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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1012, page id 1815201908:1069
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VNEVLA CFLINDEL
7012
luncincer le, e ad rorum rectansm L. C BD, Vr parces diamerri ad le muruo vel
adcocam diamerrum. ergo e leomenta luperticiei rngularis, sunc inter se, vel ad to-
tam superticiem ongulxe, ve partes diamerri incer (e vel ad corant diameerum. Ouod
erac demonstrandum.
Analosia cum sphaera.
AdCdus ex demonstraris ab Archimede ex Pappoleomenea superhcici (phaerica
placs ad diamerrum rect cua. ellc incer se ve parres diametri. In hac ersoet.
iam pulcherrima proprietate, rngula _ pLIXTA CONVENIUHE.
eROFOSIIIO. LXXVI.
Vomnibus denique supetsetem ingularem convenire cum (phaerica
Demonstratio.
DOnaneur vngula DB C alcicudinem habens
diamecro parem, et sphaera LGHI R, Sineque
circuli maximi sphaerx aequales ongulae bal
D AC, secetur quoque sphaera quacunque de-
mum ratione per circulum F PFT plano recto
ad circulum maximum F CFT. iunganeur de-
inde P FTOFT. Diuisâ deindeD C’in L, Cc.
cundum racionem qua diuita eAt P. C in R, CrC-
Ataque I. A normalicer ad D C secetur vngula
plano L AB. ponancurque AD, AC. OAten-
dic Archimedes libro de sphaera, et cylindro
propolicione erigelima prima sphaericam super-
nciem FPTTR aqualom esse circulo qui radio
E FI deseribicur nos aurema demonstranimus
vugularem saperticiem ABC aequalem esse
rectangulo L CD, hoc CAD quadratO A C. PFX -
cerea Archimedes demonstraepropolicione eri-
gelima secunda eiusdem libri superkciem sphe-
riCam FTITC absciltam aequalem esse circulo
cuius radius es FT G. nos quoque ostendimus
superhiciem vngularem ABD aequalem este
rectangulo F D C, hoc est quadrato D A. DC-
nique ostendie Archimedes eotam sphaera su-
perticiem aequari circulo cuius radius F C: 8
nos demostrauimusceocam vngularem super-
Eeiem xquari quadraco D C. IgIEULEOTArngU.
nem quam cora phara lupertcies ad luas PaTTCS.
Manifectum igicur estrngularem superticiem d sphaera rocunditare nullo alio dif-
Ferre nih lecundum lineas expanlas et circulares: vnde A quis haCFATIONC ANTCTAE AP-
chimedem devenisse in nociciam demonstracionum quibus in maceria sphaerx d cy-
lindri vlus eAt, non riderur L rero aberraturus.
a 46. huius
b8. Sensi.
45. hivius.
iC ostendo.
laris superticies D ABC ad suas parres in quas est divila candem habet propoxtio-