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When Windows are made round at the Top, the Height is to be taken in the Middle, and they are to be measured as if they were square; no Allowance being made for what is wanting at the Corners, because the Trouble, and the Waste of the Glafs, is more than is faved by it. The fame is the Custom as to round or oval Windows, which are to be measured in their wideft and longeft Parts, and computed as fquare or oblong.

Of MASONS' Work.

Mafons' Work is measured by the Foot. Some Sorts of Work are measured only fuperficially; but, in others, they meafure the Solidity, taking in all the three Dimenfions, Length, and Thicknefs.

Exam. 1. A Pavement being 96 Feet long, 16 Feet and 9 Inches wide, how many fuperficial Feet are contained in it?

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Exam. 2. How many folid Feet are contained in a Wall 64 Feet, 6 Inches long, 20 Feet, 6 Inches high, and 2 Fee, 3 Inches thick?

F. I. P.

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Having multiplied two of the Dimensions, 64 F. 61. by 20 F. 6 I. the Product, 1322 F. 3 I. I place below, to have Room for making a new Multiplicand, by Art. 51. as in the Work.

In fome Places Walling is done by the Rood of 63 Feet, fuperficial Measure, as in Bricklayers' Work; the Thickness being allowed for in the Price.

Exam. 3. A Wall being 89 Feet and 3 Inches long, 15 Feet and 6 Inches high, how many Roods of 63 square Feet, are contained in it?

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Of PAVIOURS' Work.

Paviours' Work is done by the Yard; fo that nothing more is neceffary than to multiply the Length by the Breadth, and, if it were measured by the Foot, to divide by 9, to bring it into Yards: Therefore, Examples are not neceflary, as it is the fame with Joyners' and Painters' Work,

G

Of GEOMETRY.

EOMETRY is ufually defined, The Doctrine of Extenfion. The Word ftrictly means the Measuring of Land, but is applied to every Thing capable of being measured; that is, to all Things fufceptible of more and lefs. 'Tis ufually fuppofed that the Egyptians were the first Inventors of Geometry: Their Lands being annually overflowed by the Inundations of the Nile, its Impetuofity bore away their Land-Marks, and the Mud left behind made all Distinctions of their Lands impracticable, any other Way than by keeping Plans of their Figure and Quantity; fo that the natural Circumftance of their Country obliged them to the Study and Cultivation of Geometry.

Practical Geometry, or the Refolution of Problems, which is our prefent Bufinefs, is divided into Plain and Spherical.

Of Plain GEOMETRY.

Definitions.

1. A Point in the Mathematics is confidered only as a Mark, without any Regard to Dimenfions.

2. A Line is confidered as Length, without Regard to Breadth or Thickness.

3. A Plain, or Superfice, has two Dimensions, Length and Breadth, but is not confidered as having Thickness.

4. A Solid has three Dimenfions, Length, Breadth, and Thickness, and is ufually called a Body.

5. A Line is either straight, which is the nearest Distance betwixt two Points, or crooked, called a curve Line, whofe Ends may be drawn farther afunder.

6. If two Lines are at equal Distance from one another in every Part, they are called parallel Lines, which, if continued infinitely, will never meet.

7. If

7. If two Lines incline one towards another, they will, if continued, meet in a Point; by which Meeting is formed an Angle.

8. If one Line fall directly upon another, fo that the Angles on both Sides are equal, the Line fo falling is called a Perpendicular, and the Angles fo made are called right Angles.

9. All Angles, except they are right Angles, are called oblique Angles; whether they are acute, that is, less than a right Angle; or obtufe, that is, greater than a right Angle.

Geometrical Problems.

Problem 1. To divide a Line, A B, into two equal Parts. Set one Foot of the Compaffes in the Point A, and, opening them beyond the Middle of the Line, defcribe Arches above and below the Line; with the fame Extent of the Compaffes, fet one A Foot in the Point B, and defcribe two Arches croffing the former: Draw a Line from the Interfection of the Arches above the Line, to the Interfection below the Line; this will divide the Line A B into two equal Parts.

B

Prob. 2. To erect a Perpendicular on the Point C in a given

Line.

Set one Foot of the Compaffes in the given Point C, extend the other Foot to any Distance at Pleasure, as to D, and with that Extent make the Marks D and E. With the Compaffes, one Foot in D, at any Extent above Half the Diftance of D and E, defcribe an Arch above the Line; and with the fame Extent, and one Foot in E, describe an Arch croffing the former: Draw a Line from the Interfection of the Arches to the given Point C, which will be perpendicular to the given Line in the Point C.

I

D

C

E

Prob. 3.

Prob. 3. To erect a Perpendicular upon the End of a Line, or from a Point near the End.

There are diverfe Methods of doing this; of which I fhall give two.

E

First Method. If it be required to draw a Perpendicular to the Point B, near the End of the Line A B, fet one Foot of the Compaffes in the Point B, and, opening them at Pleasure, fet the other any where above the Line A B, as at C; let C be the Cen- Ater, on which defcribe an Arch cutting the Line A B in D, and paffing through the Point B, continue it to more than a Semicircle, till it comes over the Point B; draw the Line DCE from the Interfection at D, through the Center C, till it cuts the Arch in E; laftly, a Line drawn from E to B will be perpendicular to A B in the Point B.

Second Manner. Set one Foot of the Compasses in the given Point B, open them to any convenient Diftance, and defcribe the Arch CDE; fet one Foot in C, and with the fame Extent crofs the Arch A

at D, and with the fame Ex

D

C

B

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tent cross the Arch again from D to E; then, with one Foot of the Compaffes in D, and with any Extent above the Half of D E, defcribe an Arch a; take the Compaffes from D, and, keeping them to the fame Extent, with one Foot in E, interfect the former Arch a in a; from thence draw a Line to the Point B, which will be a Perpendicular to A B.

Prob. 4. From a given Point, a, to let fall a Perpendicular to a given Line.

This Problem has two Cafes, according as the Point is fituate, over the middle Part, or the End of the Line.

Cafe 1. To let fall a Perpendicular from the Point a over the Middle of A B.

Set

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