1eſt, ſi uolo duos terminos ſemel, & dein de in minorem, & <02>
cubica producti eſt ſecundus terminus, idem facio de minore in
ſe in de in maiorem, & accipio <02> cu. Exemplum, uolo duos termi
nos inter 2 & 3, duco 3 in ſe fit 9, duco 2 in 9 fit 18, capio <02> cu. 18. hic
eſt unus terminus, & ita duco 2 in ſe fit 4, duco in 3 fit 12, capio <02> cu.
12 pro ſecundo termino. Et ſi uolo tres terminos, duco 3 in 3 fit 9, du
co 3 in 9 fit 27, duco 2 in 27 fit 54, & <02> <02> 54 eſt primus terminus.
Item duco 2 in 2 fit 4, duco 3 in 3 fit 9, duco 4 in 9 fit 36, & <02> <02> 36, id
eſt, <02> 36 eſt ſecundus terminus, ſimiliter duco 2 ad ſuum cubum fit
8, duco 3 in 8 fit 24, & <02> <02> 24, eſt tertius terminus. Similiter uolo
quatuor terminos medios, duco 3 in 3 fit 9, duco 9 in 9 fit 81, duco 2
in 81 fit 162, & <02> relata prima 162, eſt primus terminus, item duco 2
in 2 fit 4, & 4 in 4 fit 16, & 3 in 16 fit 48, & <02> relata prima 48 erit
quartus terminus, item ducendo 3 ad cubum fit 27, & 2 ad quadra
tum, & fit 4, & 4 in 27 fit 108, & <02> relata prima 108, erit ſecundus
terminus, & ſimiliter ducendo 2 ad cubum fit 8, & 3 ad quadratum
fit 9, & 9 in 8 fit 72, & <02> relata prima 72 eſt tertius terminus. Habe
bis ergo terminos in continua proportione 2, id eſt, <02> relata pri
ma 32, <02> relata prima 48, <02> relata prima 72, <02> relata prima 108, <02>
relata prima 172, & <02> relata prima 243, quod eſt 3, & ita de alijs in
infinitum.
cubica producti eſt ſecundus terminus, idem facio de minore in
ſe in de in maiorem, & accipio <02> cu. Exemplum, uolo duos termi
nos inter 2 & 3, duco 3 in ſe fit 9, duco 2 in 9 fit 18, capio <02> cu. 18. hic
eſt unus terminus, & ita duco 2 in ſe fit 4, duco in 3 fit 12, capio <02> cu.
12 pro ſecundo termino. Et ſi uolo tres terminos, duco 3 in 3 fit 9, du
co 3 in 9 fit 27, duco 2 in 27 fit 54, & <02> <02> 54 eſt primus terminus.
Item duco 2 in 2 fit 4, duco 3 in 3 fit 9, duco 4 in 9 fit 36, & <02> <02> 36, id
eſt, <02> 36 eſt ſecundus terminus, ſimiliter duco 2 ad ſuum cubum fit
8, duco 3 in 8 fit 24, & <02> <02> 24, eſt tertius terminus. Similiter uolo
quatuor terminos medios, duco 3 in 3 fit 9, duco 9 in 9 fit 81, duco 2
in 81 fit 162, & <02> relata prima 162, eſt primus terminus, item duco 2
in 2 fit 4, & 4 in 4 fit 16, & 3 in 16 fit 48, & <02> relata prima 48 erit
quartus terminus, item ducendo 3 ad cubum fit 27, & 2 ad quadra
tum, & fit 4, & 4 in 27 fit 108, & <02> relata prima 108, erit ſecundus
terminus, & ſimiliter ducendo 2 ad cubum fit 8, & 3 ad quadratum
fit 9, & 9 in 8 fit 72, & <02> relata prima 72 eſt tertius terminus. Habe
bis ergo terminos in continua proportione 2, id eſt, <02> relata pri
ma 32, <02> relata prima 48, <02> relata prima 72, <02> relata prima 108, <02>
relata prima 172, & <02> relata prima 243, quod eſt 3, & ita de alijs in
infinitum.
At pro muſica, ſi ſint exhibiti duo numeri minores utpotè 2 & 3,
uelim tertium terminum, diuido 2 per 1 differentiam exit 2, detraho
1 pro regula remanet 1, diuido 3 maiorem terminum per 1 exit 3, ad
de 3 ad 3, fit 6 maior terminus. Similiter capio 3 & 4, diuide 3 mino
rem terminum per 1 differentiam exit 3, detrahe 1 pro regula, relin
quitur 2, diuide 4 terminum medium per 2 exit 2, adde ad 4 fit 6 ma
ior terminus. Stiphelius autem erat in ſua regula, nam ſic 12 4 & 3
eſſent in continua proportione muſica ex ſua regula. Dico ergo,
quod ſi proponantur 5 & 7, & uelim muſicam proportionem con
tinuare, detraho 5 de 7 relinquitur 2, diuido 5 per 2 exit 2 1/2, detra
he 1 pro regula remanet 1 1/2, diuide 7 per 1 1/2 exit 4 & 2/3, adde ad 7
fit 11 2/3, reduc ad integra multiplicando omnia per 3, habebis
35, 21, & 15, in continua proportione muſica, nam 35 ad 15 eſt ut 7
ad 3, & 14 ad 6, eſt ut 7 ad 3, eſt autem 14 differentia 21 & 35, & 6 dif
ferentia 21 & 15, & ita poſſes continuare inueniendo quartum,
quintum, ſextum, in infinitum. Rurſus ſint propoſiti duo termini
maiores, uelut 6 & 4, detrahe 4 à 6 exit 2, diuide 6 per 2 exit 3, ad
de 1 pro regula fit 4, diuide 4 minorem terminum per 4 exit 1, de
trahe 1 ex 4, relinquitur 3 minor terminus, & ita propoſitis 6 & 3
uelim tertium terminum, diuido 2 per 1 differentiam exit 2, detraho
1 pro regula remanet 1, diuido 3 maiorem terminum per 1 exit 3, ad
de 3 ad 3, fit 6 maior terminus. Similiter capio 3 & 4, diuide 3 mino
rem terminum per 1 differentiam exit 3, detrahe 1 pro regula, relin
quitur 2, diuide 4 terminum medium per 2 exit 2, adde ad 4 fit 6 ma
ior terminus. Stiphelius autem erat in ſua regula, nam ſic 12 4 & 3
eſſent in continua proportione muſica ex ſua regula. Dico ergo,
quod ſi proponantur 5 & 7, & uelim muſicam proportionem con
tinuare, detraho 5 de 7 relinquitur 2, diuido 5 per 2 exit 2 1/2, detra
he 1 pro regula remanet 1 1/2, diuide 7 per 1 1/2 exit 4 & 2/3, adde ad 7
fit 11 2/3, reduc ad integra multiplicando omnia per 3, habebis
35, 21, & 15, in continua proportione muſica, nam 35 ad 15 eſt ut 7
ad 3, & 14 ad 6, eſt ut 7 ad 3, eſt autem 14 differentia 21 & 35, & 6 dif
ferentia 21 & 15, & ita poſſes continuare inueniendo quartum,
quintum, ſextum, in infinitum. Rurſus ſint propoſiti duo termini
maiores, uelut 6 & 4, detrahe 4 à 6 exit 2, diuide 6 per 2 exit 3, ad
de 1 pro regula fit 4, diuide 4 minorem terminum per 4 exit 1, de
trahe 1 ex 4, relinquitur 3 minor terminus, & ita propoſitis 6 & 3