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

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Page 27

Thus, PGP' is the

conceive any number of less circles, each parallel to the said great circle, this

poles also.

Thus, PGP' is the

**axis**, and P, P', are the poles, of the great circle cMD. If weconceive any number of less circles, each parallel to the said great circle, this

**axis**will be perpendicular to them likewise ; and the points P, P', will be theirpoles also.

Page 28

Lastly, we infer, that if a spherical angle be a right angle, the area of the great

circles which form it, will pass mutually through the poles of each other : and that,

if the planes of two great circles contain each the

through ...

Lastly, we infer, that if a spherical angle be a right angle, the area of the great

circles which form it, will pass mutually through the poles of each other : and that,

if the planes of two great circles contain each the

**axis**of the other, or passthrough ...

Page 39

Thus, if we wish to ascertain the solid angles at the vertices of the equilateral and

the rightangled cones; the

of each being unity. Hence, Angle at vertex. 1 : 1–3 v3 : : 1000 : 133.97464, ...

Thus, if we wish to ascertain the solid angles at the vertices of the equilateral and

the rightangled cones; the

**axis**of the former is v3, of the latter, #v2, the slant sideof each being unity. Hence, Angle at vertex. 1 : 1–3 v3 : : 1000 : 133.97464, ...

Page 62

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

an ellipse, the ratio of whose

it may, is a planet, which not only revolves in an orbit, but turns upon an

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, ... its exact sorm whatit may, is a planet, which not only revolves in an orbit, but turns upon an

**axis**. Page 63

... of the latitude ; and the ratio of the earth's

magnitude, may be ascertained by comparing the lengths of a degree on the

meridian in different latitudes. Hence appears the great importance of measuring

a degree.

... of the latitude ; and the ratio of the earth's

**axes**, as well as their actualmagnitude, may be ascertained by comparing the lengths of a degree on the

meridian in different latitudes. Hence appears the great importance of measuring

a degree.

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### 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...