123 De305 partibus unius rotuli pro partibus unius tareni

Item \({1 \over 5}\) \({1 \over 4}\) \({1 \over 3}\) unius rotuli pro \({2~~3 \over 7~~8}\) \({4 \over 9}\)306 unius tareni; quantum valent307
⑥ 431 47
tar.
\({2~~3 \over 7~~8}\) \({4 \over 9}\) \({1 \over 5}\) \({1 \over 4}\) \({1 \over 3}\)
per 17
  439
\({2~~4~~2~~\phantom{1}6~~24~~14 \over 4~~7~~9~~11~~47~~20}\) \({1~~\phantom{1}3~~\phantom{1}7 \over 6~~10~~11}\)
308 \({1~~\phantom{1}3~~\phantom{1}7 \over 6~~10~~11}\) unius rotuli? Multiplica 1 quod est super 3 per 4, que per 5: erunt 20. Et multiplica 1 quod est super 4 per 5, que per 3; erunt 15, et 1 quod est super 5 per 4, que per 3; erunt 12, et adde 20 cum 15 et cum 12; erunt 47, que pone super \({1 \over 5}\) \({1 \over 4}\) \({1 \over 3}\). Deinde multiplica 4 que sunt super 9 per 8, que per 7; erunt 224, et multiplica 3 que sunt super 8 per 7 et adde 2; erunt 23, que per 9; erunt [G:68r] 207, que adde cum 224; erunt 431, que pone super \({2~~3 \over 7~~8}\)309 \({4 \over 9}\). 124 Item multiplica 7 que sunt super 11 per 10 et adde 3, que per 6 et adde 1: erunt 439 que pone super \({1~~\phantom{1}3~~\phantom{1}7 \over 6~~10~~11}\); et multiplica 431 per 439 que sunt ex adverso: erunt 189209, que deberes multiplicare per ruptos qui sunt sub 47, scilicet per 3 et per 4 et per 5, et dividere per eadem 47 et per ruptos qui sunt sub aliis virgulis. 125 Sed relinquatur multiplicatio de 3 et de 2 que sunt in regula310 de 4, et multiplicentur 189209 tantum per 2 que remanent de ipsis 4 et per 5, hoc est per 10; erunt 1892090, et relinquatur311 quod non dividetur312 per 6 que313 sunt sub virgula de \({1~~\phantom{1}0~~\phantom{1}0 \over 6~~10~~11}\); ergo dividetur per \({1~~0~~0~~\phantom{1}0~~\phantom{1}0~~\phantom{1}0 \over 7~~8~~9~~10~~11~~47}\)314, hoc est ut habeamus \({1 \over 20}\) in capite virgule per \({1~~0~~0~~\phantom{1}0~~\phantom{1}0~~\phantom{1}0 \over 4~~7~~9~~11~~47~~20}\): exibunt grana \({2~~4~~2~~\phantom{1}6~~24~~14 \over 4~~7~~9~~11~~47~~20}\).

  • 305De ~ tareni:   om. R   spatio relicto om. F
  • 306\({2~~3 \over 7~~8}\) \({4 \over 9}\):   \({2 \over 3}\) \({7 \over 8}\) \({4 \over 9}\) A V   
  • 307valent:   valent ergo R
  • 308
    ⑥ 431 47
    tar.
    \({2~~3 \over 7~~8}\) \({4 \over 9}\) \({1 \over 5}\) \({1 \over 4}\) \({1 \over 3}\)
    per 17 (per 17:   om. F   per 17 ⑦ R   )
      439
    \({2~~4~~2~~\phantom{1}6~~24~~14 \over 4~~7~~9~~11~~47~~20}\) \({1~~\phantom{1}3~~\phantom{1}7 \over 6~~10~~11}\)
    (per 17:   om. F   per 17 ⑦ R   ) :   om. V
  • 309\({2~~3 \over 7~~8}\):   \({2 \over 3}\) \({7 \over 8}\) α
  • 310et de (de:   adde S) 2 que sunt in regula:   in regula et de 2 que sunt α
  • 311relinquatur:   relinquetur S
  • 312dividetur:   dividatur R
  • 313que:   om. F
  • 314\({1~~0~~0~~\phantom{1}0~~\phantom{1}0~~\phantom{1}0 \over 7~~8~~9~~10~~11~~47}\):   \({1~~0~~0~~\phantom{1}0~~\phantom{1}0 \over 7~~8~~9~~11~~47}\) α F

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Capitulum octavum

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