These Obfervations of Sides and Angles, as they were taken in the Field, being noted down in a Book or Paper, as in this Table; a Plot of the Field may be drawn upon Paper or Parchment, by the following Directions. To Protract the former Work. 1. Upon a Sheet of Paper or Parchment draw a Line A B, to contain 30.00 Perches, of any Scale: And upon the end thereof A, place the Centre of a Protrader, laying the Diameter of it upon the Line A B: -Then, the Exterior Angle at A, being 300.00 Deg. make a Mark against 300.00 Deg. of your Protra tor; and through that Point, and the Point A, draw a Right Line, downwards, as A F, to contain 41.00 Perches, of the fame Scale. 2. Apply the Centre of the Protractor to the Point B, and the Diameter upon the Line AB; then against 145.00 Deg. (the Angle at B) make the Mark, and through that Mark, and B, draw a Right Line B C, to contain 28.40 Perches. 3. Lay the Centre of the Protraitor upon C, and the Diameter upon B°C, and against 270.25 Deg, make a Mark; through which, and the Point C, draw the Line CD, to contain 23.40 Perches. 4. Apply the Centre of the Protractor to the Point D, and its Diameter to the Line CD; making a Mark against 263.00 Deg. through which, and the Point D, draw the Line D E, to contain 28.00 Perches. 1 5. Lay the Center of the Protractor upon the Point E, and its Diameter upon D E, and against 220.00 Deg. make a Mark; through which, and the Point E, draw a Right Line; which (if you have committed no former Error) will cut the Line, first drawn, in the Point F: And, by this Means, you will have upon your Paper, the exact Figure of your Piece of Ground: Which you may caft up, and find the Quantity thereof in Perches, (by the Directions of the Third Chapter hereof) which being divided by 160, will give the Content in Acres and odd Perches. CC2 In 4 Fig. Fig. XVIII. CHAP. V. Of STEREOMETRIA: Mensuration of Solids. I. Of the Cube ABCDEF, whose Side is 5.20 Foot. As 1: 5.20 :: 5.20 27.04 : : 27.04 : 140.61 Foot.. Logar. 5.20 Logar. 5.20 Logar. 27.04 Logar. 5.20 Log. of 140.61 Fig. 0.716003 0.716003 1.432006 0.716003 2.148009 Equal to the Solidity of the Cube in Feet. This might have been done more easily, for the Logar. of the XIX. Side 5.20, which is 0.7 16003, multiplied by 3, would haveproduced 2.148009, the Logar. of 140.61, the Solidity. II. Of a Long Cube or Parallelipipedon, GHIKL, whose Side of the Square at the End, KI, is 1.27 Foot, and of its Length GH, 5.32 Foot. As 1 : 1.27 :: L27: 1.61 :: 5.32: 8.58 Foot. Log. 1.27 Log. 1.27 Log. 5.32 0.103804 0.103804 0.725911 0.933519 II. Of III. Of an Oblong Parallelipipedon MNOPQR, whose Breadth Fig. XX: at the End NO is 3.40 Foot, and Depth M N 6.50 Foot, and the Length thereof MP, 16.25 Foot. As 1 : 3:40 :: 6.50 : 22.10 :: 16.25 : 159.12 Foot. Logar. 3.40 Logar. 6.50 Logar. 16.25 Logar. 359.12 0.531479 0.812913 1.210853 2.555245 The Solidity. IV. Of a Pyramis STVX N, whose Side of its Base ST, &c. in Fig.XXI. 1.12 Foot, and Altitude NX 12.90 Foot. As : 1.12:: 1.12: 1.25: NX: 4.30: 5.39 the Sol. Con. Logar. 1.12 0.049218 Logar. 1.12 0.049218 Logar. 4.30 0.633468 Logar. 5.39 0.73.1904 the Solid Content.i V. Of a Cone ABCD, whose Diameter BC is 6:12, and Alti- Fig. Let ABCHGF be the Fruftum of a Square Pyramid, the XXIV Side of the Square at the Leffer end A B, is 1.60 Foot, and there fore : fore the Area of that Square ABCD is 2.56 Foot: -The Side of the Square at the Greater End FG, is 2.30 Foot; and therefore the Area thereof is 5.29 Foot, and the Altitude DE 39.3 Foot. In the same manner the Fruftum of a Cone of the same Altitude, and the Area's of the Circles, at both Ends, the fame with the Area's of the Squares; the Solidity of fuch a Fruftum Cone, will be found to be the fame. Fig. VII. Of a Globe or Bullet, whose Diameter is 1.75 Foot. XXV. The Logar. of the Diameter 1.75 0.243038 Multiplied by 3. The Logar. of 355 Their Sum 0.729114 2.550228 3.279342 Logar. of [678 always] Substract Rests the Logar. of 2.806 Foot 2.831229 0.448113 Which is the Solidity of the Bullet.. ANCILLA |