A Course of Mathematics: For the Use of Academies as Well as Private Tuition : in Two Volumes, Volume 2W. E. Dean, 1831 |
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Results 1-5 of 76
Page 39
... vertical angle in one , and a the angle of inclination of each two of its plane faces ; if'n be the number of planes meeting about the vertex of the other , and a the angle of inclination of each two of its faces : then will the vertical ...
... vertical angle in one , and a the angle of inclination of each two of its plane faces ; if'n be the number of planes meeting about the vertex of the other , and a the angle of inclination of each two of its faces : then will the vertical ...
Page 64
... plane , the line AM will also be in that plane : but , because of the curvature of the earth , the prolongation MM ... vertical of the place of the observer , it will represent the prime vertical of that place . The series of all ...
... plane , the line AM will also be in that plane : but , because of the curvature of the earth , the prolongation MM ... vertical of the place of the observer , it will represent the prime vertical of that place . The series of all ...
Page 69
... plane of the horizon , and another to bring the observed angles to the true ... vertical line , previously or subsequently occupied by the centre of the ... plane mirror as a point of observation , was first suggested by ...
... plane of the horizon , and another to bring the observed angles to the true ... vertical line , previously or subsequently occupied by the centre of the ... plane mirror as a point of observation , was first suggested by ...
Page 77
... plane . Let BCA be an angle measured in a plane inclined to the horizon , and let B'CA ' be the corresponding angle ... vertical circles , measuring 6 A the zenith distances d , d , and draw the arc ab of another great circle to ...
... plane . Let BCA be an angle measured in a plane inclined to the horizon , and let B'CA ' be the corresponding angle ... vertical circles , measuring 6 A the zenith distances d , d , and draw the arc ab of another great circle to ...
Page 86
... vertical angle в we demit the perpendicular BD upon the base Ac , dividing it into the two segments a , ß , we shall ... plane triangle , gives c . sin a = a . sin c . Also , sin A. COS A = sin 2A , and sin c ( equa . xv , ch . iii ) ...
... vertical angle в we demit the perpendicular BD upon the base Ac , dividing it into the two segments a , ß , we shall ... plane triangle , gives c . sin a = a . sin c . Also , sin A. COS A = sin 2A , and sin c ( equa . xv , ch . iii ) ...
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Common terms and phrases
absciss altitude axis ball base beam becomes body centre of gravity circle conic surface consequently Corol cosine curve cylinder denote density descending determine diameter direction distance draw earth equa equal equation equilibrio EXAM expression feet find the fluent fluid force given plane ground line Hence horizontal plane hyperbola inches inclined plane intersection length logarithm measure motion moving multiplied nearly ordinate parabola parallel pendulum perpendicular position pressure prob PROBLEM PROP proportional quantity radius ratio rectangle resistance right angles right line roots Scholium side sine solid angle space specific gravity spherical excess spherical triangle square straight line supposed surface tangent theorem theref tion variable velocity vertex vertical plane vertical projections vibrations weight whole
Popular passages
Page 13 - In any plane triangle, the sum of any two sides is to their difference, as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page 469 - Or, by art. 249 of the same, the pressure is equal to the weight of a column of the fluid...
Page 74 - To prove that the exterior angle of a triangle is equal to the sum of the two interior opposite angles (see fig.
Page 299 - The workmen thought that substituting part silver was only a proper <perquisite; which taking air, Archimedes was appointed to examine it ; who, on putting...
Page 158 - MECHANICAL POWERS are certain simple instruments employed in raising greater weights, or overcoming greater resistance than could be effected by the direct application of natural strength. They are usually accounted six in number; viz. the Lever, the Wheel and Axle, the Pulley, the Inclined Plane, the Wedge, and the Screw.
Page 249 - BPC) ; or, the pressure of a fluid on any surface is equal to the weight of a column of the fluid...
Page 301 - In the doctrine of fluxions, magnitudes or quantities of all kinds are considered as not made up of a number of small parts, but as generated by continued motion, by means of which they increase or decrease ; as a line by the motion of a point ; a surface by the motion of a line ; and a solid by the motion of a surface.
Page 254 - Weigh the denser body and the compound mass, separately, both in water, and out of it ; then find how much each loses in water, by subtracting its weight in water from its weight in air; and subtract the less of these remainders from the greater. Then...
Page 494 - The reason is, all bodies lose some of their weight in a fluid, and the weight which a body loses in a fluid, is to its whole weight, as the specific gravity of the fluid is to that of the body.
Page 461 - ... horizontal *. 2. The theorems just given may serve to show, in what points of view machines ought to be considered by those who would labour beneficially for their improvement. The first object of the utility of machines consists in furnishing the means of giving to the moving force the most commodious direction ; and, when it can be done, of causing its action to be applied immediately to the body to be moved. These can rarely be united : but the former can be accomplished in most instances...