Cardano, Geronimo - Opvs novvm de proportionibvs nvmerorvm, motvvm, pondervm, sonorvm, aliarvmqv'e rervm mensurandarum, non solùm geometrico more stabilitum, sed etiam uarijs experimentis & observationibus rerum in natura, solerti demonstratione illustratum, ad multiplices usus accommodatum, & in V libros digestum. Praeterea Artis Magnae, sive de regvlis algebraicis, liber vnvs abstrvsissimvs & inexhaustus planetotius Ariothmeticae thesaurus ... Item De Aliza Regvla Liber, hoc est, algebraicae logisticae suae, numeros recondita numerandi subtilitate, secundum Geometricas quantitates inquirentis ...

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1lemæo, ęquale eſt rectangulis ex b c in de, & b d in c e, igitur 1 quad.
quad. m: 2 quad. p: 1 eſt æquale 1 producto b d in c e, & producto b
cin d e detracto 1 communi, relinquetur productum ex b c in d e 1
quad. quad. m: 2 quad. igitur diuiſo 1 quad. quad. m: 2 quad. per 1
pos, exit 1 cu. m: 2 pos æqualia d e, & d e eſt æqualis d c, ut ab initio
demonſtrauimus, & d c fuit 1 quad. m: 1, igitur 1 cu. m: 2 æquantur 1
quad. m: 1, igitur 1 cu. p: 1 æquantur 1 quad. p: 2 pos.

Aliter ut Pacciolus, concurrant latera eptagoni b d, c e in a, & du
cantur perpendiculares a f, d g & c d, & ſit c e i ca 1 pos, & quia ut

a e ad a c, ita d e ad b c, erit ergo b c (1 posp: 1)/(1 pos) quare b f (1/2 pos 1/2,)/(2 pos) &
quia d h eſt dimidium d e, erit d h, & g f

71[Figure 71]
1/2, cum ergo b f ſit (1/2 pos p: 1/2)/pos erit ergo di
uiſa 1/2 pos per 1 pos, & exit 1/2, b f 1/2p: 1/2/pos
igitur detracta g f relinquetur g b 1/2/(1 pos).
& eius quadratum 1/4/(1 quad). igitur cum qua
dratum b d ſit 1, erit quadratum g d 1 m:
2/4/(2 quad)g c autem eſt compoſita ex e f, quæ
eſt 1/2p: 1/2/(1 pos) & f g quæ eſt 1/2, erit igitur c
g 1 p: 1/2/(1 pos), & quadratum eius 1 p: 1/pos eſt 1/4/(1 quad.) quare quadratum e d q̊d eſt

compoſitum ex quadratis c g & g d erit 2 p: 1/pos c a uerò eſt æqua
lis c d, quia, ut demonſtratum eſt angulus d c e eſt ſeptima pars
duorum rectorum, & angulus b c e ei duplus, quare cum c f a ſit re
ctus erit ex trigeſima ſecunda primi Elementorum f a c tres ſepti
mæ unius recti, ergo d a c 6/7 unius recti, d c a uerò 2/7 unius recti, quia

eſt ſeptima pars duorum rectorum, ígitur a d c eſt 6/7 unius recti: igi
tur c d eſt æqualis c a, ergo quadratum quadrato: igitur 1 quad. p: 2
pos p: 1, æquatur 2 p: 1/(1 pos) igitur 1 quad. p: 2 pos, æquantur 1 p: 1/(1 pos).
Quare 1 cub. p: 2 quad. æquatur 1 pos p: 1.

72[Figure 72]
Sit etiam angulus a duplus b, & b c dupla
b a: & erit per eadem proportio a c, & a b
ad c b, ut c b ad c a. Ponamus ergo ab 1, erit
b c 2, & a c 1 pos, & a c, a b 1 pos p: 1, & du
cta in a c fit 1 quad. p: 1 pos, & hoc eſt æquale 4 quadrato b c per re
flexæ proportionis diffinitionem. Igitur a c eſt <02> 4 1/4 m: 1/2, & ita
de alijs.

Per 42. pri mi Element.

Per 32. pri mi Element.

Per ſextam eiuſdem.

Propoſitio ſexageſima ſeptima.

Si fuerint aliquot quantitates ab una quantitate, aliæque totidem

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