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equal parts, viz. the Triangle ea z = to the Triangle abz (byTheorem 103) at the point z make the Angle nzb = to the Angle F, draw n in Parallel to zb, and of equal Leogth to z b, draw mb Parallel to na and of qual Length to nz, then is the Parallelograin in nz bequal to the Triangle e ab. Now because it is required that a Paral. lelogram should have its fide equal to the Line A B, 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 x r; from the point xand b, draw the prickt Line at pleasure, continue the Line nz to intersect at the point o, draw o y Parallel to zr, and continue the Line mb to intersect at p; making P y equal and Parallel to br, and join the Line r y'; then is the Parallelogram bry p, equal to the Parallelogram nm bz; by Theorem 11. In like manner make the Parallelograin p y qs equal to the Triangle EBD.; likewise inake the parallelogram sgth equal to the Triangle DBC,then will the Parallelogram brf h be equal to the Right-line Figure ABCDE QEF and QED.
If it were required to lay out a Rightangled Parallelogram equal to the fame Right-lined Figure, and the Side (qual to the Line, AB, let the Right-lined Figure ABCDE contain 12 Acres, adding 5 Cyphers to it, the same Field will contain 1200000 Square Links : Let the Line AB ie.
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 1200000 Square Links, or 1 Square Acres.
To reduce Statute-measure to Customary-me asure,
and the Contrary. Although an Acre of Land by Statute is to contain 160 Square Perches, of 16 Feet and in the Perch ; yet in some places of the Nation, through long Cuftoin, there is at this day other P«rches used, as 18, 20, 24, and 28 Feet to the Perch ; it is therefore necessary to shew how to reduce Statute. measure to Custoinary, &c.
Suppose therefore you would reduce Statute measure 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 lesser Pärch of 16 Feet and to is the Content in Acres according to the leffer Perch, to the Content in Acres, according to the greates Perch..
Examples Let it therefore be required to reduce 36 Acres, 2 Ronds, 10 Perches, at 16 Feet and
to the Perch, into Woodland measure of 18 Feet to the Perch.
First, You must observe that the Square of 16 Feet andis 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 585.7, then i multiply the same by the Square of the lefltr Perch, 272, 25, and the Product is 1592662. 50, being divided by the Square of the greater Parch. 324, the Quotient is 4915,825, which is 30 Acres, 2 Roods, 25: Perches for the Answer,
Bat suppose you would reduce Wood-.. land-measure into S atute-measure, then say,
As the Sjuare of the lesser 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 Perches is required.
Fift, 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 sum up all the Area's of the several Triangles tous cher, gives you the Content of the whole Plot.
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 Dire&tions) into Acres, Roods and Percher.
Of laying ont New Lands.
A certain Quantity of Acres being given, how to lay out the fame in a Square Figure.
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 fhall 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 100, 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, Ladd to one five Cyphers, and then it is 100000, the Root of which is 3. Chains 16 Links, and fomething more, for the side of the Acre.