135 Alia extractio²⁶⁰

Et si \({1 \over 13}\) \({2 \over 11}\) \({3 \over 5}\) 42 \({2~~3~~5 \over 7~~8~~9}\)²⁶¹ extrahere volueris de \({2~~0~~\phantom{1}3 \over 3~~5~~11}\) 331 \({1 \over 9}\) \({1 \over 8}\) \({5 \over 7}\), reperies suprascripto ordine prescripta²⁶² 27855396 et 340380274, extrahes minorem ipsorum²⁶³ de maiori; remanebunt 312524878, que divides similiter suprascripte iunctionis ratione per \({1~~0~~0~~0~~\phantom{1}0~~\phantom{1}0~~\phantom{1}0 \over 2~~6~~7~~9~~10~~11~~13}\); exibunt \({0~~5~~1~~6~~\phantom{1}2~~\phantom{1}1~~\phantom{1}1 \over 2~~6~~7~~9~~10~~11~~13}\)²⁶⁴ 289 pro residuo quesite extractionis. Nam si per regulam de 27855396 diviseris 340380274, habebis divisionem maioris²⁶⁵ positi numeri per minorem; contrarium itaque reddit contrarium.

136 Si vis addere \(\textrm{o}{3~~2 \over 5~~9}\)²⁶⁶ cum \({2 \over 9}\), fac eandem virgulam²⁶⁷ terminare in circulo ab alia parte et habebis quesitum, scilicet \({3~~2 \over 5~~9}\textrm{o}\)²⁶⁸; que rediges ad partes unius numeri²⁶⁹ per doctrinam supradictam; erunt \({16 \over 45}\), hoc est \({1~~3 \over 5~~9}\). Et si \(\textrm{o}{3~~2 \over 5~~9}\)²⁷⁰ de \({2 \over 9}\) extrahere vis; si de \(\textrm{o}{5~~2 \over 5~~9}\)²⁷¹, hoc est de \({2 \over 9}\), extraxeris \(\textrm{o}{3~~2 \over 5~~9}\)²⁷², nimirum \(\textrm{o}{2~~2 \over 5~~9}\)²⁷³ remanebunt, hoc est \({4 \over 45}\). Vel accipe \({2 \over 9}\) de 45; erunt 10, de quibus extrahe \({3 \over 5}\) ipsorum; remanebunt 4, quibus divisis per 45, habentur similiter \({4 \over 45}\) pro residuo dicte extractionis. 137 Similiter si \({3~~0 \over 4~~6}\) vis extrahere de \({1 \over 6}\), extrahe \({3~~0 \over 4~~6}\) de \({4~~0 \over 4~~6}\)²⁷⁴, scilicet de \({1 \over 6}\); remanet \({1~~0 \over 4~~6}\). Nam de quacumque re extrahuntur \({3 \over 4}\), quartam²⁷⁵ eiusdem rei remanere necesse est. Et si ex aliqua re extrahuntur \({3 \over 5}\), ex eadem remanent \({2 \over 5}\). Unde si \(\textrm{o}{3~~4 \over 5~~7}\)²⁷⁶ extraxeris ex ipsis \({4 \over 7}\)²⁷⁷, remanebunt \(\textrm{o}{2~~4 \over 5~~7}\)²⁷⁸; et sic intelligas de omnibus similibus. Similiter si \(\textrm{o}{4~~5 \over 9~~7}\)²⁷⁹ vis de \({5 \over 7}\) extrahere, remanebunt \(\textrm{o}{5~~5 \over 9~~7}\)²⁸⁰, scilicet \({25 \over 63}\); quia de quacumque re extrahuntur \({4 \over 9}\), ex eadem re \({5 \over 9}\) remanere necesse est, cum \({4 \over 9}\) et \({5 \over 9}\) faciunt unum integrum.