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Exam. 14. Having multiplied the 4 Feet, 1 Inch, and 6 Parts, by the 4 Inches, and put down 16 Feet and 6 Inches, the Product, as before; then, instead of multiplying the 28 Feet by the 6 Inches, take the Half of 28 for Feet, because 6 Inches are the Half of a Foot, which gives 14 Feet; place this under the 16 Feet, Units under Units: Then multiply the 28 Feet into the 49 Feet, that is, multiply the 49, first by the 8, and place the Units of this Product under the Units of the 14, the Tens under the Tens, and fo on; and multiply the 49 by the remaining 2 of the Multiplier, putting this Product under the laft Product, as in common Arithmetic: Now draw a Line, then add thefe into one Sum, and it will be the Product fought.

Exam. 15. Having found the upper Multiplicand, 20 Feet, 2 Inches, and 4 Parts, as before taught, and multiplied it by the 4 Inches, put down the Product, 80 Feet, 9 Inches, and 4 Parts, as in the former Examples: But, the 4 Inches in the Multiplicand being one Third of a Foot, take the Third of 59 Feet, which is 19, and 2 Feet remains; and, the 2 Feet being 24 Inches, take the Third of 24, which is 8, and place under the Inches as ufual: Then multiply the 59 Feet into the 242, as taught in the laft Example: Now draw a Line, and add as before, and you have the Product fought.

The other Example is done in the fame Manner.

Exam. 17.

Exam. 17.

Exam. 18.

Multiply 28 F. 6I. 10 P. by Multiply 42 F. 8 I. 4 P. by

16 F. 41. 9 P.

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18 F. 9 I. 6P.

F. I. P. S. T.

3: 6 : 8:4

3:68:4

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Exam. 17. After forming the two fupplemental Multiplicands, and multiplying the 9 Parts into the upper Multiplicand, and the 4 Inches into that next above the Line, fet down each Product under the particular Denomination from whence it was produced, (dividing by 12, where necessary) as in the Work.

But now, inftead of multiplying the 16 Feet by the 6 Inches and 10 Parts in the Multiplicand, (the 6 Inches being half a Foot) divide the 16 Feet in the Multiplier by 2, and put 8 Feet, the Quotient, in the Place of Feet, as in the Work.

Now proceed to the 10 Parts in the Multiplicand; and, the 6 Parts being half an Inch, divide the 16 Feet by 2, and the Quotient 8 will be Inches, which put in the Place of Inches.

There being 4 Parts left out of the 10 Parts, and 4 being one Third of 12, divide the 16 Feet by 3, and the Quotient 5 will be Inches, which put in the Place of Inches; and, the I Inch over being multiplied by 12, to bring it into Parts, divide 12 by 3, and the Quotient is 4 Parts, which put in the Place of Parts, as in the Work.

Then multiply the 28 by 16, and place the Products as in the Work, like common Multiplication.

Now add thefe together, and it will be the Product fought,

If the Reader fhould be at any Uncertainty to fix the Denomination of the Quotient, he may remember,

That Feet divided by Inches produce Feet in the Quotient. Feet divided by Parts produce Inches in the Quotient. Feet divided by Seconds produce Parts in the Quotient. Feet divided by Thirds pr Jeconds in the Quotient. And, univerfally, the Quotient is the next higher Denomination to that in the Multiplicand whose aliquot Part divided the Feet in the Multiplier.

Exam. 18. Dividing the Multiplicand 42 Feet, 8 Inches, and 4 Parts, by 12, the Quotient is 3 Feet, 6 Inches, 8 Parts, and 4 Seconds, for the lower fupplemental Multiplicand; which, being divided by 12, gives 3 Inches, 6 Parts, 8 Seconds, and 4 Thirds, for the upper fupplemental Multiplicand.

Multiplying the 3 Inches, 6 Parts, 8 Seconds, and 4 Thirds, the upper fupplemental Multiplicand, by the 6 Parts in the Multiplier, the Product is 1 Foot, 9 Inches, 4 Parts, and 2 Seconds, as in the Work.

