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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 75, page id 1815201908:0132
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cipt
1)d
oroin
Dor
DUS
risse
3
M el
C
Vale
eioA
racio
Mad
1dC
F ilII
reio-
MIN.
 teto
ecc
EDel
e
e
erio
ad
TCK
: d
hy.
onis
CK
(11X
GEOME FRTC F
quae dimidiaea estrationis AB ad G FE, criplicaca racionis L M ad OFI; quxe dimi
diaca estracionis B F ad CrII. Ouod erac demonstrandum.
eROPOSTTIO XXZII
Vancicas ex quocuis conciue propercionandus componta; a
aliam ex parinutet cerminorum ciuldem leriei producta contla-
cam, mulciplicem rarionem habet proporrionis primx ad secur-
dam, exquolCess Alcerurra quantitacum componitur.
Demonstratio
Donacur terteslationis alicuius, constiruere quancirarem AB, _ series vlcerius
producta conticint quancicacem B C; HOC EAIEN PACEO VE verague pari nUMerO
constecrerminorum concinue proporrionalium eiuldem serici producta; verbigraria
Si numerec AB quancicas terminos octo conrinue proporcionales, de BC cocidem
eiuldem serier productae; dico AB ad B C, octuplicacam habere racionem ejus qua
AD ad D E. Cum enim rora series rarionis AD ad DE, pergac vniformicer ex
concinue ex luppolico rsque ad C, de linccorrermini eiuldem loriei in AB, quoclune
in BC, exempli causa in singulis octo; habebic erso prima AD ad B F, octuplica
cacaestracionis DP ad P HI, id est rarionis AD ad D F: quare cum rarIONCS A D scrrs
ad BF, _E DF ad F C, octuplicaca sinc eiuldem racionis AD ad DF, CrIEVE AD
ad B F, SICD P ad F Ci; codemmodoCriE vE DB ad F G, Sic F FI ad CI, & Sic devir. 9uin-
cereris. Duare omnes bancecedences, id est octo termini qui constituunE A B, (C h2- 3i.
bene ad omnes consequentes, hoc est ad octo cerminos qui consticunne BC, vevna
antecedens AD, 2d unam consequentem BF. Onare cum AD ad BF, rarionem
habede octuplicatam racionis A V, ad D F; habebic quoque AB ad B C octuplioa.
cam eius, quam habee AD ad D P. Ouod crac demonstrandum.
 L LL LC. 1
KDTOSITIC
TT
cescres comnue Ploporttohales AD, BD. C B, medialine B;
AED: rurlum incer AV, B, modia liCLD, a ine BB LD, media
sic HD: _hoCcpet Mal:
Deo ellere AB ad BC. IAC au De3 aA da BEI, a.
monsraio
Vminter tres continuas A D, B D. C D, medix SInE CD, E D, erune AD, C D;
BD, FD, CD, (vE PaceE ex clemencis) omnes concinux proportionales:
proindeque eriam cA G, G B, BE, F C CTUM CMMICA PropOrtiOnaleS: ergO A CTC L. Huius
ad EB, VEBR ad F. C: e componendo ac per convertionemracionis AB ad A Cm
ve BC ad B F. Tsicur alcernando AB ad B C; vE A C+ ad BF: Deindequonian
AD; CD, BD, L. D; lunc continua, AD cAt ad CD, ve BD ad L D: Duare
Si incet AD, OD media sIC F D, _ intel BB; LB, MCI HB, PatCE CKCC-
enEIS esse AD ad FD, vEBD ad HID. acquicum AD, FD; ED, sinc conci-
nuaes AF eA ad FC, VE AD ad Fi D. per r. huius. EE CUIm BD, ETD, FD SincCOn
cinuae eciam BFI eAt ad HIF, ve BB ad HB, hoc cM (scurran oen d H
versonem