53
De ianuinis ad imperiales168
Rursum si econtra quesieris quot imperiales habuerit pro libris \({4 \over 7}\) 8 ianuinorum, describes
|
|
|
£ ian. |
£ pis. |
£ imp. |
|
60 |
127 |
23 |
|
\({4 \over 7}\) 8 |
\({3 \over 4}\) 31 |
\({1 \over 2}\) 11 |
|
3 |
|
|
|
40 |
118 |
d. s. £ |
|
\({1 \over 3}\) 13 |
\({3 \over 5}\) 23 |
\({4~~106~~10~~\phantom{1}9 \over 7~~127~~12~~20}\) 5 |
|
|
169 questionem ut hic ostenditur, et multiplicabis \({4 \over 7}\) 8 per \({3 \over 5}\) 23, que per \({1 \over 2}\) 11, et divides per \({1 \over 3}\) 13 et per \({3 \over 4}\) 31, hoc est quod multiplicabis 60 per 118, que per 23, que per 4 que sunt sub virgula post 31, que per 3 que sunt sub virgula post 13, et divides
170 summam eorum per regulam de 40, que est \({1~~0 \over 4~~10}\) , et per 127 et per ruptos aliorum trium numerorum, videlicet per 7 et per 5 et per 2, scilicet per \({1~~0~~0~~0~~0 \over 5~~7~~127~~4~~20}\).
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Et ideo posuimus
171 \({1~~\phantom{1}0 \over 4~~20}\) in capite virgule, quia ibidem debemus habere \({\phantom{1}1~~\phantom{1}0 \over 12~~20}\) ideo quia questio est de libris. Unde scimus quia minuit nobis 3 ut habeamus \({\phantom{1}1~~\phantom{1}0 \over 12~~20}\): quare pones 3 super \({1 \over 3}\) 13 ne tradatur oblivioni cum acceperis pensam, et multiplicabis per ipsa 3 totam summam, quam divide per \({1~~0~~\phantom{1}0\phantom{1}~~\phantom{1}0~~\phantom{1}0 \over 5~~7~~127~~12~~20}\),
55
et evitabis, scilicet multiplica 118 per quintam de 60, hoc est per 12, que per 23: erunt 32568, que per 3, que per 4 que sunt sub virgulis; erunt 390816, que multiplicabis per 3 que posita sunt super \({1 \over 3}\) 13, et divides summam per \({1~~\phantom{1}0\phantom{1}~~\phantom{1}0~~\phantom{1}0 \over 7~~127~~12~~20}\): exibunt libre \({4~~106~~10~~\phantom{1}9 \over 7~~127~~12~~20}\) 5.
