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

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Page 46

Hence every particular curve will appear to have an appropriate equation,

differing from that of every other; either as to the number of the terms, the powers

of the unknown quantities as and y, or the signs of the

the ...

Hence every particular curve will appear to have an appropriate equation,

differing from that of every other; either as to the number of the terms, the powers

of the unknown quantities as and y, or the signs of the

**coefficients**of the terms ofthe ...

Page 81

... the roots is equal to the

relaxed that they may be bent into any figure at pleasure. BEVEL Angle, is a term

used by artificers to denote any angle except those of ninety or forty-five degrees.

... the roots is equal to the

**coefficient**of. by boiling, by which their fibres are sorelaxed that they may be bent into any figure at pleasure. BEVEL Angle, is a term

used by artificers to denote any angle except those of ninety or forty-five degrees.

Page 82

of all the roots is equal to the

case is 0; and that the continued product is equal to the absolute term, which is

here — 1. 1 + ra.-- roa-H roa, &c. r(n-1)a=0; or, - - - ra–H rea-- roa-H, &c. r(n-1)a ...

of all the roots is equal to the

**coefficient**of the second term, which in the presentcase is 0; and that the continued product is equal to the absolute term, which is

here — 1. 1 + ra.-- roa-H roa, &c. r(n-1)a=0; or, - - - ra–H rea-- roa-H, &c. r(n-1)a ...

Page 109

(1) a + a a' + b t a *-i- #}r + ab (2) or + c a 3 (r ab + %) a? -- ac !. + abc * } vc (3) + -i

- d ab aro-H #7 ac % b ad aua c , r3 + bc aro + acd à) *\ bcd cd X r + abcd Now it

is obvious, that in each of these formulae the

(1) a + a a' + b t a *-i- #}r + ab (2) or + c a 3 (r ab + %) a? -- ac !. + abc * } vc (3) + -i

- d ab aro-H #7 ac % b ad aua c , r3 + bc aro + acd à) *\ bcd cd X r + abcd Now it

is obvious, that in each of these formulae the

**coefficient**of the second term is ... Page 110

... the same will be expressed by the m + 1

a + 1" ;) which from the known law of the ...

(a + 1n,) wanting the first term, But the sum of all these

...

... the same will be expressed by the m + 1

**coefficient**of the expanded binomial (a + 1" ;) which from the known law of the ...

**coefficients**of the expanded binomial(a + 1n,) wanting the first term, But the sum of all these

**coefficients**is equal to 2",...

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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 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.