64 Divisio de 1357 per \({1 \over 5}\) \({1 \over 4}\) \({1 \over 3}\) 83136

Si autem volueris dividere 1357 per \({1 \over 5}\) \({1 \over 4}\) \({1 \over 3}\) 83, describe numeros, et multiplica 83 per suas virgulas; erunt sexagesime 5027. Pone ergo 5027 super \({1 \over 5}\) \({1 \over 4}\) \({1 \over 3}\) 83, et proba ea secundum quod in
5027 81420
\({1 \over 5}\) \({1 \over 4}\) \({1 \over 3}\) 83 1357
\({9\phantom{1}~~89\phantom{7} \over 11~~457}\) 16  
\({5~~7\phantom{0}~~14~~3\phantom{9} \over 6~~10~~23~~59}\)  
137 multiplicationibus per ruptum tibi demostravimus138. Est enim pensa ipsorum 1 per septenarium, ut oportet; quam pensam pone super 5027. 65 Deinde multiplica 1357 per numeros qui sunt sub virgulis post 83, hoc est per 3, que per 4, que per 5, vel in una multiplicatione per 60; erunt sexagesime 81420, que139 pone super 1357, et super ipsa140 pone pensam ipsorum per septenarium que est 3. Deinde divide 81420 per regulam de 5027, que est \({1\phantom{1}~~0\phantom{57} \over 11~~457}\); exibunt \({9\phantom{1}~~89\phantom{7} \over 11~~457}\) 16 pro quesita divisione. 66 Quare si multiplicaveris ipsa per \({1 \over 5}\) \({1 \over 4}\) \({1 \over 3}\) 83, eadem 1357 provenerint; et est pensa ipsius divisionis 3 per 7, sicuti est pensa de 81420. Et si 5027 per regulam de 81420 diviseris, habebis \({5~~7\phantom{0}~~14~~3\phantom{9} \over 6~~10~~23~~59}\) pro divisione de \({1 \over 5}\) \({1 \over 4}\) \({1 \over 3}\) 83 in141 1357, cuius divisionis pensa est 1 per 7, sicuti fuit de 5027; et sic intelligas de pensis quarumlibet divisionum similium.

  • 136Divisio (1357 \({1 \over 5}\) \({1 \over 4}\) \({1 \over 3}\) 83 divisio F) de 1357 per \({1 \over 5}\) \({1 \over 4}\) \({1 \over 3}\) 83:   om. R
  • 137
    ① (①:   om. R) ③ (③:   om. R)
    5027 81420
    \({1 \over 5}\) \({1 \over 4}\) \({1 \over 3}\) 83 1357
    \({9\phantom{1}~~89\phantom{7} \over 11~~457}\) 16  
    \({5~~7\phantom{0}~~14~~3\phantom{9} \over 6~~10~~23~~59}\) (\({5~~7\phantom{0}~~14~~3\phantom{9} \over 6~~10~~23~~59}\):   om. S3)  
    (①:   om. R) (③:   om. R) (\({5~~7\phantom{0}~~14~~3\phantom{9} \over 6~~10~~23~~59}\):   om. S3) :   om. ​α F S    add. S3
  • 138demostravimus:   demonstrabimus F
  • 139que:   quos α F S   quas R
  • 140ipsa Giusti   ipsos ω
  • 141in:   per R

Liber Abbaci

Instrumenta

Capitulum septimum

Indice