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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1 qualis relinquatur perfectionis, duc quadrantem in 10 fit 30, duc 12
in 7 fit 84, detrahe 30 ex 84, relinquitur 54, divide 54 per 9, reſidu
um 12 & 3, exit 6 perfectio reſidui.

Si quis dicat propoſitis argenti pondo 50 & dodrante perfe
ctionis 11/18, uolo partem aſſumere, & igne perficere, ita purum ar
gentum, quod relinquitur additum reſiduo, efficiat ipſum perfe
ctionis dextantis & beſsis unciæ pro libra, ſeu 8/9, divide 11/18 per 8/9 exit
11/16, duc in pondo 50 cum dodrante, fiunt pondo 34, unciæ 7 1/8, hoc
igitur erit aggregatum conflatum ex argento puro & reſiduo. De
trahe igitur 11/18 ex integro, relinquitur 7/18, detrahe pondo 34, uncia
7 1/8 ex pondo 50 cum dodrante, relinquuntur pondo 15 unciæ 6 7/8
(pondo enim uncias continet ſub hoc ſenſu, quia uſui ſeruimus o
cto) divide per 7/8, exeunt pondo 40 unciæ 6 1/4, & tanta pars debuit
igne purgari. In ea enim erunt puri argenti pondo 24, unciæ 7 /78,
quæ addita reſiduo, ſcilicet pondo 9, uncijs 7 3/4 conficiunt pondo
34 uncias 7 1/8 perfectionis dictæ.

Quidam miſcuit uncias decem auri perfectionis dextantis, &
partem perfectionis dextantis cum dimidio, & aliud perfectionis
beſsis concreuit maſſa perfectionis dodrantis unciarum octuagin
ta, quæruntur pondera reliquarum partium, ſubtrahe 10 pondus
ex 80 pondere, relinquuntur 70 perfectionis 17 5/7, inde detrahe per
modum ſuperiorem, & relinquuntur 3 2/7 & 1 5/7,

212[Figure 212]iunge ſimul fiunt 5, dico ergo, ſi 6 producit
70, quid producet 3 2/7 & 1 5/7, & inuenies quod 1 5/7
producet 24 & 3 5/7 producet 46, qui iuncti faci
unt 70. Igitur aurum perfectionis dextantis
cum dimidio fuit unciarum 46 aurum perfe
ctionis, beſsis unciarum 24. Reliqua interro
gata diſſolues per regulas Algebræ, horum
modo.

Propoſitio centeſima ſeptuageſima nona.

Si duobus totis duæ portiones ſimiles abſcindantur, ab eiſdem
denuo, & abſciſsis proportionibus partes eædem auferantur, denuoque
ac denuo, quoties libuerit à portionibus, & à reſiduis ipſarum
quantitatum partes eædem auferantur, erit reſidui ad reſiduum, ue
luti totius ad totum.

Co^{m}.

Sint duæ quanitates a b & k l, & abſciſſæ duæ partes ſimiles ex
utraque b c & l m, & ſit propoſita aliqua proportio, quæ ſit h, &
ſumatur portio b d ipſius b c, ſecundum proportionem h, & ſi

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