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

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Page 34

le=v(anot;. to.tant**.tant**.tan. =##5. The investigation of these theorems would

occupy more

vi. In every spherical polygon, or surface included by any number of intersecting ...

le=v(anot;. to.tant**.tant**.tan. =##5. The investigation of these theorems would

occupy more

**space**than can be allotted to them in the present volume. Theoremsvi. In every spherical polygon, or surface included by any number of intersecting ...

Page 35

... same plane, in one point. Others define it the angular

between several planes meeting in one point. It may be defined still more

generally, the angular

more curved ...

... same plane, in one point. Others define it the angular

**space**comprisedbetween several planes meeting in one point. It may be defined still more

generally, the angular

**space**included between several plane surfaces, or one ormore curved ...

Page 36

It is thus that mathematicians, with perfect safety and correctness, make use of

conjointly as a measure of force,

measure ...

It is thus that mathematicians, with perfect safety and correctness, make use of

**space**as a measure of velocity, mass as a measure of inertin, mass and velocityconjointly as a measure of force,

**space**as a measure of time, weight as ameasure ...

Page 114

A curve is a line whose several parts proceed in different directions, and are

successively posited towards dif. ferent points in

one right line in two or more points. If all the points in the curve may be included

in ...

A curve is a line whose several parts proceed in different directions, and are

successively posited towards dif. ferent points in

**space**, which also may be cut byone right line in two or more points. If all the points in the curve may be included

in ...

Page 151

Velocity, or Celerity, is an affection of motion, by which a body passes over a

certain

feet in - 4 seconds of time, it is said to move with the velocity of 10 feet per second

; ...

Velocity, or Celerity, is an affection of motion, by which a body passes over a

certain

**space**in a certain time. Thus, if a body in motion pass uniformly over 40feet in - 4 seconds of time, it is said to move with the velocity of 10 feet per second

; ...

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### 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...