## 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

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**become**subtractive , then would sin . c manifestly**become**subtractive also , while the cosine of c would not change its sign , since it would still continue to be estimated on the same radius in the same direction . Hence the preceding ... Page 6

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**becomes**cos . ( B + c ) = cos . B. cos . C- siu . B. sin . c . = 12. In this latter equation , if c be made subtractive , sin . c will**become**sin . c , while cos . c will not change : conse . quently the equation will be transformed to ... Page 7

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**becomes**equal to CB the radius , and the cosine cr vanishes . The point м continuing its motion beyond B , the sine r'n ' will diminish , while the cosine c'r ' , which now falls on the contrary side of the centre c will in . crease ... Page 10

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**becomes**when radius is assumed = R , R3 sin . 3A or sin . 3A = R2 3sin . A - 4sin3 . A 3R2sin . A - 4sin3 . A R2 ...**become**successively equal to 2A , 3A , 4A , & c . there will arise sin . A. cos . 2A + cos . A. sin . 2A sin . 3A ... Page 12

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**becomes**sin . A'R2 ± R / R — sin3 . 2A ' or sin . A ' = ± √2R2 ± 2r cos . A ' : } ( XII . ) by putting cos . A ' for its value R2 - sin . A ' , multiplying the quantities under the radical by 4 , and dividing the whole second number by ...### 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.