AC.
produceremanitestum cst quancirarem xqualem illi que cmersic ex plano LO du-
ccoinse, parrem scilicet P. O, gux scgmento AB C connenie, in se mulciplicacam
reguarimaonicudini quae habet basim P C incercepeam paratlelis, incer N B, A C,
consticucis, parcem limilicer L. O, qua leomento AD C convenie in sciplam du.
cram, equalem cAe moliproduccae ex bali P Cn collocaca incer parallelas A C, d P. V,
modo aequalis verique derur alcicudo AC.
ponstra
itc.
Per de-