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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 294, page id 1815201908:0351
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5I. huius.
20o huia
L. L IPSIS
At P NS F B TE, TUINEGUC AMIBE F FT. MVI
bisectX in R ee O, CrUNE+DB, X P
proporcionalicer (ecta in K et O; led
DB axismaior es quam KP. Ergore.
ctangulu BK D, hoc eA, veance osten-
di, quadrarum HIC, maius estrectan
gulo POZ, hoc cst quadtatO NS.
Ergo recta FTL maior recta NS. sed
HIC dupla cA iphuSHL, veance osten-
dis _ NR ex const. ipsuS NS dupl 2
elt. crgo HIO maior quam NR: quia
aucem N Rb maior est qua MNI; exie
HIC criam maior quam MN. Fodem
modo ostendemus FTC maiorem esse
quarumuis aliarum coniusatarum ex-
crema connectencibus. ergo HT C est
omnium maxima. quod cracprimum.
Duod aucem PEI sic omnium mini-
ma, discursu plane simili demonstrabi-
mus. Cumacur enim guauis alia diame.
ucm erorum coniusacio MI R, N O, ec cade,
quxe suprâ estadhibica, repecatur constructio. eodem modo ostendemus quadracum
FR nmus elle quadrato MO, d ectam FK minorem recta MO, ac proinde
FFT minorem quam MN. CH aurem CR N maior quam MN. ergo L HI criam
minor est quam N R. Regue ica demonstrabimus F FIminorem esse guarumuis con-
iusacarum extrema connectentibus. Omnium isitur minima est. Ouod erat secundo
locoostendendum.
e ROTDSITTOZCVTI.
reisi
Oniugacarum xqualium exerema coniunsentes simul Cumpexe mini-
me lunc omnium que quaunq; diamceros coniuzacas coniunsunE.
Demonstratio.
ac in A DC ellipK contUSAEa a qualeS R F, O FI. POna-
cur decem ee alia quanis diamecrorum coniurario, E F.
CH. dico Aneas gua exerema coniugacarum equalium
comingune, limul sumpeas minores esse lineis qud extre.
maalcerius commsarionis connectune. sunc enim F O, C F
quadraca equalia quadraris A B, B C, insoper dE F C li-
nea conneclencium minia, de FC maxima per PEXCC.
dencem. SIEUE C F G, C F lineae minores lunc lineis AB,
BC; eodem odo ostenduncuE F FL, ETF linex minores
lincis AD, DC: igicur linex, exc. Quod tuir demon-
ict
eROEOSITIC
ZCVIII.
IHC ABC CMpICDS axes AC, BD de F F vita
ex diamerris coniugatis xqualibus.
Dico quadraca A K, BK lirnul sumpra esse dupla quadrati E. H.
683. teninr.
cxbido
Demon.
trandam.
e e   p su ate  t ti  e te  e e a e  u te u e et t t  e  e e  e   s    t  t ue  site u ite   te  e p t et e  e      i it pr t ul