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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1cum hoc ſit exactior illa pars exemplum, ergo habeo 2 3829/12566, quem
uolo certa ratione ad minores diuiſiones deducere.
Deduco pri­
mò totum ad fractiones ducendo 2 in 12566, & addendo 3829, &
fit 26961/12566, multiplico 12566 per 9, quia proportio unius ad alterum
eſt fermè, ut 9 ad 4, & fit 113094, multiplico 4 in 28961 fit 115844,
hoc igitur eſt maius, igitur proportio 28961 ad 12566 eſt maior
quàm 9 ad 4, detraho igitur 12566 ex 28961, relinquitur 16395, de­
traho 113094 ex 115844, relinquitur 2750, diuido 2750 per 16395
exit 55/328 addo 2 denominatori fit 55/330, quod eſt 1/6, nam iſtæ additiones
paruæ præter quòd parum uariant quantitatem etiam dum ad ex­
amen reducuntur, nihil impediunt, detrahe igitur 1/6 à 9/4, & ducendo
per 6, & detrahendo 53/23, duco igitur primos numeros ſcilicet 28961/12566
mutuo in 53/23, fiunt 665998, & 666107, ita uides, quod proportio
53 ad 23 eſt paulo minor, quàm 28961 ad 12566, & æquiualent 27/23
& 2 3829/12566.
Co_{m}.
Propoſitio centeſima quadrageſima ſecunda.
Denominationum incrementa ex extrema cognita inuenire, &
conuerſo modo.
Quidam per uſuram rediuiuam fecit 40000 coronatos ex 40 in 40

annis.
Quęro qutana fuerit uſura, & quando habuit 1000 coronatos,
quidam uellent ſoluere per regulam trium quantitatum, in qua com­
mitterentur maximi errores.
Et in ea multi ſunt modi, & omnes fal­
ſi præter hanc uiam nulla eſt uera, adde quòd uellent multi per ſor­
tem inuentam ſoluere augendo per ſingulos annos, quod adeò
difficile eſſet, & penè foret impoſsibile.
Ideò diuides 40000 per 40
numerum ſortis exit 1000, igitur in 40 annis unum fit mille, ſunt
ergo 40 denominationes ab uno, quarum quadrageſima eſt 1000,
igitur uigeſima eſt <02> 1000 |ſcilicet |31 3913/6283, igitur decima eſt <02> eius

5 3917/12566 huius radix, erit quinta quantitas 2 7/23, cuius <02> relata prima,

erit proportio 1 13/70, cuius quadratum eſt 1 1889/4900 ſeu
1 67/165 pro ſecunda quantitate, duces ergo primam,
quæ eſt 83/70 in quintam, quæ eſt reducta ad mino­
res fractiones facilitatis cauſa 53/23, & habebis ſex­
tam quantitatem 2 118/161, duco etiam quintam quan­
titatem ſcilicet 53/23 in ſecundam quæ eſt 232/165, & fit ſe­
ptimi anni quantitas, duco igitur ſeptem anno­
rum numerum, qui eſt 3 14/61 in 31 38/61 fit 102 992/6283. At in
ſex annis additis ad uiginti, fit tanto minus, quan­
to 31 38/61 ductum in differentiam ſeptem, & ſex an­
norum quæ eſt 60/121, fit ergo 15 35/492. Quia ergo