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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1008, page id 1815201908:1065
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1008
VNAVLA CTLLNDRLCA.
Domonstratio:
Nousa AC D plato per axem estindei
cranleunce, diuidatur in duo legenca
OBCDODCAiduCaL a L, Pel.
Dedichtas, Per preced. erunc lesmera illa x
qualia duabus prramidibus, quaru balessune
duo rectansula AD L, D AL, alcicudo aucem
communis CD Cemidiamerer. Ced due illa
Prramides aquantur prramidi cuius balis est
quadrarum AD, et alcicudo eadem (7D.
cum rectangula ADF, D A F quadraco AV
lincaequalia. Lrgo duo legmenca eBCD
GB CA, hoc CstEoca rngula A C D, equacur
prramidi cuius basis est quadeacum diamecri
AD, alcicudo aucem temichanciet eD.
Ouoderar demonstrandum.
Analocia cum sphaera.
E Cec alcera vngulam incer e sphxram analogin. Ex Aechimede e PapPO
habemus spheram aequari cono cuius basis est aequalis superhcici sptieex, alcicu-
doaurem radio sphxrx. Nos vero demonstrauimus ingulam aequalem eslepreami-
di, cuius balis eA quadratum diametri (quod propol. 45. huius libri ostendimus luper-
Ecicirngulari CAex qua lc) alcicudo aurem semidiamerer CD.
Corollarium.
S X propolitione colligo sequenscheorema. DaEa sic vngula, qux supra plano per
exlindri axem eran (cunre diuila sir in lesmenea duo eBCD, CB C A, ducacures;
BF normalis ad AD.
Dicolesmencum CBC D esse ad eoram ongutam repars diametri L D ad roram
diametrum AD; ad legmencum vero alcorum eandem habere rarionem quam DF
habet ad VA.
Demonstratio.
EctangIa ADE est ad guadrarum AD; VE ED ad AD. Sed ve rectaneu.
jum AD F ad quadracum AD, ica preamis, cuins BaES est A D F rectangulum
_ alticudo CD, est ad prramidem cuius basis guadeacum AD, alcirudo aurem CD.
269. huins. Frso pyramis cuius balis est rectangulum A D F, d alcicudo ED, hoc est a seormen-
cum ongutare GB CD, est ad prramidem cuius balis elt quadracum A D, _ alcitu.
570. vel d0 CiD, hoc. Csb ad tocam vngulam, DE F D es ad A D, PATI ArGUMENEO CX69. PFO-
erhmiu. babimus sesmenca CBC D, CBC A cAC incex LC VE D F eAt ad F A.
PROPOSITIO LXXI.
AAnis rngula à crlhtuorecs abeita, aupla ccpa ltsa
midismaximae; cuiusnalirum balis est (E. A C) CrianGUITUM MAKI.
mu, qualeclo. qut balis est rngulae, inseribi porelt; alcicudo
vero AM eadem qua rngulae.
Demon.