Mensuration and Practical Geometry: Containing Tables of Weights and Measures, Vulgar and Decimal Fractions, Mensuration of Areas, Lines, Surfaces, and Solids ... To which is Appended a Treatise on the Carpenter's Slide-rule and GaugingHarper & brothers, 1858 - 322 pages |
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Page 160
... sphere may always be inscribed within , and may always be circumscribed about a regular body or polyhedron , which will have a common centre . 1. The Tetrahedron , or Pyramid , Fig . 78 , which has four triangular faces . 2. The ...
... sphere may always be inscribed within , and may always be circumscribed about a regular body or polyhedron , which will have a common centre . 1. The Tetrahedron , or Pyramid , Fig . 78 , which has four triangular faces . 2. The ...
Page 164
... is the volume of it ? 1.7323 × 1.5396 = product of cube of radius and tabular multiplier = 8 = result required . When the radius of the Inscribed Sphere is given . 164 MENSURATION OF SOLIDS . REGULAR BODIES Arc of Hyperbola 250.
... is the volume of it ? 1.7323 × 1.5396 = product of cube of radius and tabular multiplier = 8 = result required . When the radius of the Inscribed Sphere is given . 164 MENSURATION OF SOLIDS . REGULAR BODIES Arc of Hyperbola 250.
Page 165
... Inscribed Sphere is given . RULE . - Cube the radius ; and multiply it by the multiplier opposite to the figure in column C. EXAMPLE . — The radius of the inscribed sphere of a hexahe- dron is 1 inch ; what is its volume ? 13 × 8 ...
... Inscribed Sphere is given . RULE . - Cube the radius ; and multiply it by the multiplier opposite to the figure in column C. EXAMPLE . — The radius of the inscribed sphere of a hexahe- dron is 1 inch ; what is its volume ? 13 × 8 ...
Page 214
... sphere that may be inscribed within it ? Ans . 24429.0816 cubic inches . 27. In the walls of Balbeck , in Turkey , there are three stones laid end to end , now in sight , one of which is 63 feet long , 12 feet thick , and 12 feet broad ...
... sphere that may be inscribed within it ? Ans . 24429.0816 cubic inches . 27. In the walls of Balbeck , in Turkey , there are three stones laid end to end , now in sight , one of which is 63 feet long , 12 feet thick , and 12 feet broad ...
Page 220
... inscribed in a sphere 40 inches in diameter ? Ans . 23.094 inches . 63. How many cubic inches are contained in a cube that may be inscribed in a sphere 20 inches in diameter ? By rule , page 61 . Ans . 1480.2936 cubic inches . 64. If a ...
... inscribed in a sphere 40 inches in diameter ? Ans . 23.094 inches . 63. How many cubic inches are contained in a cube that may be inscribed in a sphere 20 inches in diameter ? By rule , page 61 . Ans . 1480.2936 cubic inches . 64. If a ...
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Common terms and phrases
12 inches 15 feet 20 feet 20 inches abscissa acres angle ascertain the Area ascertain the Contents base breadth cask Centre of Gravity chord of half Circular Spindle circumference cone conic section contents in cubic contents required convex surface cube cubic feet cubic foot cubic inches curve cycloid cylinder decimals diam divided equal eter EXAMPLE EXAMPLE.-The diameter EXAMPLE.-What figure fraction gauge point geometrical centre give the contents half the arc head diameter Hence hexahedron hyperbola hyperboloid Hyperboloid of Revolution inches in diameter inscribed sphere length less diameter linear edge Loomis's middle diameter middle frustrum miles multiply the sum ordinate parabolic spindle perpendicular prism product will give prolate spheroid pyramid quired quotient radii radius remainder result required rule sector segment slant height spherical square root subtract surface required transverse diameter triangle ungula versed sine vertex volume VULGAR FRACTIONS yards zone
Popular passages
Page 45 - The circumference of every circle is supposed to be divided into 360 equal parts, • called degrees, each degree into 60 minutes, and each minute into 60 seconds, etc.
Page 22 - To reduce a compound fraction to an equivalent simple one. RULE. — Multiply all the numerators together for a numerator, and all the denominators together for the denominator, and they will form the simple fraction sought.
Page 22 - To reduce a whole number to an equivalent fraction, having a given denominator. RULE. Multiply the whole number by the given denominator, and place the product over the said denominator, and it will form the fraction required.
Page 22 - To reduce an improper fraction to its equivalent whole or mixed number. RULE. — Divide the numerator by the denominator, and the quotient will be the whole or mixed number sought.
Page 31 - ... from the right hand of the quotient, point off so many places for decimals, as the decimal places in the dividend exceed those in the divisor.
Page 39 - Multiply the divisor, thus augmented, by the last figure of the root, and subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
Page 20 - Divide by any number that will divide two or more of the given numbers without a remainder, and set the quotients, together with the undivided numbers, in a line beneath.
Page 69 - ... troublesome and laborious that it must have cost him incredible pains. It is said to have been thought so curious a performance, that the numbers were cut on his tomb-stone in St. Peter's Church-yard at Leyden.
Page 84 - FIND the area of the sector having the same arc with the segment, by the last problem. Find also the area of the triangle, formed by the chord of the segment and the two radii of the sector.