A Treatise of Practical Mathematics, Part 2W. & R. Chambers, 1842 |
From inside the book
Results 1-5 of 17
Page 135
... cosine of an arc are the reciprocals of the cosecant and secant respectively ( Pl . Geom . Trig . p . 223 ) ; and therefore logarithmically , L4h = Lr + 2L cos i + L sec e + L cosec ( e — i ) — 40 . EXERCISE . Find the impetus with ...
... cosine of an arc are the reciprocals of the cosecant and secant respectively ( Pl . Geom . Trig . p . 223 ) ; and therefore logarithmically , L4h = Lr + 2L cos i + L sec e + L cosec ( e — i ) — 40 . EXERCISE . Find the impetus with ...
Page 148
... cosine of 3 of the angle of elevation ; find the potential range by article 202 ; divide this range by the reduced F , and find the quotient in the tabular column of potential ranges , and opposite to it in the preceding column of ...
... cosine of 3 of the angle of elevation ; find the potential range by article 202 ; divide this range by the reduced F , and find the quotient in the tabular column of potential ranges , and opposite to it in the preceding column of ...
Page 194
... cosine GB in the first quadrant being positive or + , those in the second and third quadrants perpendicular to the vertical diameter CK , and on the opposite side of it , are negative or , and those in the fourth quadrant are + ...
... cosine GB in the first quadrant being positive or + , those in the second and third quadrants perpendicular to the vertical diameter CK , and on the opposite side of it , are negative or , and those in the fourth quadrant are + ...
Page 195
... cosine , tangent , cotangent , or cosecant of an arc is given , its species is easily found ; for if the cosine , for example , is positive , the arc must be 90 ° ; and if the cosine is negative , the arc must be 90 ° . So if an arc a ...
... cosine , tangent , cotangent , or cosecant of an arc is given , its species is easily found ; for if the cosine , for example , is positive , the arc must be 90 ° ; and if the cosine is negative , the arc must be 90 ° . So if an arc a ...
Page 197
... cosine of the middle part is equal to the rectangle under the cotan- gents of the adjacent parts , or to that under the sines of the opposite parts . " That is , if M denote the middle part , A and a the adja- cent parts , and O and o ...
... cosine of the middle part is equal to the rectangle under the cotan- gents of the adjacent parts , or to that under the sines of the opposite parts . " That is , if M denote the middle part , A and a the adja- cent parts , and O and o ...
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Common terms and phrases
actual range bastion body breadth bung diameter called cask centre constructed content in imperial cosec cosine course declination deflexion depth dial difference of latitude difference of longitude distance ditch divide divisor draw earth elevation equal EXAMPLE EXERCISES fathoms Find the content flank frustum gauge point glacis hence horizontal hypotenuse imperial bushels imperial gallons impetus inches inclination length logarithms longitude mean diameter measure meridian middle moon's multiply number of balls oblique observed opposite parallax parallel parapet perpendicular pile place of arms plane plane sailing pole potential range preceding primitive PROBLEM projectile projection proportional quadrant quotient radius ravelin redoubt refraction right angle right ascension sailing semi-diameter Severndroog Castle side sidereal sin² sine Sliding Rule small circle specific gravity spherical angle spherical excess spherical triangle spherical trigonometry square sun's surface true altitude ullage velocity vessel weight
Popular passages
Page 196 - Fig. 9. Case 1. Let AB, AC be each less than a quadrant. Let AE, AG be quadrants ; G will be the pole of AB, and E the pole of AC, and EC a quadrant; but, by prop. 12. CE is greater than CB, since CB is farther off from CGD than CE. In the same manner, it is shown...
Page 95 - To the square of the bung diameter add the square of the head diameter ; multiply the sum by the length, and the product again by .0014 for ale gallons, or by .0017 for wine gallons.
Page 96 - RULE. — To the square of the bung diameter add the square of the head diameter ; multiply the sum by the length, and the product by .0014 for ale gallons, or by .0017 for wine gallons.
Page 42 - A magnitude which has length, breadth, and thickness. Solution. The process by which the answer to a question is obtained. Specific gravity of a substance. The ratio of the weight of a given volume of it to that of an equal volume of water.
Page 192 - A sphere is a solid, bounded by one continued convex surface, every point of which is equally distant from a point within, called the centre. The sphere may be conceived to be formed by the revolution of a semicircle about its diameter, which remains fixed.
Page 227 - ZODIAC.— The Zodiac is an imaginary belt, or broad circle, extending quite around the heavens. The ecliptic divides the zodiac into two equal parts, the zodiac extending 8 degrees on each side of the ecliptic, and therefore is 16 degrees wide.
Page 196 - BC will be greater than a quadrant : for let AE be a quadrant, then E is the pole of AC, and EC will be a quadrant. But CB is greater than CE by Prop. 12.
Page 195 - Oj the same affection with the angles opposite to them, that is, if the sides be greater or less than quadrants, the opposite angles will be greater or less than right angles, and conversely.
Page 195 - IN a right angled spherical triangle, the sides are of the same affection with the opposite angles ; that is, if the sides be greater or less than quadrants, the opposite angles will be greater or less than right angles. Let ABC be a spherical triangle right angled at A, any side AB, will be of the same affection with the opposite angle ACB. Case 1.
Page 195 - ... will be greater than a quadrant. Let ABC be a right angled spherical triangle ; according as the two sides AB, AC are of the same or of different affection, the hypotenuse BC will be less, or greater than a quadrant. The...