III. Of the Triangle KLM, whose Longest Side LM is 267.26 ASP: LM 133.63 P:: LN 160.25 P: 21414 P. Fig. XII. Logar. 160.25 2.204798 Logar. 133.63 2.125904 Logar. of 21414 4.330702 9 ) IV. Of the Trapezia (or Figure of Four un equil Sides) OPQR The Diggonal, whereof OQ is 27.32 Perches, the Perpendicu lar P S 9.53 P. and the Perpendicular R T, 21.06 P. AS1:OP 13.66:: PS+RT 30.59: 417.85 Fig. XIII. Logar. of half OQ 13.66 1,135454 Logar. of P Sand K 1.485579 Logar. of 417.85 Perches 2.621030 Which is the drea, or Content in Perches. IW. Of an Irregular Plot, consisting of many unequal Sides and Angles: As the Figure ABCDE FG. Before fuch Irregular Figures can be measured, they must be re- Fig. XIV. duced in Triangles or Trapezid's, by drawing of Lines from Angle to Angle at the best Advantage, as in this, by the Lines FC and FC, which Two Lines divides the whole Plot into the Two Trapezia's ABCF, FCD E, and One Triangle FEG. And then the Bafes and Perpendiculars being fuch as are expressed in the Figure, they may be measured, as is fhewed in the Two foregoing Seltions hereof; and according to the following Operations. I. For the Trapezia ABCF. 1 1:084933 the Area of ABCF, 98.86 1.995023 II. For the Trapezia FCDE. Logarithm of half F D, 12.96 CL and EM, 23.11 1.112605 the Area of FCDE 299.5 2 476405 IL For V. Of a Circle ABCD, whose Diameter B C let be 14.00. Fig. XV. The Proportion of the Diameter of any Circle, to the Circumference thereof, is (in the least Terms) as 7 to 22: But in greater Numbers, as 113 to 355; and of these I shall make use. I. By the Diameter, to find the Circumference. II. By the Circumference, to find the Diameter. V. By the Diameter, to find the Area. As 10 : 8.862 : : 14 Di. : 12.41 : : 12.41 : 154.00 Log. 8.862 0.947532 Log. 14 1.146128 Of GEODÆCIA: Or, Land Measuring. I. How (by any Graduated Instrument) to take the true Plot of any large Piece of Ground, as Common Field, Park, Wood, &c. IN going round about a Field to Survey it, there are Two ways; going round about it, you must either go on the infide or on the outside; and sometimes you may be constrained to go sometimes within, and fometimes without. Let ABCDEF, be such a Field to be surveyed and plotted. 1. Begin at any Angle thereof, as at A, and there setting up your Instrument, lay the Index and Sights upon the Diameter thereof, and turning it about, direct the Sights to B, and there screw Cc Fig. XVII. Fig. screw it fast; and turn the Index about, till through the Sights, XVII. you fee the Angle at F; and there note what Degrees of the Inftrument were cut by the Index, which we will suppose to be 300 Deg. for the Quantity of the Exterior Angle FAB, without the Field: Or, 60 Deg. for the Quantity of the Interior An gle within the Field: Then measure the Side A F, which suppose to be 41.00 Pole or Perches, and the Side A B 30.00 Perches. These Distances, with the Quantity of the Angle before observed 300, or 60 Deg. set down in a Book or Paper, as you fee in the following Table. 2. Remove your Instrument to B, and laying the Index upon the Diameter, turn the Instrument about, till through the Sights you fee the Place where the Instrument last stood at A, and there fcrew it faft; and turn the Index about, till, through the Sights, you fee the Angle C, and note the Degrees which the Index cutteth; which are here 145 Deg. for the Exterior, or 215 Deg. for the Interior Angle ABC; and the Distance BC measured is 28.40 Perches: Both which, note down as before. 3. Remove your Instrument to C, and placing the Index on the Diameter, look back to B, and there screw it fist; and turn the Index about, till you fee the Angle at D, where the Index cutteth 270.25 Deg. for the Exterior, or 89.75 Deg. for the Interior Angle BCD, and the measured Distance CD is 23.40 Deg. 4. Remove the Instrument to D, the Index on the Diameter, and look back to C, and then screw it faft; then turn the Index about till by the Sights you see the Angle at E; the Index cutting 263 Deg. for the Exterior, or 97 Deg. for the Interior Angle CDE, the Measured Distance DE being 28.00 Perches: Which note down as the other. 5. Place your Instrument at E, the Index on the Diameter, look back to D, and then screw it fast, and turn the Index about till through the Sights you fee the Angle at F, the Index there cutting 220 Deg. for the Exterior, or 140 Deg. for the Interior Angle DEF; the Measured Distance E F being 42.80 Perches. 6. Place the Instrument at F, and the Index lying on the Dia meter, look back to E, and then screw it; and turn the Index a bout, till through the Sights you fee the Angle at A, (or the Place where you first placed your Instrument) where the Index cuts 210 Deg. for the Exterior, or 150 Deg. for the Interior Angle EF A, the Measured Distance F A being 41.00 Perches, as before. All which being noted down according to these Obfervations, and Measured, will stand as in this Table.. The |