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equal parts, viz. the Triangle ea z = to the Triangle abz (by Theorem 10;) at the point z make the Angle nzb = to the Angle F, draw n in Parallel to zb, and of equal Length to z b, draw mb Parallel to Dz and of qual Length to nz, then is the Parallelograin in n zb equal to the Triangle e ab. Now because it is required that a Paral. lelogram should have its fide equal to the Line AB, continue the Line n m, and make m x egal to AB,continue the Line z b,and inake br equal to mx, and join, the Line xr; from the point x and b, draw the prickt Line at pleafure, continue the Line nz to interfedt at the point o, draw o y Parallel to zr, and continue the Line mb to interfect at p, making p y equal and Parallel to br, and join the Liner y; then is the Parallelogram bry p, equal to the Parallelogram nm bz, by Theorem 11. In like manner make the Parallelogran pyqs equal to the Triangle EBD.; likewise inake the parallelogram sgth equal to the Triangle DBC, then will the Parallelogram brfh be equal to the Right-line Figure ABCDE QEF and QED.
If it were required to lay out a Rightangled Parallelogram . equal to the faine Right-lined Figure, and the Side equal to the Line, AB, let the Right-lined Figure ABCDE contain 12 Acres, adding 5 Cy phers to it, the fame Field will contain 1:200000 Square Links : Let the Line AB re
present the Length of a Hedge given containing 60. Chains or 6000 Links ; Divide I 200000 by 6000 and the Quotient will be 2000 Links or 20 Chains for the Breadth of the Right-Angled Parallelogram; for 2000 Links multiplyed by 6000 Links, produces 12000CO Square Links, or 1$ Square Acres.
To reduce Statute-measure to Customary-me afure,
and the Contrary.
Although an Acre of Land by Statute is to contain 160 Square Perches, of 16 Feer and in the Perch ; yet in some places of the Nation, through long Cuftoin, there is at this day other Perches used, as 18, 20, 24, and 28 Feet to the Perch ; it is therefore necessary to shew how to reduce Statute measure to Cuftoinary, Esc.
Suppose therefore you would reduce Statute ineasure to Wood-land-measure of 18 Feet to the Perch, then say,
As the Square of the greater Perch of 18 Feet, is to the Square of the lefler Porch of 16 Feet and; fo is the Content in Acres according to the leffer Perch, to the Content in Acres, according to the greater Perch..
Example. Let it therefore be required to reduce 36 Acres, 2 Ronds, 10 Perches, at 16 Feet and
to the Perch, into Wood.land measure of 18 Feet to the Perch.
Firt, You must observe that the Square of 16 Feet and is Decimally 272, 25, and the Square of 18 Feet is 324 ; then I reduce the 36 Acres 2 Roods, 10 Perches, into perches, which makes 5850, then i multiply the same by the Square of the lefser Perch, 272, 25, and the Product is 1592662. 50, being divided by the Square of the greater Perch. 324, the Quotient is 4915;625, which is 30 Acres, 2 Roods, 25: Porches for the Answer,
Bat suppose you would reduce Wood... land-measure into S atute-measure, then say,
As the Square of the lefser Perch of 16 Feet and, is to the Square of the greater Perch 18 Feet; so is the Content in Acres according to the greater Perch to the Content in Acres, according to the lefser. Perch.
How to cajt up the Content of any Plot, in
Acres, Roods, and Perches: Fig. 112. Admit the following Figure noted with the Letters A, B, C, D, E, F, G, H, I, be the plot of a Field, whose
Content in Acres, Roods and Purches is. Fequired.
Fiil, Then ( in all such Cafes ) divide your Plot into Trapezia's and Triangles ; accordingly this Figure is divided into one Trapezium, as K, D, P, I, and four Triangles ; for finding the Area of all which, begin with any one firft, and multiply the whole of the Base by cne half of the Perpendicular, or (which is alone) the whole of the Perpendicular, by the of the Base ; the product either of the Content of that Triangle ; and then Şum up all the Area's of the several Triangles tous cher, gives you. the Content of the whole Plot.
A. R. P. Lot Area or
Trap. KDPI 7-2--25 Comment of the
Trian, ABK 0-1--00
Trian. BCD ---0--CD
The Area of the whole Field.
But the most exact way of all, is to multiply the Length of the Base of each Triangle, by the Length of the Perpendi
cular, the Sum Total of all the Triangles : being halved, gives the true Area of the whole Field in Square Links, (or Chains and
Links,) which may be reduced at laft (by the former Directions) into Acres, Roods and Perches.
Of laying ont New. Lands. A certain Quantity of Acres being given, how to lay out the fame in a Square Figure.
RU L E
Annex to the number of Acres given five Cyphers, which will turn the Acres into Links; then from the Number thus increased, extract the Square Root, which thall be the fide of the proposed Square
Example Suppose the Number given to be joo Acres, which I am to lay in a Square Figure ; I join to the too, five Cyphers, and then it is 10000000 Square Links, the Root of which is 3162 nearest, or 31 Chains 62 Links the Length of one side of the Square.
Again, If I were to cut out of a CornField one Square Acre, I add to one five Cyphers, and then it is 100000, the Root of which is 3. Chains 16 Links, and fomething more, for the fide of the Acre.