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 47
... , Ellipse , & c . , & c . , is the point of intersection of two or more of their respective diagonals , radii , or diameters . The side of a Square is equal to the square MENSURATION OF AREAS , LINES , AND SURFACES . 47.
... , Ellipse , & c . , & c . , is the point of intersection of two or more of their respective diagonals , radii , or diameters . The side of a Square is equal to the square MENSURATION OF AREAS , LINES , AND SURFACES . 47.
Page 62
... radii of the circumscribing and inscribed circles ? * 9.8506 = 7.6554-7 feet 7.8648 inches , radius of circum- scribing circle . - 9.6882 6.1938-6 feet 2.3256 inches , radius of inscribed circle . To ascertain the Radius of a Circle ...
... radii of the circumscribing and inscribed circles ? * 9.8506 = 7.6554-7 feet 7.8648 inches , radius of circum- scribing circle . - 9.6882 6.1938-6 feet 2.3256 inches , radius of inscribed circle . To ascertain the Radius of a Circle ...
Page 63
... radii of its circumscribing and inscribed circles ? √ / 144-12 , and 12 x.3605-4.326 inches , √ / 144-12 , and 12.5833-6.9996 √ / 144-12 , and 12x.5548-6.6576 66 Ans . 66 Additional uses of the foregoing Table . The sixth and seventh ...
... radii of its circumscribing and inscribed circles ? √ / 144-12 , and 12 x.3605-4.326 inches , √ / 144-12 , and 12.5833-6.9996 √ / 144-12 , and 12x.5548-6.6576 66 Ans . 66 Additional uses of the foregoing Table . The sixth and seventh ...
Page 81
... radii . To ascertain the Area of a Sector of a Circle when the Degrees in the Arc are given ( Fig . 26 ) . RULE . - AS 360 is to the number of degrees in the sector , so is the area of the circle of which the sector is a part to the ...
... radii . To ascertain the Area of a Sector of a Circle when the Degrees in the Arc are given ( Fig . 26 ) . RULE . - AS 360 is to the number of degrees in the sector , so is the area of the circle of which the sector is a part to the ...
Page 84
... radii of the sector , and the dif- ference of these areas will be the area required . NOTE . - Subtract the versed sine from the radius ; multiply the re- mainder by one half of the chord of the arc , and the product will be the area of ...
... radii of the sector , and the dif- ference of these areas will be the area required . NOTE . - Subtract the versed sine from the radius ; multiply the re- mainder by one half of the chord of the arc , and the product will be the area of ...
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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.