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& medij ad mobile, ac medium, quod reſiſtit. Quarto ex motibus
imperfectis natura ſua, & non eſt uera miſtio, & hoc apparet in mo­
tibus uoluntarijs animalium, qui non ſunt neque æquales, neque perfe
ctè circa medium: ſed ſunt potius ſimiles uoluntarijs. Et ideo de­
monſtrationes illæ Ariſtotelis quoad uſum nihil iuuant nos.
Cor^{m}.
Propoſitio trigeſima ſecunda.
Omne mobile naturaliter motum, ſeu uiolenter uelocius moue­
tur in medio rariore, quàm denſiore. Maior quoque eſt proportio fi­
nis motus in corpore rariore ad finem motus in corpore denſiore,
quàm principij. In uiolento autem celeriùs perueniet ad finem mo
tus in corpore denſiore.
38[Figure 38]
A mobile moueatur in b medio rariore, & in c denſio­

re, igitur b minus reſiſtit, quàm c & magis adiuuat, quia
uelociùs mouetur: igitur duplici de cauſa a mouebitur
uelociùs in b quàm in c: & quia per corrolarium trigeſi­
mæ, & præcedentis proportio finis (ubi æqualiter moueantur) ad
ſua principia maior erit in d, quàm in e: ergo per demonſtrata à Cam
pano poſita d prima, b ſecunda, e tertia, c quarta, maior erit propor­
tio d ad e, quàm b ad c quod fuit propoſitum in naturali.
Co^{m}.
Propoſitio trigeſima ertia.
Omnia duo mobilia æqualis undique magnitudinis, quæ æquali
in tempore æqualia ſpatia pertranſeunt in diuerſis ſubſtantia me­
dijs, neceſſe eſt, ut ſit ponderis ad pondus, quemadmodum medij
ad medium, proportio duplicata.
Co^{m}.
Sint duo mobilia a & b magnitudine, & forma omnino paria,
& ſint media c & d, exempli gratia: & pertranſeant æquale ſpatium
in utroque in eodem tempore, e dico proportionem ponderis b ad
pondus a eſſe duplicatam ei quæ eſt raritatis c ad raritatem d. Quia
enim feruntur æqualiter, nam in æquali tem­
39[Figure 39]
pore, ſeu eodem æqualia ſpatia pertranſe­
unt, erit proportio potentiæ a cum ſuo auxi­
lio ad id, quod reſiſtit ex c ut b cum ſuo au­
xilio ad id, quod reſiſtit ex d, permutando igi
tur d ad c, ut b ad a, ſed c ad d proportio rari­
tatis duplicat actionem, tum minus reſiſten­
do, tum adiuuando motum a, igitur proportio differentiæ motus
eſt duplicata proportioni raritatis: ſed proportio motus eſt æqua­
lis proportioni ponderis uiciſsim per uigeſimam ſextam ſexti Ele­
mentorum b ad a, igitur proportio b ad a ponderis eſt duplicata ei,
quæ eſt raritatis c ad raritatem d.

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