## 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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**cubic equation**. But this science , as well as other branches of ma- thematics , was , in an eminent manner ...**cubic equations**, which had been in part revealed to him by Nicho- las Tartalea . after its introduction into Europe . that ... Page 48

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**cubic**; but since , from the nature of our substitution , must be less than 1 , the**cube**of it may be omitted as ...**equation**of the product is changed . For when a positive number is substi tuted for 2 , the result is the ab- solute ... Page 49

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**cubic equation**x3 + 3x2 + 3x = 130 ; Assume 4 , then by formula ( 1 ) x'3 = 64 2x'3 128 3.x ' = 48 ax ^ 2 - W = 130 ... equation of any other degree . Application of the preceding For - w - v = mula . - In order to this it may be ... Page 84

... cubic equa- tion which being a

... cubic equa- tion which being a

**cubic equation**, the and since value of p becomes determined , and may now be considered as known ; and q and r are also de- termined from the equations = √ ( { aş + 2p — b ) ! = r = ap - c 2q . Having ... Page 105

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**equation**. Ɑ = 1 − ( p + q + r ) b = Pq + pr + gr c = - pqr and the same for every order of**equations**. The hypotheses which assumes Thus , for example , in the**cubic**the existence of vesicular vapour ,**equation**, x2 + ax2 + bx + c ...### 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.