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

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Page 42

When the

squares of the two terms has to the greater term a ratio expressiBle in numbers;

such is V 18–4, because the difference of the squares 18 and 16 is 2, and V2 is to

J. as ...

When the

**less**term is rational, and the square root of the difference of thesquares of the two terms has to the greater term a ratio expressiBle in numbers;

such is V 18–4, because the difference of the squares 18 and 16 is 2, and V2 is to

J. as ...

Page 43

Also all objects have a tendency to roundness and smoothness, or appear

angular, as their distance is greater: for, as the distance is increased, the smaller

angles and asperities first disappear; after these, the next larger; and so on, ...

Also all objects have a tendency to roundness and smoothness, or appear

**less**angular, as their distance is greater: for, as the distance is increased, the smaller

angles and asperities first disappear; after these, the next larger; and so on, ...

Page 48

For when a positive number is substituted for a, the result, is the absolute term of

an equation, whose roots are

quantity. If the result has the same sign as the given absolute term, then from the

...

For when a positive number is substituted for a, the result, is the absolute term of

an equation, whose roots are

**less**than the roots of the given equation by thatquantity. If the result has the same sign as the given absolute term, then from the

...

Page 49

The first formula being applicable to the cases in which a' is greater than unity,

and the second when a' is

equations of all dimensions, but when reduced to particular cases, they become

much ...

The first formula being applicable to the cases in which a' is greater than unity,

and the second when a' is

**less**than unity. These formnlae are general forequations of all dimensions, but when reduced to particular cases, they become

much ...

Page 53

... 12, 144, 1728, 20736 If, however, any of the scale were adopted, all these

expressions would be the same ; and each would require one character

the number of ones in m, thus, Denary 1, Ternary 1, 2, Senary 1, 2, 3, 4, 5, 6,.

... 12, 144, 1728, 20736 If, however, any of the scale were adopted, all these

expressions would be the same ; and each would require one character

**less**thanthe number of ones in m, thus, Denary 1, Ternary 1, 2, Senary 1, 2, 3, 4, 5, 6,.

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Dictionary of the Mathematical and Physical Sciences: According to the ... James Mitchell No preview available - 2017 |

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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.