197 Explicit⁵¹⁸ de cambio monetarum que venduntur ad soldum. Incipit de cambio earundem cum venduntur⁵¹⁹ ad libram denariorum

Libra pisaninorum⁵²⁰, scilicet soldi 20, valet libram 1 bononinorum⁵²¹ et amplius bononinos⁵²² 54, hoc

d. bon. d. pis. \({1 \over 2}\) 24 20     \({1~~6 \over 4~~8} 13\) \({1 \over 4}\) 11

⁵²³ est soldi 20 pisaninorum valent soldos \({1 \over 2}\) 24 bononinorum. Quare pisanini 20 valent bononinos \({1 \over 2}\) 24, et libre 20 pisa[F:43v]ninorum valent bononinorum libras \({1 \over 2}\) 24⁵²⁴. Et queritur quot bononinos habeantur⁵²⁵ pro pisaninis⁵²⁶ \({1 \over 4}\) 11. Scribe questionem ut hic cernitur, et multiplica \({1 \over 4}\) 11 per \({1 \over 2}\) 24 et divide per pisaninos 20: exibunt bononini \({1~~6 \over 4~~8}\) 13.

[S:50r] 198 Et si cambium libre pisane fuerit bononini \({1 \over 2}\) 56, hoc est soldi 20 pisanorum

s. bon. s. pis. \({1~~\phantom{1}8 \over 2~~12} 24\) 20     \({5 \over 12}\) 14

⁵²⁷ valeant⁵²⁸ soldos 24 et denarios \({1 \over 2}\) 8, hoc est soldos \({1~~8 \over 2~~12}\) 24, et vis scire quot pisaninos valeant⁵²⁹ soldi 14 et denarii 5 bononinorum; pones itaque soldos \({5 \over 12}\) 14 sub soldis \({1~~8 \over 2~~12}\) 24, et multiplicabis⁵³⁰ \({5 \over 12}\) 14 per 20 et divides per⁵³¹ \({1~~\phantom{1}8 \over 2~~12}\)⁵³² 24, hoc est multiplicabis 173 per 20, que per 12 et per 2 que sunt sub virgula, et divides per 593 et per 12 que sunt sub⁵³³ virga de 14: exibunt soldi \({20~~\phantom{1}8 \over 593~~12}\) 11⁵³⁴.

199 Rursus ⁵³⁵ cambium libre pisane sit bononini \({3 \over 4}\) 57, hoc est quod soldi 20 pisanini valent soldos \({3~~\phantom{1}9 \over 4~~12}\)⁵³⁶ 24; et queratur quot bononinos valent libre 17 et soldi 11 et denarii 5 pisanini. Descripta questione, multiplica \({\phantom{1}5~~11 \over 12~~20}\) 17 per libras \({3~~9 \over 4~~12} 24\)⁵³⁷ et divide per libras 20 pisanas: exibunt libre⁵³⁸ \({1~~2~~14~~11~~15 \over 2~~8~~20~~12~~20}\) 21⁵³⁹ bononinorum. Et si habueris libras \({\phantom{1}5~~11 \over 12~~20}\) 17 bononinorum, multiplica eas per 20 et divide per \({3~~\phantom{1}9 \over 4~~12}\)⁵⁴⁰ 24, et habebis propositum.

200 Soldus itaque imperialium valet pisaninos \({1 \over 2}\) 28; queritur quot

£ bon. £ pis. \({1 \over 2}\) 7 \({1 \over 2}\) 28 d. s.   \({3~~\phantom{1}3~~\phantom{1}5 \over 19~~12~~20}\) 1

⁵⁴¹ bononinos habeat cambium libra 1 pisaninorum. Quia soldus imperialium est bononini 36, ergo pisanini \({1 \over 2}\) 28 valent soldos 36 bononinos et libre \({1 \over 2}\) 28 pisane valent libras 36 bononinorum. Quare libre \({1 \over 2}\) 28 pisane habent cambium libre \({1 \over 2}\) 7 [V:42v] bononinorum que sunt a⁵⁴² \({1 \over 2}\) 28 in 36. 201 Et quia queris cambium unius libre⁵⁴³, pone 1 sub libris \({1 \over 2}\) 28, ut in hac cernitur descriptione; et multiplica 1 per \({1 \over 2}\) 7 et divide per \({1 \over 2}\) 28, hoc est multiplica 1 per 15, et divide per 57. Sed ut habeas in virga \({\phantom{1}1~~\phantom{1}0 \over 12~~20}\), multiplica dictam multiplicationem de 1 in 15 per 80; erunt 1200, que divide per \({1~~0~~0 \over 19~~12~~20}\): exibunt libre⁵⁴⁴ \({\phantom{1}3~~\phantom{1}3~~\phantom{1}5 \over 19~~12~~20}\), hoc est denarii \({3 \over 19}\) 63, et tot est cambium libre pisane.

