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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1tato, & ita 64 habet rationem unius, & licet comparetur ad 2 rem,
& ſit ſextus ab eo, eo computato 4096 autem à 64 ſit ſeptimus, ta­
Propoſitio centeſima trigeſima ſeptima.
Rationem numerorum ex progreſsione declarare.

nem numerorum, qui uocantur multiplicandi, & componitur hoc
modo.
Ex prima componitur 1 & 2, faciunt 3. 1. 2. 3 faciunt 6. 1. 2. 3. 4
faciunt 10, & ita prima tabula conſtituit ſecundam recta ſerie nu­
merorum iunctis o­
mnibus ab uno.
Ter

tia fit ex ſecunda &
tertia, primò aſſumi
tur 10 in tertia, ut in
ſecunda, & ex 10 ſe­
cundæ, & 10 tertiæ
fit 20, & ex 15 ſecun­
dæ, & 20 tertiæ fit
35, & ex 21 ſecundæ,
& 35 tertiæ fit 56, &
ex 28, & 56 fit 84. Et
quanta fit ex tertia,
& ex ſe ipſa.
primum
aſſumendo 35 ex ter
tia, & ponitur pro
primo numero quartæ, & ex 35 tertiæ, & 35 quartæ fit 70 numerus
ſecundæ quartæ: & ita ex 56 & 70 fit 126, & ex 84, & 126. 210. & ita
quinta ex quarta & ſe ipſa, & ſic in infinitum.
Co_{m}.
Primæ ſuæ
Arith.
1 2 3 4 5 6 7 8 1 2 3 3 4 6 5 10 10 6 15 20 7 21 35 35 8 28 56 70 9 36 84 126 126 10 45 120 210 252 11 55 165 330 462 462 12 66 220 495 792 924 13 78 286 715 1297 1716 1716 14 91 364 1001 2002 3003 3432 15 105 455 1365 3003 5005 6435 6435 16 120 560 1820 4368 8008 11440 12870 17 136 680 2380 6188 12376 19448 24310
Regula ergo eſt, quòd binarius ſeruit <02> quadratæ, & quia nihil
eſt in eius directo, ſolus ipſe ſeruiet <02> quadratæ.
Ternarius autem
cubicæ, & quia in eius directo eſt alter ternarius, ille etiam ſeruiet
<02> cubicæ.