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 78
... Fig . 25 , by 10 times the versed sine , br ; divide the product by 27 times the versed sine subtracted from 60 times the diam- eter , and add the quotient to twice the chord 78 MENSURATION OF AREAS , LINES , AND SURFACES .
... Fig . 25 , by 10 times the versed sine , br ; divide the product by 27 times the versed sine subtracted from 60 times the diam- eter , and add the quotient to twice the chord 78 MENSURATION OF AREAS , LINES , AND SURFACES .
Page 79
... eter , and add the quotient to twice the chord of half the arc ; the sum will be the length of the arc very nearly . Or , é × 2 × 10 v 60d - 27v + 2c , d representing the diameter . EXAMPLE . The diameter of a circle is 100 feet , and ...
... eter , and add the quotient to twice the chord of half the arc ; the sum will be the length of the arc very nearly . Or , é × 2 × 10 v 60d - 27v + 2c , d representing the diameter . EXAMPLE . The diameter of a circle is 100 feet , and ...
Page 84
... eter of the Circle are given . When the Segment is less than a Semicircle , as a b c , Fig . 27 . RULE . Find the area of the sector having the same arc as the segment ; then find the area of the triangle formed by the chord of the ...
... eter of the Circle are given . When the Segment is less than a Semicircle , as a b c , Fig . 27 . RULE . Find the area of the sector having the same arc as the segment ; then find the area of the triangle formed by the chord of the ...
Page 111
... eter ( internal ) is 2 inches ; what is the surface of it ? Ans . 434.2624 inches . Link . Definition . An elongated ring . To ascertain the Convex Surface of a Link , Figures 51 . RULE . - Multiply the circumference of a section of the ...
... eter ( internal ) is 2 inches ; what is the surface of it ? Ans . 434.2624 inches . Link . Definition . An elongated ring . To ascertain the Convex Surface of a Link , Figures 51 . RULE . - Multiply the circumference of a section of the ...
Page 119
... eter of the drum is 94.5 inches , and the number of revolutions 20 ; what is the length of the rope and what is its thickness ? Ans . Length of the rope , 7194.247 inches . = Area of 134.5 in . 14208.049 66 66 94.5 = 7013.802 7194.247 ...
... eter of the drum is 94.5 inches , and the number of revolutions 20 ; what is the length of the rope and what is its thickness ? Ans . Length of the rope , 7194.247 inches . = Area of 134.5 in . 14208.049 66 66 94.5 = 7013.802 7194.247 ...
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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.