167 Regula universalis in centenario435

Volumus enim quandam regulam demonstrare, que procreatur ex evitatione multiplicationum et divisionum ipsorum numerorum qui ponuntur in similibus questionibus; et436 hec est, ut cum437 proponatur quod centenarium piperis valeat libras quotlibet absque fractionibus, ut ponamus libras 13438, et queratur quantum quis pro denariis quotlibet habuerit, ut ponamus 3; semper multiplica denarios per 5, et divide per pretium centenarii. 168 Ut in hac multiplica denarios 3 per 5; erunt 15, que divide per 13: exibunt \({2 \over 13}\) 1, et tot uncias habueris pro ipsis denariis 3439. Verum si eadem ratione queratur quantum ipse pro soldis 7 haberet, multiplicabis similiter 7 per 5; erunt 35, que divide similiter per 13: exibunt libre \({9 \over 13}\) 2, et sic intelligas de omnibus similibus.

169 Item440 si econtra quesieris quantum eadem ratione uncie 7 valeant441; multiplicabis 7 per 13 et442 divides per 5; exibunt denarii \({1 \over 5}\) 18 Nam si quesieris quantum valent libre 7 eiusdem mercis; multiplicabis similiter 7 per 13 et divides443 per 5: exibunt soldi \({1 \over 5}\) 18, idest soldi 18 et denarii \({2 \over 5}\) 2, et sic facies de similibus.

[S:48v] 170 Item rotuli 14 pro tarenis \({5 \over 6}\) 5; quot rotulos habuero pro
35 tar.  
\({5 \over 6} 5\) 14
pensa est 10  
per 11  
\({2 \over 5}\) unc. ℞
\({2 \over 5} 17\) \({3~~0~~\phantom{1}9 \over 5~~5~~12}\) 41
444 tarenis \({2 \over 5}\) 17445? Describe questionem hoc modo446, et multiplica numeros qui sunt ex adverso, scilicet 14 per \({2 \over 5}\) 17, et divide per \({5 \over 6}\) 5: exibunt \({3~~0~~\phantom{1}9 \over 5~~5~~12}\) 41.

[G:71v] 171 Item rotuli \({1 \over 2}\) 17 pro tarenis \({1 \over 3}\) 11; quantum habuero ex ipsis pro
34 t. 35 ℞
\({1 \over 3}\) 11 \({1 \over 2} 17\)
29 unc. ℞
\({1~~\phantom{1}7 \over 4~~20}\) \({7~~1~~12~~6 \over 8~~10~~17~~12} 0\)
447 granis \({1 \over 4}\) 7, hoc est pro \({1~~\phantom{1}7 \over 4~~20}\) unius tareni ut fiant ex quantitate tarenorum \({1 \over 3}\) 11 suprascriptorum? Describe questionem sic, et multiplicabis \({1 \over 2}\) 17 per \({1~~\phantom{1}7 \over 4~~20}\) [V:41r] et divide per \({1 \over 3}\) 11, et fac ut habeas 12 in capite virgule propter uncias, et448 exibunt uncie \({7~~\phantom{1}1~~12~~\phantom{1}6 \over 8~~10~~17~~12}\)449.

  • 435Regula universalis in centenario:   om. R
  • 436et:   est et S
  • 437cum:   om. α
  • 438libras 13:   pro lib. 13 A F R S   per lib. 13 G   pro libra 13 V
  • 4393:   7 α F    ex 7 S
  • 440post Item habet
    13 100
    \({2 \over 5} 2\) 7
    in marg. S
  • 441uncie 7 valeant:   valeant uncie 7 R
  • 442et supra lineam S
  • 443divides:   divide α F S
  • 444
    35 tar.  
    \({5 \over 6} 5\) (\({5 \over 6} 5\):   \({5 \over 6}\) A) 14
    pensa est 10 (pensa est 10:   om. A R S)  
    per 11 (per 11:   per 11 10 A   om. R S)  
    \({2 \over 5}\) (87 post \({2 \over 5}\) A) unc. ℞
    \({2 \over 5} 17\) (\({2 \over 5} 17\):   \({2 \over 5} 12\) A) \({3~~0~~\phantom{1}9 \over 5~~5~~12}\) 41
    (\({5 \over 6} 5\):   \({5 \over 6}\) A) (pensa est 10:   om. A R S) (per 11:   per 11 10 A   om. R S) (87 post \({2 \over 5}\) A) (\({2 \over 5} 17\):   \({2 \over 5} 12\) A) :   om. G V
  • 44517:   12 α
  • 446hoc modo:   in hunc modum R
  • 447
    34 t. (34 t.:   34 R   om. S) 35 ℞ (35 ℞:   35 R   om. S)
    \({1 \over 3}\) 11 \({1 \over 2} 17\) (\({1 \over 2} 17\):   \({1 \over 2} 12\) A)
    29 (29:   om. S) unc. ℞
    \({1~~\phantom{1}7 \over 4~~20}\) \({7~~1~~12~~6 \over 8~~10~~17~~12} 0\) (\({7~~1~~12~~6 \over 8~~10~~17~~12} 0\):   \({7~~\phantom{1}1~~12~~\phantom{1}3 \over 8~~10~~17~~12} 0\) A   \({7~~\phantom{1}1~~12~~\phantom{1}6 \over 8~~10~~17~~12}\) R)
    (34 t.:   34 R   om. S) (35 ℞:   35 R   om. S) (\({1 \over 2} 17\):   \({1 \over 2} 12\) A) (29:   om. S) (\({7~~1~~12~~6 \over 8~~10~~17~~12} 0\):   \({7~~\phantom{1}1~~12~~\phantom{1}3 \over 8~~10~~17~~12} 0\) A   \({7~~\phantom{1}1~~12~~\phantom{1}6 \over 8~~10~~17~~12}\) R) :   om. G V
  • 448et:   om. α R
  • 449uncie \({7~~\phantom{1}1~~12~~\phantom{1}6 \over 8~~10~~17~~12}\):    immo \({7~~\phantom{1}1~~12~~\phantom{1}6 \over 8~~10~~17~~12}\) unius rotuli

Liber Abbaci

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Capitulum octavum

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