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

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Page 155

For, with regard to the forces P, Q, represented in magnitude and direction by AB

and AF, let T be opposed to those two forces so as to keep the whole system in

For, with regard to the forces P, Q, represented in magnitude and direction by AB

and AF, let T be opposed to those two forces so as to keep the whole system in

**equilibrio**: then it will, of necessity, be equal and opposite to their resultant, R, ... Page 156

Because the three sides co, cE, DE, are proportional to the sines of their opposite

angles E, D, c ; therefore the three forces, when in

the sines of the angles of the triangle made of their lines of direction ; namely, ...

Because the three sides co, cE, DE, are proportional to the sines of their opposite

angles E, D, c ; therefore the three forces, when in

**equilibrio**, are proportional tothe sines of the angles of the triangle made of their lines of direction ; namely, ...

Page 159

When the weight and power keep the lever in

reciprocally as the distances of their lines of direction from the prop. That is, p : w

:: cd : ce; where cd and cE are perpendicular to wo and Ao, the directions of the ...

When the weight and power keep the lever in

**equilibrio**, they are to each otherreciprocally as the distances of their lines of direction from the prop. That is, p : w

:: cd : ce; where cd and cE are perpendicular to wo and Ao, the directions of the ...

Page 160

In a straight lever, kept in

; then, of these three, the power, weight, and pressure on the prop. any one is as

the distance of the other two. 57. Corol. 6. If A B C T) E. several weights P, Q, ...

In a straight lever, kept in

**equilibrio**by a weight and power acting perpendicularly; then, of these three, the power, weight, and pressure on the prop. any one is as

the distance of the other two. 57. Corol. 6. If A B C T) E. several weights P, Q, ...

Page 161

... its distance; and in the case of an equi. librium, the sums of the effects, or of the

products on both sides, are equal. The same would also follow from art. 26. 58.

Corol. 7. Because, when two weights Q and R are in B C D

... its distance; and in the case of an equi. librium, the sums of the effects, or of the

products on both sides, are equal. The same would also follow from art. 26. 58.

Corol. 7. Because, when two weights Q and R are in B C D

**equilibrio**, Q : R :: cD ...### What people are saying - Write a review

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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...