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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 461, page id 1815201908:0518
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D
C.
tem
DM.
si
um
49.
c0
co inlcribipollune. e concra li criangula AFD, BLC. tuerine maxima,
dico FF aquidistare AB.
Demonstratio.
ronium AB, CD. FD aquidi
LstanE, recta LI a XQUaTUF RF,
adeoquecriangula F AI, F ID aequa-
lia sunc criangulis, RBP, RF. C: l
igitur AFD criarisulum non sIC
maximum, sic aliud ACD, maius
triangulo AFD: Policaque CH P2
rallela AB, iurgantur BHL C: octen-
decur veprius, criangulum BIIC, X- 2
quari criangulo AGD: sed ACD)
maius est criangulo AFD, id eA ve
octendi, B F C, criangulum isitur B FFC maius quoque esteriangulo D F C: quod
est concra hypochelm. non ixicur AOD criangulum mantaum cM, sed AFD.
Duoderat primum.
Sinciam A F D, B F. C triangulamaxima, dico iunetam E dequidistare AB: GIM
vero; ponatur FHI aequidictans AB, iungancurque BFIC: celangulum igitur BFIC
maximum est eorum quae BF C seomento inlcribi possune, adeoque d maius BF. C
criangulo, quod abCurdum: non isitur P II aequidiltar AB, sed L L. uod cracde
monstrandum.
Ouod si A B contingat parabolam,
eadem inferri portune qua prius, cadem
quo prorlus est demonstracio.
rectir
PROPOSITIO CCXXIXS
in
Seo ABC parabolae inscri-
spcum erianculum maximum
ABC.
Dico illudmaius elle dimidio pa-
rabolae AB C. vt. 1ur
Demonstratio.
Dersciatur rectangulum ACF; manifestum
idieur est P C parallelogrammum maius eNe p2-
Fabola AB C. igieur e AB C criangulum, dimi-
dium scilicee parallelogrammi P C maius est dimi-
dio parabolae ABC. Ouod erac demonstrandum.
PROPOSTTIO COXKAS
TIcad ABC parabolae diamerrum AB, polIra OEdinatim C. D; IuL
aAtaq AC diuisâ in P bitariam, ponacur diameter B F iunganeurque
AB, CB.
Dico CA D crianeulum quadruplum esse rriansuli ABC.
B2
D A R A B O L A
Dico AF D criangulum, illorum esse marimum quae AFD Termen-
MA 3
Demon-
              a     1    e e   d      1   a  5 s ee e