Mathesis enucleata, or, The elements of the mathematicks by J. Christ. Sturmius ; made English by J.R. and R.S.S.

DEFINITION XXIX.

DIvision, in general, is a manifold or complicated Sub∣traction of one quantity (which is called the Divisor) out of another (which is called the Dividend) whose multiplicity, or how many times the one is contained in the other, is shewn by another quantity arising from that Division, which is there∣fore called the Quote or Quotient. Here also the Divisor is of the same kind with the Dividend, or of a different kind, e. g. of the same kind if the product . . . . . . . . . . . . (12) be divided by (3) whence you'l have the Quotient . . . . (4) or dividing the aforementioned Line CD by the Line AB you'l again have the Line BC; but of a different kind, if the plane number a∣bove found

[illustration] 12 dots arranged in 3 rows and 4 columns

or the Rectangle ABCD be divided by a Retroduction, or a moving backwards again the erect Side AB, by whose motion the Rectangle was first formed, that so the Line BC may remain alone again. But both these kinds of Division as they have their peculiar Difficulties in Arithme∣tick and Geometry, which we shall further elucidate in their proper places; so they may be universally and very easily per∣formed in Species (or by Letters) which will be sufficient to our present purpose; or by a bare separation of the Divisor from the Dividend, if it be actually therein included; or by

placing the Divisor underneath the Dividend with a Line be∣tween. Thus if ab be to be divided by (b) the Quotient will be a; if by a, the Quotient will be (b); but if a or ab be to be divided by c which Letter since it is not found in the Dividend, cannot be taken out of it) the Quotients are a / c and ab / c i. e. a or ab divided by c, after the same manner as if 2 were to be divided by 3; which Divisor, since it is not contained in the Dividend, is usually placed un∣der it, by a separating Line thus, ⅔, 2 divided by 3.

SCHOLION.

HOW difficult Common Division is, especially of a large Dividend by a large Divisor, is sufficiently known: but how easily it is performed by Tetractical Arithmetick, we will barely bring one Example to shew. If the Product found in Schol. 1. of the preceding Definition, 1200 203 22 be again to be divided by its Multiplier 133, it may be performed after the usual way, but with much more ease, as the following Opera∣tion will shew; or according to a particular way of Weigelius, by writing down the Divisor, and its double and triple, in a piece of paper by it self, after this way:

123	312	1101
Divisor,	Double,	Triple.

and then moving that piece of Paper to the Dividend, note, which of those three Numbers comes nearest to the first Fi∣gures of the Dividend; for that barely subtracted gives the Re∣mainder, and will denote the Quotient to be writ down in its proper place; as the operation itself will shew better than any words can.

〈 math 〉〈 math 〉

Thus after Weigelius's way: 〈 math 〉〈 math 〉