## Dictionary of the Mathematical and Physical Sciences, According to the Latest Improvements and DiscoveriesJames Mitchell Sir Richard Phillips, 1823 - 576 pages |

### From inside the book

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**sine**of the star's latitude , and the**sine**of elongation for the same time . The aberration is subtractive be- fore opposition , and additive after . 3. The greatest aberration in longitude is equal to 20 " divided by the cosine of the ... Page 7

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**sine**of the angle of inclination of the plane to radius . If , therefore , the angle of inclination of the plane be a , the force down the plane will be sin . a X g ; and by using this in- stead of g , the above formula will be equally ... Page 34

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**sine**of the sun's or star's declination to the**sine**of the amplitude . EXAM . Let it be required to find the amplitude of the sun in lati- tude 51 ° 32 ; the declination being 23 ° 28 . • As cosine 51 ° 32. 9.7938317 is to radius 10 ... Page 41

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**sine**, tangent , & c . of an angle ; being the difference between them and radius . ANTIPARALLELS , in Geometry , are those lines which make equal angles with two other lines , but in contrary order ; that is , calling the former pair ... Page 50

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**sine**, cosine , tangent , & c . in the follow- ing manner : Let a represent any arc to radius 1 .; s its**sine**, c its cosine , tits tangent , Is the secant , and vits versed**sine**; then will a = tt3 + } t5—1t2 + ↓ 19— & c . ' s 1s3 155 ...### Other editions - View all

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.