Multiplying the 3 Feet, 6 Inches, 8 Parts, and 4 Seconds, the lower fupplemental Multiplicand, by the 9 Inches in the Multiplier, the Product is 32 Feet and 3 Inches, as in the Work.

But now, inftead of multiplying the Inches and Parts in the Multiplicand, by the 18 Feet in the Multiplier, out of the 8 Inches in the Multiplicand take 6 Inches, for half a Foot; then divide the 18 Feet in the Multiplier by 2, and put down 9 Feet, the Quotient, in the Place of Feet.

Now, the 2 Inches of the Multiplicand which are left being one Third of the 6 Inches before taken, divide the 9 Feet laft found by 3, and the Quotient is 3 Feet, which place under the q Feet.

9

There being 4 Parts left, they are one Sixth of the 2 Inches laft found; therefore, divide the 3 Feet by 6, and the Quotient is 6 Inches, which put in the Place of Inches.

Laftly, multiply the 42 by 18, as in common Multiplication. Now add thefe together, and the Sum will be the Product fought.

When one of the given Numbers confifts only of Feet and Inches, tho' the other has Parts, that which is without Parts being made the Multiplier, there will then be required but one fupplemental Multiplicand, as in the nineteenth Example: And, if one of the given Numbers confifts of Feet only, then the Multiplicand need not be divided by 12, as in the twentieth Example,

Exam. 19.

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Exam. 19. Inftead of multiplying the 25 Feet into the 6 Parts, take the Half, which is 12 Inches, or I Foot, and the that remains makes 6 Parts; then, dividing the 10 Inches into the two aliquot Parts, 6, the Half of a Foot, and 4, the Third, take firft the Half of 25, which is 12 Feet and 6 Inches, and then the Third, which is 8 Feet and 4 Inches.

Exam. 20. The 7 Parts being divided into 6, the Half, and I, the Sixth of that Half, take the Half of 16, which is 8 Inches, and the Sixth of that is I Inch and 4 Parts; then, dividing the 8 Inches in the Multiplicand into 4 and 4, each being the Third of a Foot, take the third Part of 16, which is 5 Feet and 4 Inches, and that, being doubled, gives 10 Feet and 8 Inches,

Art. 52.

The Meafuring of Superficies.

T

ficial Content.

O measure a Square.

Rule. Multiply the Side of the Square into itself, and the Product is the Area or fuper

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Let A B C D reprefent a Square, whofe Side is 12 Feet. Multiply 12, the Side, by itself, thus,

12

12

144 Area,

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The Product 144 is the Area or fuperficial Content of the Square ABCD; that is, a Square, whofe Side is 12 Feet, contains 144 Feet: This will appear, if each of the Sides A B, BC, CD, and DA, are divided into 12 equal Parts, and Lines drawn from thofe Divifions cross the Square; for then will the Square be divided into 144 little Squares, whofe Sides will be equal to the Divifions of the Lines.

Art. 53. To measure a Parallelogram,

Rule. Multiply the Length by the Breadth, and the Product is the Area or fuperficial Content,

Let ABCD reprefent a Parallelogram, A whofe Length is 12 Feet, and Breadth

9 Feet. Multiply 12 by 9, and the Product is the Content.

B

D

12
9

108 Area.

Therefore the fuperficial Content is 108 Feet; as may be feen by dividing the Lines A B and CD into 12 equal Parts, and drawing Lines from one to the other; then dividing the Lines AD and BC into 9 Parts each, and drawing Lines from one to the other, cutting the former; by which the Parallelogram will be divided into 108 little Squares, each of whose Sides will be equal to the Divifions of the Lines: So that, of whatever Dimenfions the Divifions of the Lines are, the Parallelogram will contain 108 Squares of the fame Dimenfions,

Article 54. To measure a Rhombus.

Definition. A Rhombus is a Figure with four equal Sides, in the Form of a Quarry of Glafs, or a Diamond on Cards, having two Angles greater, and two lefs, than the Angles of a Square: The former are called obtufe Angles, and the latter acute or fharp Angles,

Rule.

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