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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1035, page id 1815201908:1092
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VN CVEA DAR ABOLTCA
Demonstratio.
Veaneur BL, B K: aCMICCHAE RF parallela
BFT. Octensu est lioro de ductibus criangulir
BFI C. ductum in criangulu K B FI, duplam ma- 1
snicudme producere Clus quod producic BHIO.
ductum in I RB cliangulum, ac prramistra-
bensbasim C teL rectangulum, de alcicudi-
nem BC concinet precer prramidem ex bali
Octendendum igicur CA COrpUS ex BasI CIT
XI, e alcicudine BC aequari mconicudini quae
relulear ex ductu superticierum BFTG _ ARV
incer sc. nam reliquum est commune, lcilicce
prramis ex rectanoulo GTTK, ducta in alcitu.
dinem B C: aequalicacem verd iltam sc octen
d0. Ouorriam AB dupla est ex constructione
rectae KI. Tgicurre octensum est in libro de du-
aibus B C:FI. ductum in AR B aequale DEO-
ducir Colidum prramidi quae sc ex ductu BO II cL
in IRB. Igicur paret prramidem ex ductu
BOTI in BHII, hoc est prramidem ex bas
CHL e alcicudine B C, xequari solido quodresulcas ex ductu BO Hin BHK A.
PR O P OSIFIO CTI
VIEparabola A B C habens axem B E, aequalem AL. OIMMMACI POTEE,
De hac AForchosona AC, cidem qi xqualis. Duclau e aes
disterC. F, ponatur C G parallela AF. DC.
niqueponatur quaeuis LI L parallela BF,
secans parabolam in IE, producta vero
IFI, VeLIL Ccaequalis B P. dimidia nimi-
rum ipsius AF, Ponacur AL.
Dico prramidem cuius basIS ANIL.
rectangulum de alcirudo AMI, aqualem
ese Colide magnicudini qua basim habet
AKM a alticudinem BF.
Demonstratio
DRxecedenci propolicione octensum elt psta-
midem cuius balS CATMIL, SIVC AM L rC-
etangulum et alcicudo A NI, x quari solidx ma-
enicudini que tic ex ductu plani A M Tin planum
AMTIF. demonstracum quoque, cst in Corol.
lario 82. huius, cidem Colido quod hc ex ductu
plani AMI in planum AMHTF, aequari Coli-
dam magnicudinem qua balim habec lcomen-
cum parabolicum AKM, alcicudinem BB. FF-
goprramis cuius balis est rectangulum IMI,
alcicudo AMI, aquacur Colidae magnicudini cu-
iusbatis est AK M alriru doB P. Cuod erar de.
monstrandum.
GTTK, _ alcicudine B C insuper prramidem
ex bas CFI, KI, e communi alcicudine C B
Su     s     a tu u ete e  e  te pte  te   pe este pti s tt ete e   ite es p   ee e t e e e  s   t s  e e   u  e s e  s   t  t e s tu se  a A B. 1