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How to lay out any given Quantity of Acres
in a Parallelogram, whereof one fide is given.
Turn firft the Acres into Links, by adding as before five Cyphers ; that Number thus increased, divide by the given Side, the Quotient will be the other Side.
Example Let it be required to lay out too Acres in a Parallelogram, one side of which shall be 20 Chains : First to the 100 Acres I add five Cyphers, and it is 100, 00000, which I divide by 20 Chains, the Quotient is so. Chains, for the other side of the Parallelogram.
How to make a Triangle that shall contain any number of Acres, being confined ta a certain Bare
Double the given number of Acres, to which annex fivt Cyphers, which divide by the Base ; the Quotient will be the Length of the Perpendicular. This needs no Example.
How to find the Length of the Diameter of a
Circle, which shall contain any Number of
Say, as it is to 14, fo will the Number of Acres given, be to the Square of the Dizmeter of the Circle required.
Example. What's the Length of the Diameter of a Circle, whose superficial Content shall be loc Acres ? Add five Cyphers to the 100, and it inakes 100 00000 Links, which multiply by 14 it makes 1400OO COO ; which divide by 11, gives for the Quotient I 2727272; the Root of which is 35 Chains, 67 and somewhat more. And so much shall be the Diameter of the required Circle..
Of Reduction. How to reduce a large Plot of Land or Map into a lesser Compass, according to any given Proportion ; & contr, how to enlarge it.
Fig. 113. The best way to do this, is, if your plot be not too large, to Plot 'it over again by a smaller Scale ; but if it be large,
as the Map of a County, or the like, the only way is to compass in the Plot firft within one Square, and afterwards to divide that into as many little Squares, as you shall fee convenient. Also make the same number of little Squares upon a fair piece of Paper, by a leffer Scale, according to the Proportion given. This done, see in what Square, and part of the fame Square, any reinarkable Accident happens to fall, and accordingly put it down in the lesser Squares ; and that you may not mistake, it is a good way to number your Squares. I cannot make it plainer then by giving you the following Example, where the Plot ABCD, made by a Scale of 10 Chains in an Inch, is reduced into the Plot EFGH, of 30 Chains in an Inch.
What has been hitherto faid concerning reducing of a Plot from a greater to a Jeffer Volumn, the fame is to be underftood vice verfw, of enlarging a Plot from a lesser to a greater. But this seldom comes in Practice.
Knowing the Content of a piece of Land, to find out what Scale it was plotted by.
First, By any Scale measure the Content of the plot ; which done, the Proportion is as the Content found, is to the Square of the Scale it was tried by; so is the Content, to the Square of the true Scale it was plotted by.
Example Example. Admit, there is a plot of a piece of Land containing 10 Acres, and I measure it by a Scale of ui in an Inch, find it contain 12 Acres.
Then I say; if 12 gives for its Scale i 21, What shall 10 give?
Answer, 10. Therefore I conclude it was plotted by a Scale of 10 in an Inch.