## A Course of Mathematics: For the Use of Academies, as Well as Private Tuition, Volume 2 |

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Page 2

The cotANGENT, cosroANT, and coversed sine of an arc, are the tangent, secant,

and versed sine, of the complement of such arc. 3. Since arcs are proper and

adequate measures of plane angles, (the

The cotANGENT, cosroANT, and coversed sine of an arc, are the tangent, secant,

and versed sine, of the complement of such arc. 3. Since arcs are proper and

adequate measures of plane angles, (the

**ratio**of any two plane angles being ... Page 16

The last equation, however, only shows the sums of sines and cosines of arcs or

angles in arithmetical progression, when the common difference is to the first

term in the

of ...

The last equation, however, only shows the sums of sines and cosines of arcs or

angles in arithmetical progression, when the common difference is to the first

term in the

**ratio**of 2 to 1. To investigate a general expression for an infinite seriesof ...

Page 36

And the

or other surfaces thus formed, will be ...

angles, constituted by the meeting of the several planes or surfaces, at the centre

...

And the

**ratio**which subsists between the areas of the spheric triangles, polygons,or other surfaces thus formed, will be ...

**ratio**which subsists between the solidangles, constituted by the meeting of the several planes or surfaces, at the centre

...

Page 62

It may be either an ellipsoid of revolution, that is, a body formed by the rotation of

an ellipse, the

or it may approach nearly to the form of such an ellipsoid or spheroid, while its ...

It may be either an ellipsoid of revolution, that is, a body formed by the rotation of

an ellipse, the

**ratio**of whose axes is nearly that of equality, on one of those axes ;or it may approach nearly to the form of such an ellipsoid or spheroid, while its ...

Page 63

... poles, will be increased in the duplicate

and the

ascertained by comparing the lengths of a degree on the meridian in different

latitudes.

... poles, will be increased in the duplicate

**ratio**of the right sine of the latitude ;and the

**ratio**of the earth's axes, as well as their actual magnitude, may beascertained by comparing the lengths of a degree on the meridian in different

latitudes.

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absciss altitude axis ball base beam becomes body centre of gravity chords 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 angle spherical excess spherical triangle square straight line supposed surface tangent theorem 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 465 - Or, by art. 249 of the same, the pressure is equal to the weight of a column of the fluid...

Page 70 - To prove that the exterior angle of a triangle is equal to the sum of the two interior opposite angles (see fig.

Page 295 - 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 154 - 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 245 - BPC) ; or, the pressure of a fluid on any surface is equal to the weight of a column of the fluid...

Page 297 - 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 250 - 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 490 - 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 457 - ... 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...