A Course of Mathematics: For the Use of Academies as Well as Private Tuition, Volume 2Campbell, 1812 |
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Page 5
... proposition in the theory of sines , & c , must be deduced , and the method explained by which Tables of these quantities , confined within the limits of the quadrant , are made to ex- tend to the whole circle , or to any number of ...
... proposition in the theory of sines , & c , must be deduced , and the method explained by which Tables of these quantities , confined within the limits of the quadrant , are made to ex- tend to the whole circle , or to any number of ...
Page 28
... proposition is a necessary consequence of the truth , that the shortest distance between any two points , measured on the surface of the sphere , is the arc of a great circle pass- ing through these points . THEOREM II . The Sum of the ...
... proposition is a necessary consequence of the truth , that the shortest distance between any two points , measured on the surface of the sphere , is the arc of a great circle pass- ing through these points . THEOREM II . The Sum of the ...
Page 30
... proposition . 2dly . The respective measures of the angles of the triangle DEF are supplemental to the opposite sides of the triangles ABC . For , since the arcs AL and BG are each 90 ° , therefore = 180 ° - ᎪᏴ ; is AL + BG is 30 ...
... proposition . 2dly . The respective measures of the angles of the triangle DEF are supplemental to the opposite sides of the triangles ABC . For , since the arcs AL and BG are each 90 ° , therefore = 180 ° - ᎪᏴ ; is AL + BG is 30 ...
Page 31
... proposition only obtains with regard to the central triangle ( of each hemisphere ) , which is distinguished from the three others in this , that the two angles a and F are situated on the d F e KE same side of BC , the two в and E on ...
... proposition only obtains with regard to the central triangle ( of each hemisphere ) , which is distinguished from the three others in this , that the two angles a and F are situated on the d F e KE same side of BC , the two в and E on ...
Page 97
... proposition . A like demonstration will apply , mutatis mutandis , to any other polygon . Cor . When the sides of the polygon are reduced to three , this theorem becomes the same as the fundamental theorem in chap . ii , from which the ...
... proposition . A like demonstration will apply , mutatis mutandis , to any other polygon . Cor . When the sides of the polygon are reduced to three , this theorem becomes the same as the fundamental theorem in chap . ii , from which the ...
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Common terms and phrases
absciss altitude axis ball base beam becomes body centre of gravity circle column consequently Corol correct fluent cosine cubic curve cycloid cylinder denote density descending determine diameter direction distance earth elevation equa equal equation equilibrio EXAM expression feet find the fluent fluid force gives greatest Hence horizontal hyperbola inches inclined plane length lever logarithm measured motion moving nearly oblique ordinate parabola parallel pendulum perp perpendicular pressure prob PROBLEM projectile prop proportional PROPOSITION quantity radius ratio rectangle resistance right angles right line roots Scholium sides sin² sine solid angle space specific gravity spherical excess spherical triangle square supposed surface tangent theorem theref tion trapezium variable velocity vertical vibrations weight whole
Popular passages
Page 437 - Or, by art. 3 14 of the same, the pressure is equal to the weight of a column of the fluid...
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 155 - 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 241 - 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 240 - As the weight lost in water is to the whole, or absolute weight ; so is the specific gravity of water ' " to "the specific gravity 'of the body . 2.
Page 155 - LBVER is any inflexible rod, bar, or beam, which serves to raise weights, while it is supported at a point by a fulcrum or prop, which is the centre of motion. The lever is supposed to be void of gravity or weight, to render the demonstrations easier and simpler.
Page 451 - It has been found, by these experiments, that no difference is caused in the velocity, or range, by varying the weight of the gun, nor by the use of wads, nor by different degrees of ramming, nor by firing the charge of powder in different parts of it.
Page 82 - The surface of a spherical triangle is measured by the excess of the sum of its three angles above two right angles, multiplied by the tri-rectangular triangle.
Page 304 - ... 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 128 - Forces, are true in the Motions of Bodies freely descending by their own Gravity; namely, that the velocities are as the Times, and the Spaces as the Squares of the Times, or as the Squares of the Velocities. FOR, since the force of gravity is uniform, and constantly the same, at all places near the earth's surface, or at nearly the same...