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 100
Page 5
... whole circle , or to any number of quadrants whatever . In order to this , expressions must be first ob tained for the sines , cosines , & c . of the sums and differences of any two arcs or angles . Now , it has been found ( I. ) that a ...
... whole circle , or to any number of quadrants whatever . In order to this , expressions must be first ob tained for the sines , cosines , & c . of the sums and differences of any two arcs or angles . Now , it has been found ( I. ) that a ...
Page 6
... whole circle . NM B Imagine that the radius Mc of the circle , in the marginal figure , coinciding at first with Ac , turns about the point c ( in the same manner as a rod would turn on a pivot ) and thus forming successively with ac ...
... whole circle . NM B Imagine that the radius Mc of the circle , in the marginal figure , coinciding at first with Ac , turns about the point c ( in the same manner as a rod would turn on a pivot ) and thus forming successively with ac ...
Page 42
... whole doctrine may be comprehended in the subsequent problems and theorems . PROBLEM I. To find equations , from which may be deduced the solution of all the cases of spherical triangles . Let ABC be a spherical triangle ; AD the ...
... whole doctrine may be comprehended in the subsequent problems and theorems . PROBLEM I. To find equations , from which may be deduced the solution of all the cases of spherical triangles . Let ABC be a spherical triangle ; AD the ...
Page 61
... whole line intervening between two extreme points is not absolutely measured ; for this , on account of the in . equalities of the earth's surface , would be always very difficult , and often impossible . But , a line of a few miles in ...
... whole line intervening between two extreme points is not absolutely measured ; for this , on account of the in . equalities of the earth's surface , would be always very difficult , and often impossible . But , a line of a few miles in ...
Page 66
... whole of the series . It is requisite how . ever , previous to these calculations , to draw , by any suitable scale , the chain of triangles observed , in order to see whether any of the subsidiary triangles ACN , NFP , & c , formed to ...
... whole of the series . It is requisite how . ever , previous to these calculations , to draw , by any suitable scale , the chain of triangles observed , in order to see whether any of the subsidiary triangles ACN , NFP , & c , formed to ...
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.