dijs, will be 20; then count five of the grand Divisions, where stop, for that is the place which represents 25. Where note, that if you had esteem'd the I at the be. ginning of the Line but I, that is, one tenih, ihe place which now represents 25, would fignify but 2.5: Also if efteer'd it as 10, then would the place .of 25, be 250; if 100, then 2500, if but ol then but 225, ETC. you had Example II. To find upon the Line the the place of 3552. First, efteem the r at the big nning . of the Line to be 100, then will that in the middle be 1900, and the chree towards the middle 3000.; trom which count fix of the Grand-divisions and a half towards (4000) and then you will come to the place of 3650. Now you must imagine the 2 to be a little beyond that half Division; for in this and the like examples, where we are to find 4 places, that which is Uuites must be taken by estimation. So have you the place 3652. Note, By these Examples last medtioned, you may perceive that the Figures 1, 2, 3,4, 5, 6, 7, 8, 9, do sometimes: lig ify them selves alone, fometimes 10, 20, 30, 8C. Sometimes 100, 200, 300, &C.' As the work perform'd thereby Thall require : The firft Figare of every Number is always that which is here set down, and the rest ofthe Figures are to be supplied according as the question shall require. And by the varia- . tion and change of the power of these Num. bers fromı, to 10, or 100, or iono, any Proportion, may be wrougit by this, General Rule. Always extend the Compallis from the fiift Number to the second, and that distance, or extent, applied the same way upon the Line, shall reach from the third to the fourth Number required. Or otherwise,' extend the Compasses from the firft Number to the third, and that extent applied the' fame way, shall also reach from the second to the tourih. Either of thefe ways will effect the same thing, by Exainples following shall be made appear. And it is neceflary thus to vary the roportion, so as to avoid the opening of the Compasses two wide. as Multiplication by the Line. This Rule whether it be perform'd Arithmerically or Instruinentally, depends upon Euclids Elem, Prop. 1. lib. 2. where it is demonstrated, that if two Lines 'be pro pos'd, whereof one is divided into diverse parts, the Rectangle contained under those iwo Lines is equal to the Rectangles contained under The Line which is divided, and the parts of the Line divided. The proportion is, as one is the Multiplyer : So is 'the Multiplicand to the Product. Example I. Let it be required to multiply 8 by 7 the Proportion is, as 1: is to 8:: so is 7: to 56. Therefore extend the Coinpaffes trom 1 to 8; the fame extent will reach from 7 to só, which is the product. Example II, Let it be required to Multiply 37, bys The proportion is; As 1 : to 5:: fo is 37 : to 185. Set one Foot of the Compasses in 1, and extend the other Foot tos; that fame extent will reach from 37 to 185, which is the product or 37, being Multiplied by s. Otherwise, Tet one Foot in i and extend the other to 37; the same extent will reach from 5 to 185 Example |