Casati, Paolo, Terra machinis mota : dissertationes geometricae, mechanicae physicae hydrostaticae

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1Ratio ad Conſequentem triplum aut qua­
druplum, quàm ad alium Conſequentem̨
terminum Rationis triplicatæ aut quadru­
plicatæ, etiam ſi propoſita Ratio ſubduplą
eſſet: ſic ſi fuerit Ratio 2 ad 4, triplus Con­
ſequens eſt 12. Conſequens verò Rationis tri­
plicatæ eſt 16: eſt autem maior Ratio 2 ad
12, quàm 2 ad 16.
X
Maior est
Ratio ad ter
minum̨
Multipli­
cem, quàm
ad termi­
num Ratio­
nis ſimiliter
Multiplica­
tæ.
Hinc infero maximum eſſe diſcrimen iņ
augendo potentiæ momento, vtrùm trochleæ
augeantur orbiculis, an verò trochleæ mul­
tiplices ex iiſdem orbiculis conſtituantur.
Si
enim trochleæ duæ S & R, quas nuperrimè
deſcripſiſti, binis prætereà orbiculis augean­
tur, ita vt ſingulæ quaternos habeant, mani­
feſtum eſt potentiam in K, quæ priùs mo­
tum habebat quadruplum motûs ponderis in
R conſtituti, factâ huiuſmodi orbiculorum
acceſsione, motum habere octuplum, vel
quæ priùs quintuplò velocior erat pondere in
S adnexo, factam eſſe noncuplò velociorem.

At ſi quatuor hoſce orbiculos non adijcias
prioribus, ſed duas alias trochleas ex illis com­
ponas, iam multò maior eſt potentiæ motus
cum ponderis motu comparatus.
Sint duæ trochleæ binos orbiculos haben­
tes A & B: huic autem tum pondus P, tum
funis extremum adnectatur.
Vtique poten­

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