Dictionary of the Mathematical and Physical Sciences, According to the Latest Improvements and DiscoveriesJames Mitchell |
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Page 118
... section is called an hy- perbola , and its equation is sin A cos B yy = equation expresses a hyperbola , we may suppose co , and then we have cx sin Bxxy2 = sin ( A + B — 180 ° ) - ( pl . conic sec . fig . 4. ) sin A sin ( A + B - 180 ...
... section is called an hy- perbola , and its equation is sin A cos B yy = equation expresses a hyperbola , we may suppose co , and then we have cx sin Bxxy2 = sin ( A + B — 180 ° ) - ( pl . conic sec . fig . 4. ) sin A sin ( A + B - 180 ...
Page 121
... conic of geometrical figures , which is sections may be so assumed as to effected by lines or curves , accord- make this equation coincide with ing to the order or degree of the any proposed biquadratic ; so that equation . the ...
... conic of geometrical figures , which is sections may be so assumed as to effected by lines or curves , accord- make this equation coincide with ing to the order or degree of the any proposed biquadratic ; so that equation . the ...
Page 130
... conic sections , because they all result from sections of the cone , and consist of four species only , viz . the circle , ellipse , para- bola , and hyperbola . The parti- cular equations of these , when the abcisses begin at the ...
... conic sections , because they all result from sections of the cone , and consist of four species only , viz . the circle , ellipse , para- bola , and hyperbola . The parti- cular equations of these , when the abcisses begin at the ...
Page 142
... Conic Sec- tions , is a certain right line per- pendicular to the axis of the curve , and frequently referred to in ... sections , will be inversely as the areas of the sections . 3. If a fluid , flowing through a small orifice in the ...
... Conic Sec- tions , is a certain right line per- pendicular to the axis of the curve , and frequently referred to in ... sections , will be inversely as the areas of the sections . 3. If a fluid , flowing through a small orifice in the ...
Page 184
... Conic Sections , is the distance of the focus from some fixed point ; viz . from the vertex of the parabola , and from the centre in the ellipse and hyperbola . FOCUS , is that point in the transverse axis of a conic section , at which ...
... Conic Sections , is the distance of the focus from some fixed point ; viz . from the vertex of the parabola , and from the centre in the ellipse and hyperbola . FOCUS , is that point in the transverse axis of a conic section , at which ...
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Dictionary of the Mathematical and Physical Sciences: According to the ... James Mitchell No preview available - 2017 |
Dictionary of the Mathematical and Physical Sciences: According to the ... James Mitchell No preview available - 2017 |
Common terms and phrases
absciss Algebra altitude appears Arithmetic Astronomy axis body called centre circle co-efficients conic sections consequently cosine cube cubic equation 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 lever logarithm longitude means measure mercury meridian method moon motion multiplied 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 sine solid space specific gravity sphere spherical square stars subtangent supposed surd surface tance tang tangent telescope tion triangle tube velocity weight whence wind
Popular passages
Page 440 - 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 508 - 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 292 - 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 203 - ... 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 74 - 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 209 - 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 476 - ... 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 398 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
Page 459 - 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 11 - ... 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.