84 De192 cantare vendito pro soldis et ruptis

Item cantare valet soldos \({1 \over 4}\) 27, hoc est soldos 27 et denarios 3; quantum
⑩ 109 s.
\({1 \over 4}\) 27 100
pensa per 11 127
\({\phantom{1}3~~\phantom{1}4~~\phantom{1}6 \over 10~~10~~12}\) 11 \({1 \over 3}\) 42
193 valent ergo194 rotuli \({1 \over 3}\) 42? Multiplica 27 per 4 et adde 1; erunt 109. Item multiplica 42 per 3 et adde 1; erunt 127, que multiplica per195 109; erunt 13843, que divide per 100 et per 3 et per 4, hoc est per \({\phantom{1}1~~\phantom{1}0~~\phantom{1}0 \over 10~~10~~12}\): exibunt soldi \({\phantom{1}3~~\phantom{1}4~~\phantom{1}6 \over 10~~10~~12}\) 11.

85 De196 eodem pro soldis et denariis

[F:38r] Item cantare valet197 soldos 26 et denarios 5, hoc est soldos \({5 \over 12}\) 26; quantum valent ergo rotuli \({5 \over 8}\) 31? Multiplica 26 per 12 et adde 5; erunt denarii 317. Item multiplica 31 per 8 et adde 5; erunt 253, que multiplica per 317; erunt 80201198, que divide per \({1~~\phantom{1}0~~\phantom{1}0~~\phantom{1}0 \over 8~~10~~10~~12}\): exibunt \({1~~\phantom{1}5~~\phantom{1}2~~\phantom{1}4 \over 8~~10~~10~~12}\)199 8

86 De200 eodem pro soldis et denariis et ruptis

Item cantare, hoc est rotuli 100, valet201 soldos \({1~~1~~\phantom{1}5 \over 4~~3~~12}\) 28, hoc est soldos 28 et denarios \({1 \over 4}\) \({1 \over 3}\) 5; quantum valent ergo libre \({2 \over 7}\) 7? Quamvis rotuli 100 et libre \({2 \over 7}\) 7 sunt unius generis, tandem non sunt ex una qualitate202 vel pondere, quia 100 sunt rotuli et \({2 \over 7}\) 7 sunt libre. 87
⑦ 4099 s. l.
\({1~~1~~\phantom{1}5 \over 4~~3~~12}\) 28 158
pensa per 11 51
\({5~~2~~59~~\phantom{1}3 \over 7~~8~~79~~12}\) 1 \({2 \over 7}\) 7
203 Quare aut de libris \({2 \over 7}\) 7 faciendi sunt rotuli aut de rotulis 100204 faciende sunt libre, ut sicuti sunt ex uno genere ita sint unius quantitatis, scilicet unius ponderis, vel rotuli sint205 ambo vel libre. Faciamus quidem de rotulis 100 libras, et erunt libre 158 Pisis, sed alias sunt libre 150, que ponantur in questione pro venditione pretii. 88 Deinde multiplica 28 per suam virgulam; erunt 4099. Item multiplica 7 per 7 et adde 2; erunt 51, que multiplica per 4099; erunt 209049, que divide per 158 et per fractiones que insimul coaptate206 faciunt \({1~~0~~0~~\phantom{1}0~~\phantom{1}0 \over 3~~7~~8~~79~~12}\): exibunt soldi \({0~~5~~2~~59~~\phantom{1}3 \over 3~~7~~8~~79~~12}\)207 1. Vel multiplica tantum tertiam de 51, scilicet 17, per 4099, et tolles 3 de virgula, quia semper in omnibus questionibus in quibus multiplicatio et divisio cadunt208, debes observare modum evitandi209 supradictum.

  • 192De ~ ruptis:   om. R
  • 193
    ⑩ 109 (109:   107 S) s.
    \({1 \over 4}\) 27 100
    pensa per 11 (11:   11 est S) 127
    \({\phantom{1}3~~\phantom{1}4~~\phantom{1}6 \over 10~~10~~12}\) (\({\phantom{1}3~~\phantom{1}4~~\phantom{1}6 \over 10~~10~~12}\):   \({\phantom{1}3~~\phantom{1}4~~\phantom{1}8 \over 10~~10~~12}\) R) 11 \({1 \over 3}\) 42
    (109:   107 S) (11:   11 est S) (\({\phantom{1}3~~\phantom{1}4~~\phantom{1}6 \over 10~~10~~12}\):   \({\phantom{1}3~~\phantom{1}4~~\phantom{1}8 \over 10~~10~~12}\) R) :   om. V
  • 194ergo:   om. α R
  • 195per:   om. R
  • 196De ~ denariis:   om. R S
  • 197valet:   valent F S
  • 19880201 Giusti   80221 ω
  • 199\({1~~\phantom{1}5~~\phantom{1}2~~\phantom{1}4 \over 8~~10~~10~~12}\) Giusti   \({1~~\phantom{1}5~~\phantom{1}1~~\phantom{1}4 \over 8~~10~~10~~12}\) ω
  • 200De ~ ruptis:   om. R
  • 201hoc est rotuli 100, valet (valet:   valent α):   valet hoc est rotuli 100 R
  • 202qualitate:   equalitate S   
  • 203
    ⑦ 4099 s. l.
    \({1~~1~~\phantom{1}5 \over 4~~3~~12}\) 28 158
    ⑤ (⑤:   om. F)
    pensa (pensa:   om. R S) per 11 51
    \({5~~2~~59~~\phantom{1}3 \over 7~~8~~79~~12}\) (\({5~~2~~59~~\phantom{1}3 \over 7~~8~~79~~12}\):   \({0~~5~~3~~59~~3 \over 3~~7~~8~~79~~12}\) ex \({0~~5~~2~~59~~3 \over 3~~7~~8~~79~~12}\) S   \({0~~5~~2~~59~~3 \over 3~~7~~8~~79~~12}\) R   ) 1 \({2 \over 7}\) 7
    (⑤:   om. F) (pensa:   om. R S) (\({5~~2~~59~~\phantom{1}3 \over 7~~8~~79~~12}\):   \({0~~5~~3~~59~~3 \over 3~~7~~8~~79~~12}\) ex \({0~~5~~2~~59~~3 \over 3~~7~~8~~79~~12}\) S   \({0~~5~~2~~59~~3 \over 3~~7~~8~~79~~12}\) R   ) :   om. V
  • 204rotulis 100:   100 rotulis R
  • 205sint:   sunt α
  • 206coaptate:   coaptate F   
  • 207\({0~~5~~2~~59~~\phantom{1}3 \over 3~~7~~8~~79~~12}\):   \({0~~5~~3~~59~~\phantom{1}3 \over 3~~7~~8~~79~~12}\) F R S   
  • 208cadunt:   cadit R
  • 209evitandi:   et vitandi F

Liber Abbaci

Instrumenta

Capitulum octavum

Indice