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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 372, page id 1815201908:0429
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P AR A BOL A
in FFpOnAEUEPeF FL xeguIaanS diamerro B F. dico illam axem ese. quoniam enim
Ehaini diameero B Fxquidileae, erica illa quoqe diamerer sectionis, de quia xequidistancium
cr. Desnii. F C, C M vnam ad Cbsbilccat angulos, bile cabic erb alceram, ad rectos: axis cigi.
iuo. cur sectionis est K B exhibuimus ergo, _c. Ouod crarFaciendum.
PR OPOSIFIO XXTV.
Mnis linea in parabId axi xquidistans, sectioni in vuocantum pun-
Demonstratio.
DOnacur ABC parabolE axis BD; e aliaqueuis ei aequi.
ailtans AC. dicos AC in vno cancum puncto fectionioc.
currere: Ha vero, occurrac icerum in C: d ponantur ordi.
narim ad AXeM RectE AF, CD: CFiE igIEUIF VE BF linca ad
lineam BD, AC F. A quadracum ad quadrarum D C; quod
feri non porest, cum AF, CD quadeaca aequalia sine
incer(e, (ob A D Parallelogrammum) _ BP. linea minorre.
cta BD. isicur AC diamecer, parabolx cancum semel oc.
curric: Ouod Fuic demonstrandum.
PROPOSITIO ZXV.
Mnislinca in parabcha, quae non est diameter lectioni occurrie in
a2g. huius.
rrhuius
Demonstrario.
OnaluE ABC parabOI~ axis BD, de linca
RD quae non sc diamerer. dieo illam sectio.
nibis occurrere: Ouoniam R D non est diame-
cer 2d eoqueaxinon aequidistac, productanecel
Cario illi occurrec in puncto quonis D (cum in
eodem plano existac) quod E D punctum Fuerit
DOCCUTTIE.
obus punctis.
Coroli
rima
45.
vuo catum puncto: ae gula cacem dalaquidi
Aac produeta quoque occurrer R Roduca
in F puncto, quod exera sectionem elt. viiu
KD F peiusneccslario occurric in punclo quo
uis F. ductaisitur ex F. ordinarim F. C hancpio.
porcionales BC, BD, BEI Policaque ad HI ol.
dinacim linca, occurrar ipEK D in Puncco quo
nis A. quoniam BC, BD, B FT POnunEur prO-
Polllehales, eric HID ad. DC, DE HIB ad BD.
e IID quadrarum c ad quadrarum D6, ve
TIB quadrarum ad quadratum DB, id est re
ETB linca, ad lincam BC: scd ve HID qua-
dracum dd quadratum DG, SC FI A quddracum ad quadratum C F: igitur MH B
linea ad lineam BC, SiC FI A quadracum ad quadracum CtF, vndepinelu 
est ad parabolam, et D K, linca 2xi non palaltetu tusue seccioni occurrie.
Si vero DR linea occurrar axi exrra seccionem, Pacet ance parabole occurrere
in puncco quonis F: ex quo ducca ordinarim linea R. C, hanc BC, BD, BHI
proporrionales, d ex HE duCATF EL A parallela E C, OCCUrrenS K D linex in A.
10
incra parabolam, ponacur ex D ordinacim DC,
_ per C diameter P F; occurrecilla sectioniin
o su pe e tate e tu e sue te ete ptt e pe e set ti  t  eit pt est te u pe t pit   ta tt t  s ta  et e pti e t te a t  e  et e ti e   te tt  et     tt  t e  l s e 
1. DCprO
cessionibus