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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1013, page id 1815201908:1070
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2013
PROPOSITTOLAATII
lnem impono recensendis ac demonstrandis sphaerx acque vngula
alticudo s C Pal Maelto Balcos LH, lic aurem _e spherA FF PIIHI, ex
eiusdem Cemicirculi P. PH circumuolurione circa diametrum (ive axem
E HI, producta. Ducatur deinde IKE N perpendicularis ad F FI, per quam
ductis planis IDN, IIL, rectis ad F.HI, tam sphaera quam ingula in
duo leomenca dirimatur.
Dico leomencarngularia F. C L. II, HIK IL, candemincer se habere
proxorrionem quam lesmenta sphaerica LF F. H, THN.
Lanalogiis, si ostendero non minus solida legmenta vngularia ec lphe-
rica quam superticierum portiones symbolizare.
Daca (ic cylindri rectirngula P FOHI cuius baliS F PII Cemicirculus,
Semonsitaio.
Vngancur BBHE, TO, N O, O F. Ouoniam exhypochen css a quo abletm.
dirur onsula, rectus elt. erie PI recta plano F IFI, adeoque per defin. 3. vndec. an
SuluS. RIL rectuS. ergo RI est alcieudo rriangul LLR. Leus Gua L CA par
diaCErO E FI, EIvC FM, eric ec Y. I par IN, repacele raris in q1. huius
criangulum igicur L FK dimidium est rectanguli NPK. ac Prentete dequacur qua-
craco IK, hoc eAt rectansulo FIK B: Prramides ergda Bales lune rriangu-
sum F TK, et rectanoulum FIK F, alcirua adc CMMS KC aquales sunC.
Peaetere a legmencum vngulare F OT. LO, aGuatEPSCaC CuLUS BAIS LCCLAHS I- 3. huiros
IuM TIE R; alcicudoradius OF, siuc OHI. GuaceCum pla, cum vanstecca
susum ITE R, alticudo OFI, ad prramidem cuius BaIIS TCCtAHSCI. LIKL, alC
KO, rarionem habeac composicam exracione alcicudims, a  
e exratione balis rectangulae HI F R ad Va CC am FIRF, HOC CAD CxFa- Bi. SexII
tione FIP ad HIK, habebic quoque lesme state L.C L. lO ad prranidem
tionibus TTO ad KO, _ ITE 2d TTR.
Jam vero sermentum sphaericum TF NY concentum sphaerica superficie lL H. LC Archi
conica TON, aequacur ccono cuius balis est circulus radio lF. delcripeus, alcirud prop. 38. l. 1.
aucem radius sphaerae 11O. ledille conus a Con o Lactonenabet Cosn. e
KLIO cuiusbalis est rrians. L. IK, alcacu O tallodem composicam ex la-
litam ex racione alcirudinis FTO au aue RO, a ex racione balis ad balim, 3
ITER ad rectangulum FXKB, aCCH CL FatIONC HIF ad TIK. Ergo et SegMEn. CB. Seniim
cum
hoc cAd ex racione quadrari P P ad Gaal. HI HoC CH c’ex Fatione rectangut d 2. duodes
   s   p  e ospn