Page:The Algebra of Mohammed Ben Musa (1831).djvu/41

 product is one dirhem; then one dirhem by minus one-sixth, that is one-sixth negative; then, again, one dirhem by minus one-sixth is one-sixth negative: so far, then, the result is two-thirds of a dirhem: but there is still minus one-sixth to be multiplied by minus one-sixth, which is one-sixth of a sixth positive; the product is, therefore, two-thirds and one sixth of a sixth.

If the instance be, “ten minus thing to be multiplied by ten and thing,” then you say, ten times ten is a hundred; and minus thing by ten is ten things negative; and thing by ten is ten things positive; and minus thing by thing is a square positive; therefore, the product is a hundred dirhems, minus a square.

If the instance be, “ten minus thing to be multiplied by thing,” then you say, ten multiplied. by thing is ten things; and minus thing by thing is a square negative; therefore, the product is ten things minus a square.

If the instance be, “ten and thing to be multiplied by thing less ten,” then you say, thing multiplied by ten is ten things positive; and thing by thing is a square positive; and minus ten by ten is a hundred dirhems negative; and minus ten by thing is ten things negative. You say, therefore, a square minus a hundred dirhems; for, having made the reduction, that is to say, having removed the ten things positive by the ten things