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

### From inside the book

Results 1-5 of 32

Page 44

... useful in reducing

the three sides of a spherical triangle : it is required to find expressions for the

determination of the angles. Retaining the notation of prob. 1, in all its generality,

...

... useful in reducing

**inclined**lines to the**plane**of the horizon. PROBLEM II. Giventhe three sides of a spherical triangle : it is required to find expressions for the

determination of the angles. Retaining the notation of prob. 1, in all its generality,

...

Page 76

... m'm v3. o Prople.M. iii. To reduce angles measured in a

TRIGONOMETRICAL SURVEYing.

... m'm v3. o Prople.M. iii. To reduce angles measured in a

**plane inclined**. 76TRIGONOMETRICAL SURVEYing.

Page 77

To reduce angles measured in a

angles in the horizontal

to the horizon, and let B'cA' be the corresponding angle in the horizontal

To reduce angles measured in a

**plane inclined**to the horizon, the correspondingangles in the horizontal

**plane**. Let BoA be an angle measured in a**plane inclined**to the horizon, and let B'cA' be the corresponding angle in the horizontal

**plane**... Page 136

Now, from this, the nature of curves formed by

different directions, may readily be inferred. Let it be supposed, first, that the

cutting

and passes ...

Now, from this, the nature of curves formed by

**planes**cut. ting the cone indifferent directions, may readily be inferred. Let it be supposed, first, that the

cutting

**plane**is**inclined**to the base of a right-angled cone in the angle of 45°,and passes ...

Page 158

These are usually accounted six in number, viz. the Lever, the Wheel and Axle,

the Pulley, the

the fixed point about which a body moves. And the Axis of Motion, is the fixed line

...

These are usually accounted six in number, viz. the Lever, the Wheel and Axle,

the Pulley, the

**Inclined Plane**, the Wedge, and the Screw. 43. Centre of Motion, isthe fixed point about which a body moves. And the Axis of Motion, is the fixed line

...

### 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...