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This Method of finding the mean Dimensions of a Square, though much in Use, is in many Cafes very erroneous, and gives the Content less than the Truth; which is reckoned by Workmen as an Allowance for the Slabs. But to have the true Content without any Deduction of Bark or Slabs, it must be measured as the Fruftum of a Cone; or it may be reduced to a Cylinder, making the mean Circumference, when truly found, the Circumference of a Cylinder, and finding its Content accordingly.

But to get the Content very near the Truth, by having the Circumference given; multiply the Square of of the Girth by twice the Length, and the Product will be the Solidity near enough.

Problem 15.

To measure an Irregular Body another Way, and more exactly.

Rule.

Put the Body into a regular Vessel (either square or round) and fill it to the Brim with Water; then take out the Body, and measure the Vacuity of the Veffel left between the Surface of the Water and the Top of the Vessel, and that will give the Solidity of the Body taken out.

Problem 16.

To find the Side of a Cube equal to any given Solid, whether Parallelopipedon, Cone, Cylinder, Sphere, &c. Only extract the Cube Root of the Content of the given Solid in Inches, and that Root will be the Side of a Cube equal to it.

Note. By these Problems are measured Timber, Stone, &c. as well as the Vacuity of any Veffel in Shape of, or reducible to any of those Figures.

Also note. If any Chest, Bing, Veffel, &c. in Form of any of the foregoing Figures, have its Content found in Inches, the Quantity of Water, Ale, Wine, Malt, Corn, &c. it will contain may be found by dividing the Inches by

282 for Gallons of Water, Ale, Beer.
231 for Gallons of Wine, Cyder.

2152.42 for Bushels of Malt, Corn.
1728 for Feet Solid.

THE CONIC SECTION S.

A

Cone is a solid Figure having a circular Base, as A B, and growing regularly smaller till it ends in a Point at the Top, called its Vertex, at V. Every such Solid may be cut by Planes into five Sections following:

(1st.) If a Cone be cut directly down the Middle or Axis VC, the Plane or Superficies of that Section will be a Triangle, as AV B.

C
A

B

(2d.) If the Cone be cut through any where parallel to its Base, the Plane of that Section will be a Circle. The Point C in the Middle is called its Center or Focus; and the Line going through it, its Diameter, or Latus Rectum, as A B.

AB

(3d.) If the Cone be cut through any where in an oblique Pofition, as at A B, the Plane of that Section will be an Ellipsis, or oblong Circle, as ABCD. The Line A B is called the Transverse Diameter, and the Line CD the Conjugate Diameter.

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As every Circle hath one Center, called its Focus, or Burning Point; so every Ellipsis hath two Centers, called the Foci, or Burning Points of that Ellipsis, as ff.

All Lines drawn across the Transverse Diameter at right Angles are called Ordinates; and those two Lines which pass through the two Focii are more observable than the reft, and are called each the Latus Rectum.

Note. The Comets all revolve round the Sun in Orbits of this Elliptic Figure; the Sun being situated in one of the Foci.

(4th.) If a Cone be cut in two Parts by a Line A E parallel to one of its Sides, this Section will be a Parabola, as GAH. The Line A E drawn through the Middle is called its Axis; any Line crossing this at Right Angles is called an Ordinate; and that Part of the Axis which is contained between the Vertex and the Ordinate is called the Abscissa. The Focus or Burning Point (for every Parabola hath but one) is always in the Axis towards the Top, as at f; and the Ordinate, or Line that goes through it, is called the Latus Rectum, as 11.

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All Bodies projected, as Arrows, Stones, Cannon Balls, and spouting Fluids, move (whether upward or downward) in a Curve Line of this Kind, which never returns into itself, but opens wider and wider, as extended and carried on.

N. B. On this Principle depends the whole Art of

Gunnery.

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