Rule. As1 Square of Depth:: Length. a 4th Num. then say, { .524 } Example. A Spheriod, whose Length or Tranfverfe Axis is Inches {7.2 Depth or Conjugate 4. I } Tenths. What's the Solid Content? Anfw. Inches 63.4 Tenths. For it's, As 1. Square 4.1 :: 7.2 121; here the Extent from 1 to 4.1 is turned twice from 7.2, and it reacheth to 121. Then say, S 11. S Inches 63.4 tenths, the 2.524 Content required. Or thus; As I 4.1 0.524 2.15 2.15.8.81; That is, the Extent on the Line of Numbers from 1 to 4.1 will reach from 0.524 to 2.15; and the fame Extent from 2.15 to 8.81 Parts of 100. Then; As 1.8.81 :: 7.2 ·. 63.4; that is, the Extent from . I to 8.81, will reach from 7.2 to Inches 63.4 Tenths, the Solid Content required. Prob. XXXI. The Dimenfions of a Prism given; to find the Solid Content. Definition 1. A Prifm, is a ftrait Solid, whofe two Bases or Ends are equal, parallel, a-like, and a-like fituate. 2. A Prifm, takes its Sir-Names from its Bafe; as a Round Prism, a Triangular, a Quadrangular, or a Multangular Prism, are all measured by this one General Rule. As I .. Area of one Bafe :: Length.. Solid Content, Example 1. A Round Prism, called by fome a Cylinder, whose Diameter at each End is - - 21 Inches. And Length is - 30 S What's the Solid Content? Anfw. 10392 Inches. A Cylinder's two Bafes are two equal Circles, and therefore the Area of it's Bafe is found by Prob. 30. to be Inches 346.4 Tenths; Then it is, the As I 346.4 30 10392, Inches the Solid Content required. Tranfverfe? Axis of each is {12 What's the Solid Content? Anfw. Inches 2262, For its Bafe being an Ellipfis, the Area by Prob. 27, is Inches 75.4, and then it is, As 175.4 30. 2262 Inches the Solid Content required. Example 3. A Triangular Prism, whofe Bafes are equal Triangles, in each of which, The S Bafe Perpendicular } is { 12. 16.2 Inches given. And the Length of the Solid is 20 Inches. What's the Solid Content? Anfw. Inches 1920. The Area of the Bafe. (by Prob. 24) in Page 22, is 96 Inches; and then it is, As I 96 20. 1920 Inches, Solid Content required. Example 4. A Cube which is a Quadrangular Prism, of equal Length, Breadth and Depth, bounded by fix equal Squares, each Side being Inches 12: What's the Solid Content? Anfw. Inches 1728. For, As I Square of 12 :: 12. 1728: That is the Extent from 1 to 12, turned over 2 times from 12, reacheth to Inches 1728 the Solid Content required. Example 5. A Parallelopipedon, or Quadrangular Prism, whose Bases are two equal Squares, of each, one Side Length } is is Feet [21:25} Parts of 100 given; What the Solid Content? Anfw. Fect 3.39 Tenths. For, As Square of 1.25: 21.75 Feet 3.39: That is, the Extent from 1 to 1.25, being turned two Times from 21.75 with reach to 3.39, the Solid Content required. Example 6. A Parallelopipedon, or a Quadrangular Prism, whose Bases are two equal Long-squares in each, Breadth is The {Depth is 2.5 Feet given. And Length of the Solid 15.5 What's the Solid Content? Anfw. Feet 62. For it is, As, I 1.6 2.54 Feet, the Area of the Base. Then, As 14: 15.562 Feet, Solid Content required. In like manner may the Solid Content of any Prism be found, let its Bafe be of what Form foever; for its Area may be found by Prob. 20, 21, 22, 23, 24, 25, 26, or 27, and the Solid Content of the Prifm, by the General Rule in Problem the 31st. Prob. XXXII. The Dimenfions of a Pyramid given; to find the Solid Content. Definition 1. A Pyramid is a ftrait Solid, having only one Bafe, and the other End a Point, called the Vertex. 2. A Pyramid, takes its Sir-name from its Base, as a Round, an Elliptic, a Triangular, a Quadrangular, or a Multangular Pyramid; all are meafured by this General Rule. As 3 Area of the Bafe: Length Solid Content, Note; By Length understand a Perpendicular from the Vertex to the Base, and not the Length of the Pyramid on its Surface or outfide from Vertex to Base. Example. A Round Pyramid, called by fome a Cone, whose Diameter at Bafe Perpendicular Length 30 21 Inches given. What's the Solid Content? Anfw. 3465 Inches. by Prob. 20. And, Then; As 3 346.5 :: 30. 3456 Inches, which is the Solid Content required. The like do for any other Pyramid, which I pafs over, having. given fix Examples in a Prism, and leave you to apply them here. Prob. XXXIII. The Dimenfions of a Prifmoid given; to find the Solid Content. Definition 1. A Prifmoid, is a ftrait Solid having two unequal Bafes or Ends, but are parallel, like, and a-like fituate. 2. A Prifmoid, is as various as a Prism, and is no other than the Fruftum of a Pyramid. 3. Fruftum of a Pyramid, is the lower Part of it, when the upper Part of it is cut off parallel to the Bafe; and all of them may be measured by this General Rule. 1. Multiply the Area of each Bafe together, and extract the Square Root of the Product. 2. Add the Area of each Bafe and that Square Root into one Sum: Then, 3. Say, as 3 that Sum :: Length .. Solid Content. But for a Square Prifmoid, take this particular Rule; 1. To the Square of each Side, add the Product of the Sides into one Sum; then, Say, as 3 that Sum :: Length. Solid Content. 1. Add the Square of each Diameter, and the Product of the two Diameters into one Sum: And then, 2. Say, as 3.82 that Sum: Length. Solid Content. Or more largely thus, As 38197, is to the aforefaid Sum; so is the Length to the Solid Content, Example 1. A Square Prifmoid, (or the Fruftum of a Square Pyramid) whofe Greatest } Side is Inches. [15 Perpendicular Length 9 Inchés given; 60 What's the Solid Content? Anfw. 8820 Inches. 225 Square. 81 Square. 135 Product. - 441 Inches; Sum of the two Squares and Product is Then, as 3441 :: 60-8820 Inches, the Solid Content required? Example 2. A Round Prifmoid (or a Fruftum of a Cone). whofe Greatest } Diameter is { 1.5 0.9 Feet given; Perpendicular Length is 60.0 What's the Solid Content? Anfw. Feet 69.25. For; As I.. S1.57 1.5 2.25 Square. 0.81 Square. .0.9. 1.35 Product. Sum of the two Squares and Product 4.41 Feet. - Then as 3.82 4.41: 60. 69.25 Feet, the Solid Content, Example 3. An Elliptic Prifmoid, or the Fruftum of an Elliptic Cone, whofe Greatest Diameter at Top, Inches 7.57 Leaft Diameter at Bottom |