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First, set down upon your Paper the Multiplicand, and orderly under it the Multiplier. It matters not greatly which of the two given Num∣bers be made Multiplicand or Mul∣tiplier, but it is usual and best to make the greatest Number Multipli∣cand, and the lesser Multiplier. Then
draw a Line with your Pen under them, and having Tabulated your Multipli∣cand (or greater number) look what Numbers in your Rods stand against the first Figure towards your right hand, and that Number which you shall finde upon your Rods standing a∣gainst that first Figure found in your Tabulat, set down under your Line which you formerly drew under your Multiplicand and Multiplier: And having so done with the first Figure of your Multiplier, do so with the rest, setting them down one under another, removing every Figure one place more towards the left hand, then that which went before it, as is done in common Multiplication, and as you see in the following Example.
Example 1. Let it be required to multiply 3496, by 489. As if it were required to know how much 489 times 3496 would amount unto.
First, Set down your given Num∣ber
3496, and 489, one under ano∣ther, and draw your Line under them, as here you see done.
Secondly, 3496 your Multipli∣cand being Tabulated, and 9 being 〈 math 〉〈 math 〉 the first Fi∣gure to the right hand in your Multiplier, look upon your Rods, what sum there stands against 9 in the side of your Tabulat, and you shall finde (as by the Rules in the second Prop. of the Fifth Chap. you were directed) 31464, which is the Product of 3496 multiplied by 9, wherefore set down this number 31464 under your Line, as you see in the Example.
Thirdly, Look what sum upon the Rods stands against 8, which is the second Figure of your Multiplier, and
you shall finde 27968, set this num∣ber under the former, moving it one place forward towards the left hand.
Fourthly, Look what sum upon the Rods stands against 4 which is the third Figure in your Multiplier, and you shall finde 13984, which set down under the other, one place more to the left hand.
Lastly, Under these three Sums draw a Line and add the three sums together, and they make 1709544, which is the Product of 3496 multi∣plied by 489, and this 1709544 the Product, contains 3496 the Multi∣plicand, 489 times.
Practise well this first Example, and compare it with the Rods as they are Tabulated in Figure 4 at the be∣ginning of the Book, as also with the Rules in the Fifth Chapter, and you may perform any Multiplication. However I will give you one or two
more Examples, and some other ways of Multiplication.
Example 2. Let it be required to multiply the same sum 3496 by 261.
〈 math 〉〈 math 〉
Set the Numbers down as here is done, then look up∣on the Rods for the Pro∣duct of 3496 by 1, and you shall finde it to be the same, wherefore set down 3496 under the Line— then look upon the Rods for the Pro∣duct of 3496 by 6, and you shall finde it to be 20976, which set down under the other number one place more towards the left hand.—A∣gain, look in the Rods for the Pro∣duct of 3496 multiplied by 2, and you shall finde it to be 6992, which set down under the other two.
Lastly, Draw a Line under them, and add the three numbers together in order as they stand, and the sum
of them will be 912456, which is the Product of 3496 multiplied by 261.
Example 3. Let it be required to multiply the same number 3496 by 520.
Set down your Numbers as here you see done—Then because the first Fi∣gure 〈 math 〉〈 math 〉 of your Multiplier to∣wards your right hand is a Cypher, wholly omit it, and multiply 3496 by 52 only, so shall you finde the Product of 3496 by 2 to be 6992, which set down: Also the Product by 5 will be 17480, which set down under the other one place further, Then draw a Line — and add these two sums together, and they make 181792, to the which if you add a Cypher for the Cypher which you omitted in your Multiplier, the sum will be 1817920, which is the Product of 3496 by 520.
Example 4. Let it be required to
multiply the same 3496 by 7003—
Set down your Numbers as before, and as you see here done, Then ha∣ving 〈 math 〉〈 math 〉 Tabulated 3496, see what the Product thereof is upon the Rods being multiplied by 3 the first Figure in your Multi∣plier, and you shall finde it to be 10488, which set down un∣der the Line—Then the two next places of your Multiplier being Cy∣phers, make two pricks under the former number, one under 8, the o∣ther under 4, as you see in the Ex∣ample, or instead of 2 pricks you may make two Cyphers,—Then look in the Rods for the Product of 3496 by 7, and you shall finde it to be 24472, which set down under the o∣ther sum, beginning your number at the fourth place, or beyond the two Pricks or Cyphers. Lastly, draw a Line and add these two sums toge∣ther,
and their sum is 24482488, which is the Product of 3496 mul∣tiplied by 7003.
Thus have you four Examples in Multiplication, in which are inclu∣ded all the Varieties that may at any time happen in that Rule, viz. Two where the Multiplier consisted all of Figures, as in the first and second Example they did.—Another where the latter place of the Multiplier con∣sisted of a Cypher—And this last Example where Cyphers were inter∣mixed among the Figures.
And thus much for this kinde of Multiplication, but before I leave, I will shew you