Page:The Algebra of Mohammed Ben Musa (1831).djvu/210

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from which it appears that the inconvenience attending the solution of this problem has already been felt by Arabic readers of the work.

Page 45, line 16.

This instance from Mohammed’s work is quoted by Cardan (Ars Mugna, p. 22, edit. Basil.) As the passage is of some interest in ascertaining the identity of the present work with that considered as Mohammed’s production by the early propagators of Algebra in Europe, I will here insert part of it. Nunc autem, says Cardan, subjungemus aliquas quæstiones, duas ex Mahumete, reliquas nostras. Then follows Quæstio I. Est numerus a cujus quadrato si abjeceris ${\tfrac {1}{3}}$ et ${\tfrac {1}{4}}$ ipsius quadrati, atque insuper 4, residuum autem in se duxeris, fiet productum æquale quadrato illius numeri et etiam 12. Pones itaque quadratum numeri incogniti quem quæris esse 1 rem, abjice ${\tfrac {1}{3}}$ et ${\tfrac {1}{4}}$ ejus, cs insuper 4, fiet ${\tfrac {5}{12}}$ rei m: 4, duc in se, fit ${\tfrac {25}{144}}$ quadrati p: 16 m: ${\tfrac {1}{33}}$ rebus, et hoc est æquali uni rei et 12; abjice similia, fiet 1 res æqualis ${\tfrac {25}{144}}$ quadrati p: 4 m: $3{\tfrac {1}{3}}$ rebus, &c.

The problem of the Quæstio II. is in the following terms, Fuerunt duo duces quorum unusquisque divisit militibus suis aureos 48. Porro unus ex his habuit milites duos plus altero, el illi qui milites habuit duos minus contigit ut aureos quatuor plus singulis militibus daret; quæritur quot unicuique milites fuerint. In the present copy of Mohammed’s algebra, no such instance occurs. Yet Car-