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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 692, page id 1815201908:0749
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iotm
in
PIR A L1S
PROPOSTTIO. KLl.
iDGF, HLLK.
apeis aequalibus LF, BK; diicaneur diz-
Dico lempet LG, R L esse aquales.
Demonstratio.
OF ad LK, vi rectangulum A FB ad rectan.
lum AK B. vei deMonstravimus in libro de a para
2. Acqui rectansulaunc xqualia, cum exhypoch. AP
quales Hnc. L.180 X rectx F C, R L, aquales lune.
PLICAEVR SPIRALI
Impris in recta AC aequalibus AD, C. H.
contro A per Dae H, describancur periphe
Darabolam subrendat quaeuis recta AB, et
rix concenericae secances spiralem in O de L.
Dicoarcum GOD arcui HIL. eescam eAe.
Demonstrat.
DEE G _ L ducancurrect L  D, et L. I. PC.
adL. N per 19. lapp
ripheria FIO L S est ad arcuM L. SFI, VE AN
es DE AC a LLC
hoc est quia ex hypoch. XquacurHIC, AD, vE C A
ad D A, sed rariO C A ad D A, COmpONIEUE CX
racionibus C A ad HI A, _ HIA ad D A: Fr∞O
ratio peripherix IIOLS ad arcum L SFIcom
ponicur exhilce duabus rationibus C A ad FIA,
e TIA ad D A. Simi
acio ciusdem periphe
riae TIOLS adarcum GOD. componituE ex
racionibus peripheriae TTOI S ad peripheriam
DGO, (hoc est per FT. l. 4. Pappi, radii FTA ad
radium D A) ee peripherixe DCO ad arcum
COhoc est rectae C A ad FT A:) nam arcuS
cum BFB C, hoc cst per Fg. Pappi AD. 4. H A C ad G B: ergo componendo periphe-
orcus illi. uod crac demonstrandum.
Similieaso in eo posica, in veraque Agura lumpexe fuerunc aequales, in parabole
DP C est ad arcum COD re arcus C B Tad ar.
FC. R ln quaslmiler a quales etle demonllcavumus, incratisuraS luaS exiltunE, dt.
cus nempe incra spiram, linex ver o incraparabolam.
ria DOO cA adarcum GOD, ve AD ad BC; hoc cstve AC ad C D, hoc cltrt
CA ad FT A. Exii dem igicur rationibus componicur racio peripherix HOLS ad
arcum CS HI, ex racio eiuldem peripheriae HI OI. S ad arcum COD: quare can-
dem adriasue arcum pepea L S rationem habec. Eroo aequales CHE
nempe AL, BK  ALCH. Belphena Pet B. a lrercture amettos
DF, HIK. Tamarcus vero COB LSH Guoen aquales elC, Guam linex
PR
et anto ito ite tet  ee tete ite te e e te  se e e a e tat uta  i at te e e te at e te ut e se   ta ste t e t e    e 1 t  t  a    a  tat  t d