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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 607, page id 1815201908:0664
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a
3quo
De
It
AY P E AB OL A.
ad GK O C LETMENEUM, lEGMEnEO F L GR, PACCE F L. OC scgmeneum eriplum
esC leomenti DMF P. Ouod Fuic demonstrandum.
PROPOSITIO CXLVII
Adem ponantur quae prius: ductaque BH occutat spe
LtI: iungantur aucem D FI, III.
Dico segmenca conuexa DH, TIL esse aqualia.
Demonstratio.
Donacur HIP, aequidictans AB. cricigi-
cur perpraecedence legmentum HPFI
eriplum Cegmenci D MIIP. es aurem sc-
BIMENEUM a FCIR, aequale segmento
DMR BB IBICUIFIEOMENCUm DMR I, vn a
cu legmmento FLP R I, criplum est segmenri
DMHP.isicur IIPR Ilcomencum equalo
CA (ESMENEO DMKP: _ED R conuexum
xquale convexo KI.
Corollarium
CTInc sequitur: E D FI, FTI segmenea fuerincxqualia, d Pet HL L Cx BCenero
Lrectae eductae BFTK, BIF occurrences parabola u L a B, Punctis, C quibus
reCtE PONANEUE KI, EC, asymproco AB aequidistances e per D, recta ponacue
DOO parallela BC: quod BE, D 9, RL. lince in eodem sese decussenc puricto
O: vei F C, BF, DO in puncto 9. est converls peacedentis, ex qua demonstra-
ciomanitesta elt.
PROPOSITIO BLLVIII
Udent PolMesmenta AB, BC ooaDC Manpicto
rectum ansulum concinenres consticurae, aqualia fuerine, de ccenero
per B _ C PONanEuT DBF, DC F occurrences parabolxe in F de F, de-
MicEanEUTQ; FG, C. HI, AI; BK, CL alympeoro xequidictances:
Dico leGmenta MHC, AIHM, quadrupla esse Scomencorum AIR,
Demonstian.
111. 1 . 1. 11 1
lL
Laequalia, communes incerle.
Etiones linearum RFI, D F, icem
DMF C in eadem sunc cum A
puncto linca, b parallela DC
inde GP, MHL, AIC PTODOE-
eionales sunE _E d AIMH.
ALEP C sexmenca xequaliaiquod
crac demonstrandum.
607
Voniam AB, B C (CBMEnEA
Aihhh 2
t
A ti  ute ta et et   et    a s t t at  te ia te e este t ite  est e  ete tt u ut t e  pet  ee e e t so it   pi ete  s t i