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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 862, page id 1815201908:0919
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862
aequales F F. F G, C D parer per propolicionem quadragelimam gulam huiusli.
BEI COTPOTAOR V, PS Z, t O PY, esse inter se aequalia. quod oportuic demonsteare.
PR OPOSTETO COXLIV
axes consticure: lic aurem CD linca xgualicer ab axibus dictans; ad quam
collocentur sicu subalterno HIK X HE MI parabolx.
Dicosolidum ex ductu plani C LI in planum M N emersens, duplum
esse quanticatis quae producitur ex superticierum HK, KM mucua mul-
ciplicationere lulcantis; live dico C H ductum in se lubalcerne producere
duplum ejus quod producie HK in HM.
DV. CFVS ELRHL
AcabOla A BC, D E F habean aequale lacus rectum ad axem consti-
L CUTUM, CInEque (VDAIEErNE PO(IEX, QuaS SCCENE A F, B F ordinacim ad
Demonstratio.
Prop. 257. P) Vetis C N quae aequidistent A P, hanc rectis FII, aequales OP, e simiticer lineis
LMI RanE aequales OD, libro de parabol2 a Osten sum CA R L, R FI, RG, _EKL,
RMI KN esse proportionales lineas. Inscper octensum b Cs, li rectis E P, HanC Xqua-
les HI, _ rectis NO, hanc equales I. MI, denuo lincas RL, IFT, ITP; _E RL, LM,
MO esseproportionales, ac proinde rectangula PK L, HIL L, MI, et PFL, M OprOPOr-
eionali esse; est gurem rectangulum P HI, MO quadruplum rectanguli IK L, cum
linex PFT, duplG SInE RL, ex lincE M O, duplae linearum LR; igieur rectangulum
FTT, LM, quod est mediumincer LK P _ P IT. NO, SCiliCCLINCCF VnUIM _ QuaLHOE,
duplum est rectanguli TK L. Quoniam aurem proporcionales sunc linex OK, FTR.
TR, _E RNF, RN, RP CrIE vE R G ad GFC, itA RFT ad FL, _ VE R N ad NM,
ita RM ad M I: proportionalia luncigitur rectangula G FF, M N _E FII, LMCum
rectangulis LIRM _E LK L: nam racio C FI, MN ad rectangulm FTL, L M com-
ponicur exratione C FY ad FTI, hoc est FTK ad TK, _ EX FaTIONC M N ad L M.
hoc estRM ad R I; ac proinde ve rectangulum GLTM NT ad rectanBUIUIM HKM,
ita FTT, LM cectangulum ad rectangulum TR T: sed rectangolum FI LF M duplum
estrectonouli LR L, ve paulo ance ostendimus; ergo eriam rectanrulum GHI NH
duplum est FTKM. Ouapropcer per quadragesimam quincam truius, lolidum ex du-
cu planorum C FI, MN exorrum, duplum est quancicaris que sc ex mucua luperh.
cierum HIR, KMincer le mulciplicarione. Quod demonstrandum Fuit.
ab
eproer.
Prop.