## Dictionary of the Mathematical and Physical Sciences, According to the Latest Improvements and Discoveries |

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Page 164

... ellipse, namely, describe a semi-circle upon the transverse, produce the

ordinate till it meet this circle, from the point of contact draw a radius, and a

perpendicular to it at the point of contact, will cut the transverse produced in the

... ellipse, namely, describe a semi-circle upon the transverse, produce the

ordinate till it meet this circle, from the point of contact draw a radius, and a

perpendicular to it at the point of contact, will cut the transverse produced in the

**subtangent**. Page 178

... have the ratio to each other, not of the ordinate and absciss, but of the ordinate

and

will give the

... have the ratio to each other, not of the ordinate and absciss, but of the ordinate

and

**subtangent**; and, of consequence, { the absciss and ordinate being known,will give the

**subtangent**; or, which amounts to the same, the tangent itself. Page 231

... centre C we may draw two right lines clo, Car which will be the limits of the

tangents to the hyperbola, these lines, whose position we shall soon determine,

are called the asymptotes of the layperbola. The

ara.

... centre C we may draw two right lines clo, Car which will be the limits of the

tangents to the hyperbola, these lines, whose position we shall soon determine,

are called the asymptotes of the layperbola. The

**subtangent**PT = z — 24 - - zz -ara.

Page 276

The

modulus of the logarithms; and the area between any two ordinates is equal to

the rectangle of the constant

The

**subtangent**of this curve is always equal to the same constant quantity a themodulus of the logarithms; and the area between any two ordinates is equal to

the rectangle of the constant

**subtangent**, and the difference of the ordinates. Page 339

Therefore, in the parabola, the subnormal * is always equal to the semi-

parameter. As for the : * In any curve AM, (fig. 4.) o T M is a tangent to the curve at

the point M and A P and P M coordinates to the same point; then p : *led the

Therefore, in the parabola, the subnormal * is always equal to the semi-

parameter. As for the : * In any curve AM, (fig. 4.) o T M is a tangent to the curve at

the point M and A P and P M coordinates to the same point; then p : *led the

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### Common terms and phrases

absciss Algebra altitude appears Arithmetic Astronomy axis body called centre circle co-efficients conic sections consequently cosine cube curve cycloid cylinder degree denominator denote diameter distance diurnal motion divided divisor earth ecliptic ellipse equa equal equation feet figure fluid fluxion force formula fraction frustrum Geometry given glass gravity greater greatest heat Hence horizon hyperbola inches instrument latitude length less logarithm longitude means measure mercury meridian method moon motion multiplied neral object observed orbit ordinate parabola parallax parallel passing perihelion perpendicular plane poles produced proportion quantity radius ratio rays refraction right angles right ascension right line roots side signs sine solid space specific gravity sphere spherical square stars subtangent supposed surd surface tangent telescope tion triangle tube velocity weight whence wind

### Popular passages

Page 456 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.

Page 524 - In higher works on trigonometry, it has been demonstrated that, in any triangle, the sines of the angles are proportional to the lengths of the sides opposite to them. In other words, sin A : sin B :: BC : AC; or, sin A : sin C:: BC : AB, and sin B : sin C::AC : A B. Hence, we have sin 44° 40' : sin 56° 20

Page 312 - A law presupposes an agent ; for it is only the mode, according to which an agent proceeds : it implies a power ; for it is the order, according to which that power acts. Without this agent, without this power, which are both distinct from itself, the law does nothing ; is nothing. The expression, ' the law of metallic nature...

Page 209 - ... winch, with as little labour as it takes to wind up a jack, though the weight of the iron, tin, and wooden circle, is about 1000 pounds.

Page 78 - In foul weather, when the mercury rises much and high, and so continues for two or three days before the foul weather is quite over, then expect a continuance of fair weather to follow.

Page 215 - Specific Gravity of a body is the relation of its weight, compared with the weight of some other body of the same magnitude. A body immersed in a fluid will sink if its specific gravity be greater than that of the fluid; but if it be less, the body will rise to the top, and will be only partly uncovered.

Page 490 - ... the object he views. There is no small speculum, but the magnifiers are applied immediately to the first focal image. From the opening of the telescope, near the place of the eye glass, a speaking-pipe runs down to the bottom of the tube, where it...

Page 412 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.

Page 467 - And in measuring any of these station-distances, mark accurately where these lines meet with any hedges, ditches, roads, lanes, paths, rivulets, &c ; and where any remarkable object is placed, by measuring its distance from the station-line ; and where a perpendicular From it cuts that line. And thus as you go along any main...

Page 15 - ... of the motion seemed to be from the upper part downwards. It appears also that they were in some danger of having the balloon burnt altogether; as the Marquis observed several round holes made by the fire in the lower part of it, which alarmed him considerably, and, indeed, not without reason.