a Line under these two Products, then add them as at the third Example, and we have 182 Feet, 6 Inches, and 8 Parts, the Product required. Exam. 5. The Multiplicand, 56 Feet and 3 Inches, being didivided by 12, as in the former Examples, gives 4 Feet, 8 Inches, and 3 Parts, for the new Multiplicand; then multiplying this new Multiplicand by the 7 Inches, as taught in the former Examples, it gives 32 Feet, 9 Inches, and 9 Parts: The 17 Feet, being multiplied into the 3 Inches, makes 51 Inches, which, being divided by 12, gives 4 Feet and 3 Inches; fet down the 3 Inches, and multiply the 56 Feet, firft by the 7, remembering to carry the 4 when the 7 is multiplied into the 6; this produces 396 Feet and 3 Inches: Then multiply the 56 Feet by 1, the remaining Part of the Multiplier, and fet the Product 56 under the 396, as in common Multiplication: The Products, being added, make 989 Feet and 9 Parts. In the fixth Example, the 5 Inches in the Multiplicand, being multiplied by the 23 Feet in the Multiplier, gives 115 Inches, or 9 Feet and 7 Inches; put down the 7 Inches, and Feet to the Product of the 112 multiplied by 3: carry the 9 And, in the feventh Example, when the 10 Inches are to be multiplied by the 15 Feet, the Product is 150 Inches, or 12 Feet and 6 Inches: The reft of the Work is the fame as before.. But, when Feet, Inches, and Parts, are to be multiplied by Feet, Inches, and Parts, there will be produced lower Di vifions, vifions, called Seconds and Thirds; a Second being the twelfth Part of what we here call a Part, and a Third the twelfth Part of a Second. In thefe Operations, it is neceffary to make two fupplemental Multiplicands, one for the Inches, and the other for the Parts. Ex. 8. Multiply 9 F. 41. 7 P. Ex. 9. Multiply 12 F. 9I. 5 P. by 5 F. 61. 4P. by 8F. 41. 10 P. Exam. 8. Having placed the given Numbers under each other, draw a Line over the Multiplicand, and divide it by 12, which is done by placing each Figure one Place lower in Denomination, they being all under 12; this is the Multiplicand for the Inches: Now divide this first fupplemental Multiplicand by 12, thus, the 9 Inches, being divided by 12, gives 9 Parts, which place over the 4 Parts: The 4 Parts in the first fupplemental Multiplicand, being divided by 12, gives 4 Seconds, which put over the Place of Seconds in the firft fupplemental Multiplicand: The 7 Seconds in the firft fupplemental Multiplicand, being divided by 12, gives 7 Thirds in the fecond fupplemental Multiplicand, which place as in the Example. Multiply the upper fupplemental Multiplicand by the 4 Parts in the Multiplier, thus, 4 Parts by 7 Thirds is 28 Thirds, or 2 Seconds and 4 Thirds; put down the 4 Thirds under the Thirds in the upper fupplemental Multiplicand, and carry the 2 Seconds: Then, 4 Parts by 4 Seconds is 16 Seconds, and 2 that was carried is 18 Seconds, or 1 Part and 6 Seconds; put down the 6 Seconds in the Place of Seconds, and carry the Part: And 4 Parts by 9 Parts is 36 Parts, and I that was carried carried is 37 Parts, or 3 Inches and 1 Part, which put down as in the Work. Multiply the lower fupplemental Multiplicand, 9 Inches, 4 Parts, and 7 Seconds, by the 6 Inches in the Multiplier, thus, 6 Inches by 7 Seconds is 42 Seconds, or 3 Parts and 6 Seconds; put the 6 Seconds under the Seconds in the last Product, and carry the 3 Parts: Then, 6 Inches by 4 Parts is 24 Parts, and the 3 that was carried is 27 Parts, or 2 Inches and 3 Parts; put the 3 Parts under the Parts of the former Product, and carry the 2 Inches: And 6 Inches by 9 Inches. is 54 Inches, and 2 that was carried is 56 Inches, or 4 Feet and 8 Inches, which place as in the Work. Multiply the given Multiplicand, 9 Feet, 4 Inches, and 7 Parts, by the 5 Feet in the Multiplier, and put the Product, 46 Feet, 10 Inches, and II Parts, as before taught. Now add these three Products together, and their Sum