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

### From inside the book

Results 1-5 of 100

Page 5

Hence we may immediately deduce a very important theo. rem : for, the first of

these equations, divided by the second, gives #: ~ +, and the first divided by the

third gives # at > — = + , whence since two

we ...

Hence we may immediately deduce a very important theo. rem : for, the first of

these equations, divided by the second, gives #: ~ +, and the first divided by the

third gives # at > — = + , whence since two

**equal**fractions denote an equation,we ...

Page 7

describing point M has passed over a quadrant, and arrived at B: in that case, PM

becomes

continuing its motion beyond B, the sine P'M' will diminish, while the cosine c'P', ...

describing point M has passed over a quadrant, and arrived at B: in that case, PM

becomes

**equal**to CB the radius, and the cosine CP vanishes. The point Mcontinuing its motion beyond B, the sine P'M' will diminish, while the cosine c'P', ...

Page 20

First, with regard to the arc of 45°, the sine and cosine are manifestly

they form the perpendicular and base of a right-angled triangle whose

hypothenuse is

cosine of 45° ...

First, with regard to the arc of 45°, the sine and cosine are manifestly

**equal**; orthey form the perpendicular and base of a right-angled triangle whose

hypothenuse is

**equal**to the assumed radius. Thus, if radius be R, the sine andcosine of 45° ...

Page 24

Demonstrate that the sum of the sines of two arcs which together make 60°, is

gr. sin 3+sin 59°57' = sin 60°3'; and thus that the tables may be continued by ...

Demonstrate that the sum of the sines of two arcs which together make 60°, is

**equal**to the sine of an arc which is greater than 60° by either of the two arcs: Ex.gr. sin 3+sin 59°57' = sin 60°3'; and thus that the tables may be continued by ...

Page 25

sines of two arcs, is

sum and difference of those arcs. Ec. 20. Convert the equations marked xxxiv into

their equivalent logarithmic expressions; and by means of them and equa. Iv, find

...

sines of two arcs, is

**equal**to the difference of the squares of the chords of thesum and difference of those arcs. Ec. 20. Convert the equations marked xxxiv into

their equivalent logarithmic expressions; and by means of them and equa. Iv, find

...

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Other editions - View all

### Common terms and phrases

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...