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Fig. IX

Fig. X

Fig. X

III. Of the Triangle K L M, whofe Longeft Side LM is 267.26
Pole or Perches; and its Perpendicular LN 16p.25 Perches.
As + PLM 133.63 P:: LN 160.25 P: 21414 P.
Logar. 160.25

Logar. 133.63

Logar. of 21414

Fig. XII.




IV. Of the Trapezia (or Figure of Four unequal Sides) O PQR The Diagonal, whereof ŎQ is 27.32 Perches, the Perpendicular P S 9.53 P. and the Perpendicular R T, 21.06 P.

As 1 OP 13.66: PSRT 30.59: 417.85

Logar, of half OQ 13.66

Logar. of P S and K T, 30.59.

Logar. of 417.85 Perches.

Which is the Area, or Content in Perches:

Fig. XIII.




IV. Of an Irregular Plot, confifting of many unequal Sides und Angles: As the Figure A B CDEFG.

Before fuch Irregular Figures can be measured, they must be re- Fig. XIV. duced in Triangles or Trapezia's, by drawing of Lines from Angle to Angle at the beft Advantage, as in this, by the Lines F C and F C, which Two Lines divides the whole Plot into the Two Trapezia's ABCF, FCD E, and One Triangle FE G. And then the Bafes and Perpendiculars being fuch as are expreffed in the Figure, they may be measured, as is fhewed in the Two foregoing Sections hereof; and according to the following Operations.

I. For the Trapezia A B C F.

half A C, 12.16


Logarithm of BH and H F, 8.131 ad


the Area of ABCF, 98.86


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Fig. XV.

The Area of ABCDEFG

V. Of a Circle A B C D, whofe Diameter B C let be 14.00.

The Proportion of the Diameter of any Circle, to the Circumference thereof, is (in the leaft Terms) as 7 to 22: But in greater Numbers, as 113 to 355; and of thefe I fhall make use.

I. By the Diameter, to find the Circumference.

As 113: 355:: 14 Diam. : 43.98 Cir.

Logar. of 113

Logar. of 355


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Logar. of 14.00 the Diameter

The Logar. of 43.98 the Circumference

II. By the Circumference, to find the Diameter.

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V. By the Diameter, to find the Area.

As 10: 8.862 :: 14 Di. : 12.41 :: 12.41: 154.00

Log. 8.862


Log. 14

Logar. 12.41



The double of it

2.187320 Log. of 154 the Area.

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Of GEODECIA: Or, Land Measuring.

I. How (by any Graduated Inftrument) to take the true Plot of any large Piece of Ground, as Common Field, Park, Wood, &c.


going round about a Field to Survey it, there are Two ways; for in going round about it, you must either go on the infide or on the outfide; and fometimes you may be constrained to go fometimes within, and fometimes without.

Let ABCDEF, be fuch a Field to be furveyed and plotted. 1. Begin at any Angle thereof, as at A, and there fetting up your Inftrument, lay the Index and Sights upon the Diameter thereof, and turning it about, direct the Sights to B, and there

C c




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