is the Product fought. The ninth Example is done in the fame Manner; only, the given 12 Feet, when divided, make 1 Foot in the first Multiplicand; and this Multiplicand, being divided by 12, gives 1 Inch, 9 Seconds, and 5 Thirds, for the fecond fupplemental Multiplicand. Exam. 10. The Multiplicand and Multiplier confifting of Feet, Inches, and Parts, we muft find two fupplemental Multiplicands, as in the two laft Examples; then drawing a Line Q 2 over over the Multiplicand, and dividing the 20 Feet in the Mul tiplicand by 12, the Quotient is 1 Foot, and 8 over; put th I over the Place of Feet; and, dividing the 8 Feet over by 12, it gives 8 Inches, which put over the Place of Inches: Then, the 6 Inches in the Multiplicand, being divided by 12, gives 6 Parts, which put over the Place of Parts: And, lastly, the 3 Parts in the Multiplicand, being divided by 12, gives 3 Seconds, which place as in the Example. To form the fecond fupplemental Multiplicand, divide the I Foot in the first fupplemental Multiplicand by 12, and it gives Inch, which put over the Place of Inches: The 8 Inches in the firft fupplemental Multiplicand, being divided by 12, gives 8 Parts, which put over the Place of Parts: The 6 Parts in the firft fupplemental Multiplicand, being divided by 12, gives 6 Seconds in the fecond Multiplicand: And the 3 Seconds in the firft fupplemental Multiplicand, being divided by 12, gives 3 Thirds in the fecond fupplemental Multiplicand. The upper fupplemental Multiplicand, 1 Inch, 8 Parts, 6 Seconds, and 3 Thirds, being multiplied by the 5 Parts in the Multiplier, gives 8 Inches, 6 Parts, 7 Seconds, and 3 Thirds, by the Directions at the eighth Example. The under fupplemental Multiplicand, 1 Foot, 8 Inches, 6 Parts, and 3 Seconds, being multiplied by the 8 Inches in the Multiplier, gives 13 Feet, 8 Inches, and 2 Parts, by the Directions at the eighth Example. And the Multiplicand, 20 Feet, 6 Inches, and 3 Parts, being multiplied by the 10 Feet in the Multiplier, gives 205 Feet, 2 Inches, and 6 Parts, by the Directions at the eighth Example. Now draw a Line, and add these three Products together, and their Sum is the Product required, Exam. 11. The Multiplicand, 18 Feet, 7 Inches, and 2 Parts, being divided by 12, gives 1 Foot, 6 Inches, 7 Parts, and 2 Seconds, for the firft fupplemental Multiplicand; which, being divided by 12, gives 1 Inch, 6 Parts, 7 Seconds, and 2 Thirds, for the fecond fupplemental Multiplicand. The upper fupplemental Multiplicand, 1 Inch, 6 Parts, 7 Seconds, and 2 Thirds, being multiplied by the 4 Parts in the Multiplier, gives 6 Inches, 2 Parts, 4 Seconds, and 8 Thirds, by the Directions at the eighth Example. The under fupplemental Multiplicand, Foot, 6 Inches, 7 Parts, and 2 Seconds, being multiplied by the 5 Inches e Multiplier, gives 7 Feet, 8 Inches, 11 Parts, and 10 iftly, adding thefe together, we have the Product fought. 12: 29 Reciprocally 7:17:3 130 23:39 Exam. 13. Multiply 15F. 6I. 1 P. by 7 F. 5I. 2 P. F. I. P. S. T. I: 36: 1 I: 36: I 15: 6: I 7:5:2 270: 6:56:5 108: 6.: 7 115 28: 5:2 But, when the Feet in the Multiplier are more than 12, as in the fifth, fixth, and feventh Examples, it may be more convenient to do it by taking the aliquot Parts of a Foot. If the Number of Inches or Parts in the Multiplicand happen not to be aliquot Parts of 12, they may be divided into fuch as are: The aliquot Parts of 12 are, I, which is a twelfth Part; 2, a Sixth; 3, a Fourth; 4, a Third; and 6, the Half. The others may be made into two Parts, thus, 5 may be parted into 4, which is a Third, and the remaining is the Fourth of that: So, 7 may be parted into 4, a Third, and 3, the Fourth of 12; or elfe into 6, the Half, and 1, the Sixth Part of that Half: And 8 may be parted into 4, the Third, to be taken twice; and 9 into 3, the Fourth, taken three times. Of this I fhall fubjoin some Examples. Exam. 14 |