23 Extractio de \({1 \over 7}\) \({1 \over 5}\) de \({1 \over 4}\) \({1 \over 3}\)

Si vero \({1 \over 7}\) \({1 \over 5}\) de \({1 \over 4}\) \({1 \over 3}\) extrahere volueris,
144 245
\({1 \over 7}\) \({1 \over 5}\)
\({1 \over 4}\) \({1 \over 3}\)
extractio \({5~~2~~2\phantom{0} \over 6~~7~~10}\)
  \({1~~2~~6 \over 2~~8~~9}\) 1
  \({4~~0~~4 \over 5~~7~~7}\)
51 reperies prescripta 245 et 144 per qualem volueris modum de duobus prescriptis modis, et extrahe 144 de 245: remanebunt 101, que suprascripta ratione divide per \({1~~0~~0\phantom{0} \over 6~~7~~10}\): exibunt \({5~~2~~2\phantom{0} \over 6~~7~~10}\) pro residuo dicte extractionis. 24 Et si \({1 \over 4}\) \({1 \over 3}\) per \({1 \over 7}\) \({1 \over 5}\) dividere vis, divide 245 per regulam de 14452, exibunt \({1~~2~~6 \over 2~~8~~9}\) 1. Et si 144 per regulam de 245 diviseris, habebis \({4~~0~~4 \over 5~~7~~7}\) pro eo quod53 contingit integre parti ex divisione \({1 \over 7}\) \({1 \over 5}\) in \({1 \over 4}\) \({1 \over 3}\), ut in questione ostenditur.

  • 51
    144 245
    \({1 \over 7}\) \({1 \over 5}\)
    \({1 \over 4}\) \({1 \over 3}\)
    extractio (extractio:   om. S) \({5~~2~~2\phantom{0} \over 6~~7~~10}\) (\({5~~2~~2\phantom{0} \over 6~~7~~10}\):   \({5~~2~~3 \over 6~~7~~10}\) R)
      \({1~~2~~6 \over 2~~8~~9}\) 1 (\({1~~2~~6 \over 2~~8~~9}\) 1:   om. α F R   \({1~~2~~6 \over 2~~7~~9}\) 1 S)
      \({4~~0~~4 \over 5~~7~~7}\) (\({4~~0~~4 \over 5~~7~~7}\):   om. α F R   \({7~~0~~4 \over 5~~7~~7}\) S)
    (extractio:   om. S) (\({5~~2~~2\phantom{0} \over 6~~7~~10}\):   \({5~~2~~3 \over 6~~7~~10}\) R) (\({1~~2~~6 \over 2~~8~~9}\) 1:   om. α F R   \({1~~2~~6 \over 2~~7~~9}\) 1 S) (\({4~~0~~4 \over 5~~7~~7}\):   om. α F R   \({7~~0~~4 \over 5~~7~~7}\) S) :   om. V
  • 52per regulam de 144:   per 144 vel per eorum regula R
  • 53quod:   om. S

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