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

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Page 116

... name of coxic src 10Ns, because they all result from sections of the cone. The

different kinds of these lines are the ellipse, the circle, or ellipse with equal axes,

the parabola, and the

...

... name of coxic src 10Ns, because they all result from sections of the cone. The

different kinds of these lines are the ellipse, the circle, or ellipse with equal axes,

the parabola, and the

**hyperbola**; the properties of all which may be deduced with...

Page 117

Ilcre, when the first term fro is affirmative, the curve expressed by the equation is

a

absent, the curve is a parabola. When r is taken upon a diameter, the equations ...

Ilcre, when the first term fro is affirmative, the curve expressed by the equation is

a

**hyperbola**; when fro is negative, the curve is an ellipse ; when that term isabsent, the curve is a parabola. When r is taken upon a diameter, the equations ...

Page 121

Let this parallel be bisected in x, and then will the locus of that point x be the

conical or common

asymptote be AB. Then the equation by which the relation between the ordinate

Bo = y, ...

Let this parallel be bisected in x, and then will the locus of that point x be the

conical or common

**hyperbola**xa, one of whose asymptotes is As. Let its otherasymptote be AB. Then the equation by which the relation between the ordinate

Bo = y, ...

Page 122

This kind of

neither the term ey be wanting, nor bo – 4ac =ae V a, the curve will have no

diameter: but ...

This kind of

**hyperbola**is called redundant, because it exceeds the conic**hyperbola**in the number of its hyperbolic legs. In every redundant**hyperbola**, ifneither the term ey be wanting, nor bo – 4ac =ae V a, the curve will have no

diameter: but ...

Page 123

Thus, if all the roots Ap, Az, Air, Ap, be real, and have the same sign, and are

unequal, the curve will consist of three

...

Thus, if all the roots Ap, Az, Air, Ap, be real, and have the same sign, and are

unequal, the curve will consist of three

**hyperbolas**and an oval: viz. an inscribed**hyperbola**, as Ec; a circumscribed**hyperbola**, as Tóc ; an ambigeneal**hyperbola**,...

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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...