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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1203, page id 1815201908:1260
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OV ADRA TVYRA CFRCVEI
Demonstratio.
Voniam P. C, axis ellipleos ponitur maior
Ldiamerro BD. isicur rectangulum R IG
ad F. A C rectansulum maiorem habebicratio-
nem quam rectangulum BIID ad B AD rC
ctangulum; vnde quadrarum FHI ad M A, qua-
deacum maiorem habecracionem, quam quadra-
cum FFL ad N A quadracum. minor isicur est
AM quam sIC AN; vndc _ SCCtOF FMT AF
minorest lectore C AINC. Quod tuic demon.
Arandum.
PROPOSITIO CXVII
IIdem poliris: Ouod R ellipHS EORC,
LcirCUIONON OCCUTTAE, _ AO, AR iun-
SanEUT:
Dicolectorem O A R. maiorem esse lectore C A I.
Demonstratio.
DRoducta AN IM L, AUCATUT C F, OT. cric igicur criangulum AC L Xquale
TC A criansulo, adcoque d 9ST aequale PS A criangulo. cAt aurem crian-
sulum AFS maius sectore F AV. Igicur eciam criangulum 1ST maius cA sectoro
eodem F A V: sed eriam criangulum S A F maius est sectore V AN. Ipitur crian
sulum O A Y maius es sCCtOTC P ANY, _ a ForriOri EOTUS SeCtOT O ATYC
maiorsectore F AN. Ouare, de sector O A R maior eAt lectore C A I: ostensum
enim est dimidium vnius, alcerius dimidio esemaius.
eR OPOSLTIO
XlX
IIdem poliris:
DicoGuaae pCalinea OYR e ciculast C. Nl incercen
ptam, elle convexam.
demonsita.
superticies alicuius segmenri quod aliquories sumprum adxe quar segmencum arcus
circularis ex segmentum arcus elliprici, Secundum ca guxe libro de elliph explicara
(unC) sicque illa seomencut arcus C. V, producta deinde A C in X, dividacur sector
OAR per seomencum OZ, cric enim O X mensura quae commensurabic scomen-
cum, sectOris O AR quoniem sesmencum arcus V C commeural L’Allcemen.
CUM, CUmGUENOTA sEFaCIO sESIMENEI C V ad Z O SeBMENEM, CrIE qUOquC NOTAF2
tiolesinenci CN ad seomencum OP: eAt vero sesmeneum OY Mm au
sesmenEO CN: Sc igicur sectOr C A V cerria pars verbi graris SectolC HI, a
hac V Z aequalis CV, _ ducatuT AZ X. cruncigicur seementa O Y, Y T maiora
quam nclesmenca CV, V Z, Z N, ablacis igicur cribus illis scemencis 2 scomencis
duobus OY et Y F remanebir adhuc aliqua pars convexa iptius sectoris O AY.
Quod tuic demonctrandum.
niam arcus CMT commensurabilis est arcui ONP: InvenIAEUE MCMII.S
Loux verumque commensurer (mentura aurem de quà loquor non linearis est se d
S  .   t i    .   .     e t.        te e s   . .        t 1   e       te         atus