A Complete Treatise on Practical Mathematics: Including the Nature and Use of Mathematical Instruments: Logarithmic Tables, Trigonometry, Mensuration of Heights and Distances,--of Surfaces & Solids, Land Surveying, Gunnery, Gauging, Artificer's Measuring, Miscellaneous Exercises. With an Appendix on Algebra ... Principally Designed for the Use of Schools and Academies |
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Page 31
... miles , & c . , and the angle at A 30 ° 40 ° , ( and confequently the angle at C 59 ° 20 ′ ) Required the fides BC , AC . Variety 1. making AB rad . BC becomes the tangent , and AC the fecant of angle A. Whence arife the following pro ...
... miles , & c . , and the angle at A 30 ° 40 ° , ( and confequently the angle at C 59 ° 20 ′ ) Required the fides BC , AC . Variety 1. making AB rad . BC becomes the tangent , and AC the fecant of angle A. Whence arife the following pro ...
Page 54
... miles above the level of the fea , and the angle of depreflion taken from the fartheft vifible point , be 87 ° 25 ' 55 " . Required the diameter of the earth , alfo the fartheft vifible point that can be feen from the Peak . If the ...
... miles above the level of the fea , and the angle of depreflion taken from the fartheft vifible point , be 87 ° 25 ' 55 " . Required the diameter of the earth , alfo the fartheft vifible point that can be feen from the Peak . If the ...
Page 56
... miles higher at the equator , than at the poles . A degree has likewife been measured at the equator , and found ' to be confiderably lefs than in the latitude of Paris , which confirms the oblate figure of the earth . Hence it appears ...
... miles higher at the equator , than at the poles . A degree has likewife been measured at the equator , and found ' to be confiderably lefs than in the latitude of Paris , which confirms the oblate figure of the earth . Hence it appears ...
Page 59
... mile 1285 yards . EXAMPLE II . After obferving the firing of a cannon , 24 feconds elapfed , before I heard the report , required the distance . Anf . 5 miles 336 yards . EXAMPLE III . After observing a man ftriking a bell with a hammer ...
... mile 1285 yards . EXAMPLE II . After obferving the firing of a cannon , 24 feconds elapfed , before I heard the report , required the distance . Anf . 5 miles 336 yards . EXAMPLE III . After observing a man ftriking a bell with a hammer ...
Page 54
... miles above the level of the fea , and the angle of depression taken from the farthest visible point , be 87 ° 25 ′ 55 ′′ . Required the diameter of the earth , alfo the fartheft vifible point that can be feen from the Peak . If the ...
... miles above the level of the fea , and the angle of depression taken from the farthest visible point , be 87 ° 25 ′ 55 ′′ . Required the diameter of the earth , alfo the fartheft vifible point that can be feen from the Peak . If the ...
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Common terms and phrases
abfciffa acres againſt alfo alſo altitude amplitude axis bafe baſe becauſe breadth centre chain chord of half circle circumference Co-fec Co-tan column cone conjugate cube defcribe dift diſtance divide divifor elevation Engliſh equal Euclid EXAMPLE fame fecond fegment fhall fimilar find the area find the folidity firſt fquare root fquare yards fruftum ftraight line fubtract fuch fuperficies furface girt given greateſt half the arch height horizontal houſe hypothenufe inftrument laft acquired velocity laſt lefs logarithm malt bufhels meaſure obferved off-fets oppofite ordinate parabolic perpendicular plane Plate quantity quotient rectangle Required the area Required the content Required the folidity rhombus right angles RULE Secant Secant Co-fec ſpace ſphere ſpindle ſquare ſteeple Suppofe tangent theodolite theſe thickneſs tranfverfe trapezium triangle triangular uſed verfed whofe diameter whofe fide whofe length whoſe wine gallons
Popular passages
Page 27 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; and each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds ; and these into thirds, etc.
Page 115 - Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 3 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Page 232 - E, is equal to twice as many right angles as the figure has sides, less four right angles.
Page 1 - ... common to the two triangles AFE, BFE, there are two sides in the one equal to two sides in the other, each to each ; and the base EA is equal to the base EB ; (i.
Page 38 - BG; that is, the fum of the fides is to their difference, as the tangent of half the fum of the angles at the bafe to the tangent of half their difference.
Page 372 - Subtract the square number from the left hand period, and to the remainder bring down the next period for a dividend. III. Double the root already found for a divisor ; seek how many times the divisor is contained...
Page 38 - AB the greater side for a distance, let a circle be described, meeting AC, produced in E, F, and BC in D; join DA, EB, FB; and draw FG parallel to BC, meeting EB in G. The angle EAB (32.
Page 38 - ACB (32. 1.) is equal to the angles CAD and ADC, or ABC together ; therefore FAD is the difference of the angles at the...
Page 395 - TO divide a given ftraight line into two parts, fo that the rectangle contained by the whale, and one of the parts, fhall be equal to the fquare of the other part. Let AB be the given ftraight line; it is required to divide it into two parts, fo that the rectangle contained by the whole, and one of the parts, fhall be equal to the fquare of the other part. Upon AB...