A Treatise of Practical Mathematics, Part 2W. & R. Chambers, 1842 |
From inside the book
Results 1-5 of 20
Page 181
... quadrant ; draw DF , cutting AB in G ; and the circle CGD , through the points C , G , D , is the required circle . F G C D E P B For , considering APB as the primitive , and D its pole , PG is evidently the projection of a quadrant EF ...
... quadrant ; draw DF , cutting AB in G ; and the circle CGD , through the points C , G , D , is the required circle . F G C D E P B For , considering APB as the primitive , and D its pole , PG is evidently the projection of a quadrant EF ...
Page 186
... quadrant from G , a point of the circle LGM . Also , the distance between F and G , the poles of AKB and DCE , is ... quadrants , FHCK . Now , FH must not exceed FN , the measure of the angle , otherwise the circle LHM would not meet IGN ...
... quadrant from G , a point of the circle LGM . Also , the distance between F and G , the poles of AKB and DCE , is ... quadrants , FHCK . Now , FH must not exceed FN , the measure of the angle , otherwise the circle LHM would not meet IGN ...
Page 187
... quadrant . The same small circle will be determined by finding the more remote pole , that is , the projection of the pole nearest to the projecting point , and then describing a small circle about it , at a distance equal to the ...
... quadrant . The same small circle will be determined by finding the more remote pole , that is , the projection of the pole nearest to the projecting point , and then describing a small circle about it , at a distance equal to the ...
Page 193
... quadrant ; and consequently the same term is applied to angles in reference to a right angle . The species of the sides and angles of spherical tri- angles can generally be easily determined by means of the algebraical signs of their ...
... quadrant ; and consequently the same term is applied to angles in reference to a right angle . The species of the sides and angles of spherical tri- angles can generally be easily determined by means of the algebraical signs of their ...
Page 194
... quadrant is also + , and those in the third and fourth quadrant NL , EI , are negative or So the cosine GB in the first quadrant being positive or + , those in the second and third quadrants perpendicular to the vertical diameter CK ...
... quadrant is also + , and those in the third and fourth quadrant NL , EI , are negative or So the cosine GB in the first quadrant being positive or + , those in the second and third quadrants perpendicular to the vertical diameter CK ...
Contents
207 | |
209 | |
218 | |
225 | |
234 | |
241 | |
247 | |
259 | |
95 | |
103 | |
111 | |
112 | |
119 | |
127 | |
129 | |
137 | |
144 | |
151 | |
165 | |
172 | |
178 | |
187 | |
192 | |
200 | |
206 | |
267 | |
273 | |
283 | |
291 | |
299 | |
309 | |
316 | |
329 | |
336 | |
338 | |
344 | |
352 | |
363 | |
370 | |
376 | |
382 | |
389 | |
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...