202 Et si econtra dicatur cambium [R:71r] unius libre pisane esse

s. bon. s. pis. \({\phantom{1}3~~\phantom{1}3 \over 19~~12}\) 25 20 3 \({1~~\phantom{1}4 \over 2~~12}\) 2

⁵⁴⁵ soldos 5 et denarios \({3 \over 19}\) 3, hoc est soldi 20 pisaninorum valent soldos \({\phantom{1}3~~\phantom{1}3 \over 19~~12}\) 25 bononinorum, et queratur quot pisaninos valeat soldus imperialium. Pro ipso soldo pones soldos 3⁵⁴⁶ sub soldis \({\phantom{1}3~~\phantom{1}3 \over 19~~12}\) 25, cum soldus imperialium sit soldorum 3 bononinorum; et multiplicabis ipsa 3 per 20 que sunt eis ex adverso, et divides per \({\phantom{1}3~~\phantom{1}3 \over 19~~12}\) 25, hoc est per \({5 \over 19}\) 25 que idem sunt, cum \({\phantom{1}3~~\phantom{1}3 \over 19~~12}\) sint \({5 \over 19}\) tantum; exibunt soldi \({1~~\phantom{1}4 \over 2~~12}\) 2, hoc est denarii \({1 \over 2}\) 28 pro pretio unius soldi imperialium.

[G:74r] 203 Rursus valeat soldus imperialium pisaninos \({3 \over 4}\) 28 minus

£ bon. £ pis. \({1~~7 \over 4~~20}\) 7 \({3~~12 \over 4~~20}\) 28       1

⁵⁴⁷ denariis \({1 \over 4}\) 2 per quamlibet libram imperialium; et queratur quot bononinos habeat cambium libra 1 pisaninorum pro predictis denariis \({1 \over 4}\) 2. Extrahe \({1~~\phantom{1}2 \over 4~~20}\) de pisaninis \({3 \over 4}\) 28, scilicet de pisaninis \({15 \over 20}\) 28; remanebunt pisanini \({3~~12 \over 4~~20}\) 28 pro pretio soldi imperialium. 204 Ergo libre \({3~~12 \over 4~~20}\) 28 pisaninorum⁵⁴⁸, scilicet libre 28 et soldi 12 et denarii 9 pisaninorum⁵⁴⁹ valent libras 36 bononinorum. Quare cambium de libris 28 et soldis 12 et denariis 9 est libre 7 et soldi 7 et⁵⁵⁰ denarii 3 bononinorum, que sunt a libris 28 et soldis 12 et⁵⁵¹ denaris 9 usque in libras⁵⁵² 36. Quare describes questionem ut hic ostenditur, et multiplicabis 1 per \({1~~\phantom{1}7 \over 4~~20}\) 7 et divides per \({3~~12 \over 4~~20}\) 28: exibunt \({1609~~\phantom{1}1~~\phantom{1}5 \over 2291~~12~~20}\)⁵⁵³.

[F:44r] 205 Item⁵⁵⁴ cambium libre pisane sit bononini \({1 \over 2}\) 64, hoc est soldi \({3 \over 8}\) 25

s. bon. s. pis. \({3 \over 8}\) 25 20 3 \({1~~14~~\phantom{1}7~~\phantom{1}4 \over 7~~29~~20~~12} 2\)

⁵⁵⁵ bononinorum valent soldos 20 pisaninorum, et queratur pretium de soldis 3 bononinorum, scilicet de soldo 1 imperialium. Descripta itaque questione, multiplica 25 per suam virgulam; erunt 203. Multiplicabis⁵⁵⁶ ergo 3 per 20, que per 8; erunt 480, que dividenda sunt per 203, scilicet per \({1~~\phantom{1}0 \over 7~~29}\). Sed multiplica ea⁵⁵⁷ per 20 et per 12; erunt 155200⁵⁵⁸, que divide per \({1~~\phantom{1}0~~\phantom{1}0~~\phantom{1}0 \over 7~~29~~20~~12}\): exibunt⁵⁵⁹ \({1~~14~~\phantom{1}7~~\phantom{1}4 \over 7~~29~~20~~12}\) 2, hoc est denarii \({1~~14~~\phantom{1}7 \over 7~~29~~20}\) 28

206 Et nota quia ideo aptavi \({1 \over 20}\) post \({1 \over 12}\), ut caderent super ea vigesime⁵⁶⁰ denariorum⁵⁶¹ que contingunt soldo⁵⁶²; quia quot vigesime contingunt soldo, tot denarii contingunt uni libre. Ergo soldus imperialium valet denarios 28 pisaninorum, et insuper denarios⁵⁶³ \({1~~14 \over 7~~29}\) 7⁵⁶⁴ per unamquamque libram imperialium. 207 Sed ex denariis quinque contingentibus libre contingit soldo quarta unius denarii; et pro denariis 10 contingit⁵⁶⁵ \({1 \over 2}\); et pro denariis 15 contingunt⁵⁶⁶ soldo \({3 \over 4}\) unius⁵⁶⁷ denarii. Ergo soldus imperialium valet \({1 \over 4}\) 28, et amplius denarios \({1~~14 \over 7~~29}\) 2 per libram, hoc est parum minus denariis \({1 \over 2}\) 2. Unde soldus imperialium valet pisaninos \({1 \over 2}\) 28 minus denariis \({1 \over 2}\) 2 per unamquamque libram; et sic studeas facere in similibus.