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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 476, page id 1815201908:0533
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A R A B O L A
DicOF F ad C H duxlicaram habettationem eius quam habet AD
ad DC.
76
Demonstratio.
266. hio-
pstu
Fgmenem L1 da a legmentum
B C in CIIPHCACA CIE FATIONC AD
ad DC; sedrario segmenci AB ac
seomentum bBC compolca clt Cn
racione siL, au IL _ ex AD ac
DC racio igirur FF ad CFI.
duplicaca cAracionis ejusi quam lia-
DeE AD ad D C. Duod tuic demon-
ltrandum.
Corollarium.
neam C K. Veparet ex demonstracione.
PROPOSITIO CCLXIII.
metrr EB, CC, occurrences AD concingentiin F. e D.
Demonstratio.
Voniam AII, AF lincx ordi-
Lnacim ponuneur ad diamerros
BF, C C, d AD linca concingensi
linex FB, BF, icem DC. CC in-
cer le c aquales lunc. vnde ABFI
crianoulum eequalotriangaloA F. F,
_ ACI criangulum aequale crian-
gulo ADC: CA AUECI DE ABHI
criangulum ad criangulum ACI
SiCd ABFT segmentum ad segmentum AC Psigitur ex legmentum A B FI cRad (C.
Sencum ACT, ve AL F. criangulum ad criangulum AD C. Sed ratio erianguli
AF F ae Erlangulu AD C, composita est ex racione A F 2d AD, e ex racione
F F ad D C teC B B ad DC: isicur _ SEgMENEUM AB FI ad SCgMEnEUM AOI
rationem habet compolicam exrarione AL ad AD,  PB ad DC. Quod crat
demonstrandum.
PROPOSITIO CCLXIW
D ArabOlaS duas ABC, F G FT CuBCendanE reCFX A C, F HI legmeta
auterentes aequalia; rectis aurem AC, FHI diuilis in D _ Ibitariam,
ponancur diameeri BD, OL, ex ex B e C, demictantur B F, C HC nOr-
males ad AC, FII.
DicocsereBE ad CK, sic FHI ad AC.
TInc sequicur, ductis A F, CK normalibus ad diamerrum B D; rectam LF ad
CFI duplicatam quoque habere rationem eius quam obtince A I linca; ad H-
Darabolam AB C contingar in A linca A D: ducanEurG; ex A LnCX
quaeus AFI, AI, quibus in F a C bitariam dinilis, ponantur dia-
Dico ABHI Scomencum, ad segmentum A C P, rationem habere com
policam exratione A F ad AD, _ F. B ad DC.
DeMotm
(e s i     1    A    . . u u .  A  u H 1e 1    .   t H.  A   A t  t   p           a ua u  ) p u1 1