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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1003, page id 1815201908:1060
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NOVLA CZLLHDRICA.
Demonsratio.
Dpunctum A in quo B A concingic peripherian
LbalIS K AF, ducacet Centro recta L. A.. Suo
niam exhypochenrectus elterlindrus, LA cxlindri la-
tus ae balim R A R rectum cric. CFgO L A ad F A, nOr
malis est. Est vero P R 2 eciam normalis ad B A. ErgO
T A ad planum cansens BGF A recta b cst. ergo
temidiamerer baseos est alcicudo prramidis BCF AI
Fodem modo demonstrabicur lemidiamerrum baleos co-
munem esse alcicudinem omnium prramidum, quarum
bales lunc plana rngulam tangencia, ap ex verO Centrum
L. cum erso pyramides xeque aleae, sinc rebales, crunt
omnes illae prramides jua solidum ongulam includens
componur ad prramidem cuius basis est quadracum R F.
alcicudo Cemidiamerer LK Cinc P A, ve omnia plans
ambiencia rrigulam, ad guadracum R F. led omnia pla-
na ambiencia, dempris duobus criangulis laceralibus, a
quancur c quadrato KF. Ergo omnes illx pyramides,
dempris duabuslaceralibus, hoc estcocum corpus rngulam includens; mulctarum
duabus laceralibus prramidibus, xquatur prramidi cuius balis est quadrarum, K I
alcicudo semidiamerer L K. Ouod crac demonstrandum.
PROPOSITIO LX
lx sine binx ungula aquales ac similes 2 cylindris recris abscista.
LGuarum alticudines Mucbalium diameeris pares. Circumlcribantur
auccilrerilqi corpoluaca tenum propolitionis pracedenris, (IC ve co-
rum lupelticiesau planorum cangencium numerum complecran-
cur; vniuis, exempi salla, luperticies continear decem plana cangenria, al-
reriusmille:
Dicoraque illa corpora visulas includentia, mulerata pyramidi-
buslaceralibus semver ese xqualia.
Ldco
i
Xprecedeni eltmanitesta, lingula enim aqualitur Pramia curs vaus cu qua
dratum diamerri balcosrngulx, alcirudo autem lemidiam eret eiuldem bale05. c. 17
13. 31. 2)C OEC) AE 2) E
Semonstrar
c 43. huius.
St 11
PROP OSITIO LXIV
Aexe sinebina vrigule à cylindris receisrelecrx, quarum alcirudines
nc diametris balium agates, vales autemme qualeicunque, ldc
aequales nimirum sive inaequales. I.
 ab ae
SICoCorporarngulaS CETA LIHICLLALALELALBUS pyFaMIAIOUS cri-
plicaram incer le habere racionem diameerorum balium ungularium.
 edatt onslat
DEmonstearumenim el, a corpora illa aequari pyramicibus que bales habene  asc tuiui-
Quales quadracis diamerrorum scracu valum, de alelcuames Cemidiameeris
pares. lsicur quam racionem habebune prramides illa, candem quoque habebune
corporai