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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 601, page id 1815201908:0658
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ripsi
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id
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Ext
Et Y P E R B O Y
601
in ratione quadrupla: quia vero F cerminus est prosressionis A B ad AC, _C. procC.
denciuMMTacone GHAaBIICaLLC Wguogdecems e proseion pluton
in ratione guadrupla, ex GF planum coriseriei aequale: vnde C: C planu, (I 1C pFI -
musseriei cerminus ad religuum R F eA ve cera adrnu. Nam vel pacec ex construct. 2.
propol. 80. de prooressionibus, primus cerminus seriei magnirudinum in ratione qua
drupla, eAt ad reliquam seriem veprimi cermini qui est A, e lecundi qui cA I, a
rencia, ad secundum terminum, hoc es ve z adr. eroo arario R C ad CFB criplica. 2 ENcon
ca raciohis est NF an C, sa est AB ad. AC, criplicacam habcE LatlOI LC al huus.
_. F. Duoderac demonstrandums
Scholion.
Qniene Lector, ex hac vltima propositione clare perspectum hades, Quo lendebant praeceden.
res propositiones, scilicet ut aliquaratio posset inveniri etiam per stones ex hyper-
bolas exhibendi anas medias proportionales inter duas a (signatas quantitates; quod profecto
successisset, hanc alrimam propositione problematico more proponere soluere aeque feliciter
licuisset atque priores resoluiae ac demonstrata sunt. Certe prima fronte remintuenti, facilior
lonce videri posset ratio exhibendi terminum proeressionis quadruplicatae rationis, quam tri-
plicatae vel saltem non minus facilis ac racionis duplicatae terminum eometu inuenimus.
lonce tamen aliter rem curiosius incuenei apparet; interim viam aliquo  uimusribii
Et. scilubet, viteriore conatu eo pervenire studeas, quo nobis pondum licur.
eR OBOSITLO
2=
11.
Ociris alympeoris AB, BC, AY BCIDOI DL eibuluIs I E FC
alympeoco paralens; Aac IlCMeatamer L, LC. DeindeIKme-
dia incer HC, L C. Sennque L. M licaa Piopoenanst ; H1O:
e NO media incer L. M, IlE ex lacPe al. alea ae protet.
Sionis huius terminus ponatur P O. iuvvV
1101
mDico PO Forername duabus mediisincer Destl.
Demonstratio.
) Vomam DF, FG, FC cune
Eut platioCCa qua 1+6, LR.
C, eciam lunc in concinua, Plantunt
HIC duplum est plani ILR. 1SICM
planum D C duplum es plani HR.
sed quia FIG, LMI, TR IOHCMACOI-
cinua, planum FK duplum cst pla-
ni HIM. ergo planum Des Guacu
plum cA plani FTMI. Ergo proerento
Planor DCHM. 80. Proceate in laciolie quadrupla quae cerminatur in l.
SECIHO PTAHOTHI F K, LO, AC. LIIIIITEE PEOCEAIEI FaTIOIe GUAMMPTACCTMIatuE
Plau LH. Ica, Verehabe umm nmmum proscessonum. cerm, plana, Heme
DerLR. alenabem d cosetonestola, oc cplata .atCem eo ve
Diatum Des duptum e pa LR. cist a plaum Des alpium plahit. f. (. C188 sression
racio DF ad PO; duplicaca eA rarionis PO. ad. F C. c180. L CH Md. 6, 9114045
medijsinter D e FC). Quod erac demonstrandum.
88E
Lconinux, planum DG D aequa-
19. hit
Deinde quoniain FTG, LR. F. C sunc in continua; plana FR, TC X. quantur: Ccd;
GHIaHB.LMi LKluncin concinua, planum IC duplum cst plani IM. ergo pla-
huM FK aopIu CMBIAM TMT. led quia P M. NO. TK Cunc in concinua, planum
Lus adplum est plani l0. ergo planum FK quadruplum est plani I0. Frgo pro-
uremn S. Lat veco Guoam (Deapia ocendimus) planum D C+ Zguaeur bld-
HO ELC; d planum TIC duplum est plani fi K, eric quoqueplanim DC dupiaul
oouoeotsMatoa1019