The semicircle on a sector in two books. Containing the description of a general and portable instrument; whereby most problems (reducible to instrumental practice) in astronomy, trigonometry, arithmetick, geometry, geography, topography, navigation, dyalling, &c. are speedily and exactly resolved. By J. T.

PROBL. 2.

To multiply two numbers, given by the Line of Numbers. The proportion is this.

As 1 on the line is to the multiplicator, so is the multiplicand to the product. Ex. gr.

As 1 is to 4, so is 7, to what?

Extend the Compasses from the first term, viz. I unto the second term, viz. 4. with that distance, setting one point in 7 the third term, turn the other point of the Compasses toward the same end of the rule, as at first, and you have the fourth, viz. 28. There is only one difficulty remaining in this Problem, and that is to determin the number of places, or fi∣gures in the product, which may be resolved by this general rule. The product alwayes contains as many figures as are in the multi∣plicand, and multiplicator both, unless the two first figures of the product be greater than the two first figures in the multiplicator, and then the product must have one figure less than are in the multiplicator, and multi∣plicand both. Ex. gr. 47 multiplied by 25, is 2175, consisting of four figures; but 16 mul∣tiplied by 16, is 240, consisting of no more than three places, for the reason before men∣tioned.

I here (for distinction sake) call the multiplicator the lesser of the two numbers, although it may be either of them at plea∣sure.