A Course of Mathematics: For the Use of Academies as Well as Private Tuition : in Two Volumes, Volume 2W. E. Dean, 1831 |
From inside the book
Results 1-5 of 43
Page 13
... rectangle of the sum and dif . ference of the sines ; it follows , that the first of these equa tions converted into an analogy , becomes sin ( A — B ) : sin a — sin B :: sin + sin B : sin ( A + B ) ( XX . ) That is to say , the sine of ...
... rectangle of the sum and dif . ference of the sines ; it follows , that the first of these equa tions converted into an analogy , becomes sin ( A — B ) : sin a — sin B :: sin + sin B : sin ( A + B ) ( XX . ) That is to say , the sine of ...
Page 24
... secant of 45 ° is a mean proportional between the tangent of 45 ° and the secant of 60 ° . Ex . 19. Demonstrate that 4 times the rectangle of the sines of two ares , is equal to the difference 24 ANALYTICAL PLANE TRIGONOMETRY .
... secant of 45 ° is a mean proportional between the tangent of 45 ° and the secant of 60 ° . Ex . 19. Demonstrate that 4 times the rectangle of the sines of two ares , is equal to the difference 24 ANALYTICAL PLANE TRIGONOMETRY .
Page 104
... rectangle of the coefficient of the second and third terms , made less by the cube of the coefficient of the second term , and 3 times the coefficient of the fourth term : viz . a3 +63 + c2 + & c . = —ƒ3 + 3fg — 3h . For we shall by ...
... rectangle of the coefficient of the second and third terms , made less by the cube of the coefficient of the second term , and 3 times the coefficient of the fourth term : viz . a3 +63 + c2 + & c . = —ƒ3 + 3fg — 3h . For we shall by ...
Page 124
... rectangle under the ordinate of a given conic section and a given right line , by the common abscissa . 21. When the term ca is negative , the figure expressed by the equation xy2 + ey = ca + d , is either a serpentine hyperbola ...
... rectangle under the ordinate of a given conic section and a given right line , by the common abscissa . 21. When the term ca is negative , the figure expressed by the equation xy2 + ey = ca + d , is either a serpentine hyperbola ...
Page 129
... rectangle of the ordinates is equal to the rectangle of the abscissa and latus rectum : so , in those curves of the second kind , or lines of the third kind , which have only two vertices to the same diameter , the solid under the three ...
... rectangle of the ordinates is equal to the rectangle of the abscissa and latus rectum : so , in those curves of the second kind , or lines of the third kind , which have only two vertices to the same diameter , the solid under the three ...
Other editions - View all
Common terms and phrases
abscissas altitude axis ball base beam becomes body centre of gravity chords circle consequently Corol cosine curve denote density descending determine diameter direction distance draw earth equa equal equation equilibrio EXAM expression feet find the fluent fluid fluxion force given plane ground line Hence horizontal plane hyperbola inches inclined plane intersection length logarithm measure motion multiplied nearly ordinates parabola parallel pendulum perpendicular pressure prob PROBLEM PROP proportional quantity radius ratio rectangle resistance right angles right line roots Scholium side sine solid angle space specific gravity spherical angle spherical excess spherical triangle square straight line supposed surface tangent theorem theref tion velocity vertex vertical plane vertical projections vibrations weight whole
Popular passages
Page 459 - Or, by an. 249 of the same, the pressure is equal to the weight of a column of the fluid...
Page 66 - To prove that the exterior angle of a triangle is equal to the sum of the two interior opposite angles (see fig.
Page 195 - VI, its Corollaries and Scholium, for Constant 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 distance from the centre of the earth ; and since • this is the force by which bodies descend to the surface ;...
Page 239 - BPC) ; or, the pressure of a fluid on any surface is equal to the weight of a column of the fluid...
Page 289 - 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 35 - Two planes are said to have the same or a like inclination to one another which two other planes have, when the said angles of inclination are equal to one another.
Page 75 - Let a, b, c, be the sides, and A, B, c, the angles of a spherical triangle, on the surface of a sphere whose radius is r ; then...
Page 385 - Multiply the number in the table of multiplicands, by the breadth and square of the depth, both in inches, and divide that product by the length, also, in inches; the quotient will be the weight in Jbs.t Example 1.
Page 244 - 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 140 - Body is either Hard, Soft, or Elastic. A Hard Body is that whose parts do not yield to any stroke or percussion, but retains its figure unaltered. A Soft Body is that whose parts yield^to any stroke or impression, without restoring themselves again ; the figure of the body remaining altered.