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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 223, page id 1815201908:0280
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1
ladeaio
di elaiu
A D SE CZLONES CONI
Demonstratio.
Vplex est calus; primus quo conus A B C cuius
BasiS BDC, habec B A perpendicularem à pc-
rimetro aliquo puncto ad vercicem crectam; alcer
dum linea a vertice ad balim ducta perpendiculari.
ter intra balim cadIE. Igitur hac sectio per cenerum
F, e apicem A, exhibens criangulum AD E: osten-
dere isitur oporrec, normalem ex A ad basim D F.
dermillaminera conum, hoc est inter puncta D e F
occurturam diameero DP. Dueantur enim BD et
B F; deinde ex puncto B ponacur B G, normalis ad
diameerum D F (cadec haec necellario inter puncta
D, F) _ jungantur A C. quoniam AB CX hyp. nOr-
malis estbali, recta F. B in bali ad iplam ducta per
dckin. 3. Ir. nOrmalis est. ergO quadraEUM A R, XqUAEUF
quadratis AB, BF: hoc es aquacrariS A B, BIS, G F. guadracum aurem AC quod bibid.
angulus AB Cb etiam rectus hcx quatur quadraris AB, B C, igICur quadratum A F
excedic quadrarum A C, quadraco G F. vnde quadrarum A F, xquale est quadracis
A G, CF. angulus ergo ACB, rectus cst, et AC Porpendicularis. Aequihac ducta
est  verrice coni de occureu bali crianguli inera conun. Perspicua ell igi Vericas
propolitionis in calu primo.
Eodem modo procedet demonstracio si loco linca A Ps veamur LInCA AD
Ouod si perpendicularis a vercice coniad coniba-
m demissa cadac incra conum re AF rurlum duca.
cur F G normalis ad F, D, innoacurque AG. Fodem
plane discurtu demonstrabimus quadratum A P X-
quari quadratis AO, P C; adeoque angulum AOF
rectum este, e AC perpendicularem ad balim
crianguli ADP, ex quo manifecta in hoc eriam calu
propolicionis est vericas.
DROPOSTTTO II
Acerum quadraca cuiuscun que crianguli
in cono lcaleno per axem tacti aequalia
lunc quadraris laterum cuiuscunque alierius
crianguli per eundem axem.
Semonstratio.
Cc enim ABC. conus lcalenus cutus dAls BL.
per quem hiac quaenis sectio BF. F: tiac aurem
AB C criangulum aliud sectum por axem BD. Di-
Coguadraca AB, BC, quadraris BF, BF esse x-
qualia, quadrataenim AB, B C octenla sune libro
quem de lincarum pocenciis scripsimus, aequalia c-
sc quadraris AD, DC, _ BD biS sUMPEO; AE CF-
iam eodem discursu octenlum est quadracis BF,
B P aquari quadeaTA FD, D F vna cum quadrato
BD bis Cumipeo: isitur cum PF, A C linCx C2-
rumque dimidix FD, DF, AD, CD SnE inter (C
aquales, patec verieusdemonstracionis.
Corella