A Treatise on Practical Gauging1822 |
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Page 39
... versed sine is part of the diameter cut off by the chord , as G H. 43. A segment is any part of a circle , bounded by an arc and its chord . 44. A semicircle is half of a circle , or a segment cut off by the diameter , as A D B. 45. A ...
... versed sine is part of the diameter cut off by the chord , as G H. 43. A segment is any part of a circle , bounded by an arc and its chord . 44. A semicircle is half of a circle , or a segment cut off by the diameter , as A D B. 45. A ...
Page 118
... versed sine , are sides of a right - angled triangle ; any two of which being given , the third may be found by ... sine CD 16 ; what is the length of the arc ACB ? Ans . 70.666 inches . 4. If the chord A C of half the arc measure 42.5 ...
... versed sine , are sides of a right - angled triangle ; any two of which being given , the third may be found by ... sine CD 16 ; what is the length of the arc ACB ? Ans . 70.666 inches . 4. If the chord A C of half the arc measure 42.5 ...
Page 124
... versed sine CE 18 in- ches ? D E Here √36 + 18 = √1296 + 324v 1620 40.2492 = DC , the chord of half the arc ; and 40.2492 x 8-72 3 321.9936-72 3 = DCB ; then 249.9936 3 83.3312 x 45 2 83.3312 , the length of the arc 3749.904 ...
... versed sine CE 18 in- ches ? D E Here √36 + 18 = √1296 + 324v 1620 40.2492 = DC , the chord of half the arc ; and 40.2492 x 8-72 3 321.9936-72 3 = DCB ; then 249.9936 3 83.3312 x 45 2 83.3312 , the length of the arc 3749.904 ...
Page 125
... versed sine are given , divide the square of half the chord by the versed sine ; to the quotient add the versed sine , and the sum will be the diameter of the circle ; hence its area may be found by Prob . 13. Or , multiply the square ...
... versed sine are given , divide the square of half the chord by the versed sine ; to the quotient add the versed sine , and the sum will be the diameter of the circle ; hence its area may be found by Prob . 13. Or , multiply the square ...
Page 126
... versed sine , or height of the segment ; and 303 120 x 2 27000 240 - = 112,5 , the cube of the height divided by twice the chord ; then 2400 + 112.5 = 2512.5 , the area in square inches ; whence , 2512.5 ÷ 282 = 8.9095 , the area in ale ...
... versed sine , or height of the segment ; and 303 120 x 2 27000 240 - = 112,5 , the cube of the height divided by twice the chord ; then 2400 + 112.5 = 2512.5 , the area in square inches ; whence , 2512.5 ÷ 282 = 8.9095 , the area in ale ...
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Common terms and phrases
40 inches ale gallons angle area and content area in square area in wine Area Seg barrels base bottom diameter breadth bung diameter cask centre chord circle cistern cone conjugate diameters contain content in ale content in cubic content in malt content in wine cooler copper cross diameters cube root cubic inches decimal diagonal Dimension Book dry inches ellipse EXAM EXAMPLES Excise figure find the area find the content foregoing frustum gauge and fix gauge and inch gauge-point given number guile-tun head hence liquor malt bushels mash-tun gallons mean diameter measure Method of Gauging middle diameter Multiply ordinates perpendicular depth pounds Prob PROBLEM quotient required the area required the content rhombus segment side Sliding Rule square divisor square inches square pyramid square root subtract take the dimensions top diameter trapezium triangle ullage ungula versed sine vulgar fraction wet inches whole content wine gallons
Popular passages
Page 42 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds.
Page 62 - ... are equal to two right angles. Let ABC be a triangle, and let one of its sides BC be produced to D ; the exterior angle ACD is equal to the two interior and opposite angles CAB, ABC ; and the three interior angles of the triangle, viz. ABC, BCA, CAB, are together equal to two right angles.
Page 182 - RULE.* To the sum of the areas of the two ends add four times the area of a section parallel to and equally distant from both ends, and this last sum multiplied by £ of the height will give the solidity.
Page 41 - A circle is a plane figure, bounded by a curved line, called the circumference, which is every where equidistant from a certain point within it, called the centre.
Page 42 - A circle is a plane figure bounded by a curved line called the circumference, every point of which is equally distant from a point within called the center, Fig.
Page 16 - 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 41 - A Segment is any part of a circle bounded by an arc and its chord.
Page 496 - The length shall be taken on a straight Line along the Rabbet of the Keel of the Ship, from the Back of the Main sternpost to a perpendicular Line from the Forepart of the Main Stem under the Bowsprit...
Page 64 - ... proportionally : and if the sides, or the sides produced, be cut proportionally, the straight line which joins the points of section, shall be parallel to the remaining side of the triangle.