80 Extractio de \({1 \over 3}\) 12 de \({3 \over 4}\) 126160

Verum si \({1 \over 3}\) 12 de \({3 \over 4}\) 126 extrahere volueris, describes questionem ut supra et
1521 148
\({3 \over 4}\) 126 \({1 \over 3}\) 12
residuum extractionis
\({5 \over 12}\) 114
161 reperies prescripta 148 et 1521, et162 extrahes 148 de 1521; remanebunt duodecime 1373, quas163 divide suprascripta ratione per 12, exibunt integra \({5 \over 12}\) 114 pro residuo dicte extractionis, ut in questione ostenditur.

81 Vel aliter: extrahe integra de integris, videlicet 12 de 126; remanent 114. Deinde extrahe \({1 \over 3}\) de \({3 \over 4}\); remanent \({5 \over 12}\), quas adde cum 114; erunt \({5 \over 12}\) 114 similiter.

82 Et si dividere volueris \({3 \over 4}\) 126 per \({1 \over 3}\) 12, divides 1521 per regulam de 148164,
1521 148
\({3 \over 4}\) 126 \({1 \over 3}\) 12
divisio maioris per minorem
\({1~~10 \over 4~~37}\) 10
165 que est \({1~~0\phantom{7} \over 4~~37}\), exibunt \({1~~10 \over 4~~37}\) 10 pro quesita divisione, ut in sua demonstratur descriptione166.

83 Item si167 minorem per maiorem dividere volueris, scilicet \({1 \over 3}\) 12 per \({3 \over 4}\) 126168,
1521 148
\({3 \over 4}\) 126 \({1 \over 3}\) 12
divisio minoris per maiorem
\({4~~3\phantom{3}~~1\phantom{3} \over 9~~13~~13}\)
169 repertis quidem 148 et 1521, divides 148 per regulam de 1521, que est \({1~~0\phantom{3}~~0\phantom{3} \over 9~~13~~13}\); exibit \({4~~3\phantom{3}~~1\phantom{3} \over 9~~13~~13}\) unius170 integri pro quesita divisione.

  • 160Extractio de \({1 \over 3}\) 12 de \({3 \over 4}\) 126:   om. R
  • 161
    1521 148
    \({3 \over 4}\) 126 \({1 \over 3}\) 12
    residuum extractionis (residuum extractionis:   Extractio S)
    \({5 \over 12}\) 114
    (residuum extractionis:   Extractio S) :   om. V
  • 162et:   om. S
  • 163quas:   quare R
  • 164per regulam de 148:   per 148 vel per eorum regulam R
  • 165
    1521 148
    \({3 \over 4}\) 126 \({1 \over 3}\) 12
    divisio (divisio:   descriptio divisionis F R) maioris (maioris:   maiorem F) per minorem
    \({1~~10 \over 4~~37}\) 10 (\({1~~10 \over 4~~37}\) 10:   om. F   \({1~~10 \over 4~~37}\) 37 R)
    (divisio:   descriptio divisionis F R) (maioris:   maiorem F) (\({1~~10 \over 4~~37}\) 10:   om. F   \({1~~10 \over 4~~37}\) 37 R) :    una cum insequenti tabula R   om. V
  • 166descriptione:   descriptione per \({3 \over 4}\) 126 α
  • 167si ~ per \({3 \over 4}\) 126:   si \({1 \over 3}\) 12 per \({3 \over 4}\) 126 dividere volueris R
  • 168per \({3 \over 4}\) 126:   om. α
  • 169
    1521 148
    \({3 \over 4}\) 126 \({1 \over 3}\) 12
    divisio (divisio:   om. R) minoris per maiorem
    \({4~~3\phantom{3}~~1\phantom{3} \over 9~~13~~13}\) (\({4~~3\phantom{3}~~1\phantom{3} \over 9~~13~~13}\):   \({5~~3\phantom{3}~~1\phantom{3} \over 9~~13~~13}\) R)
    (divisio:   om. R) (\({4~~3\phantom{3}~~1\phantom{3} \over 9~~13~~13}\):   \({5~~3\phantom{3}~~1\phantom{3} \over 9~~13~~13}\) R) :   om. V
  • 170unius:   unus S

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Instrumenta

Capitulum septimum

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