A Course of Mathematics: In Three Volumes : Composed for the Use of the Royal Military Academy ...J. Johnson, 1811 |
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Page 77
... angles of spherical triangles . Def . 3. A right - angled spherical triangle has one right angle : the sides about the right angle are called legs ; the side opposite to the right angle is called the hypothenuse . Def . 4. A quadrantal ...
... angles of spherical triangles . Def . 3. A right - angled spherical triangle has one right angle : the sides about the right angle are called legs ; the side opposite to the right angle is called the hypothenuse . Def . 4. A quadrantal ...
Page 78
... spherical trigonome- try , where the sides are circular arcs , whose values depend on their proportion to the whole circle , that is , on the num- ber of degrees they contain , the sides may always be deter- mined when the three angles ...
... spherical trigonome- try , where the sides are circular arcs , whose values depend on their proportion to the whole circle , that is , on the num- ber of degrees they contain , the sides may always be deter- mined when the three angles ...
Page 79
... spherical triangle BCA , we take the arcs CN , CM , each equal 90 ° , and through the radii GN , GM ( figure to art . 7 ) draw the plane NGM , it is manifest ... angle BCA ; though it is customary suring SPHERICAL TRIGONOMETRY . 79.
... spherical triangle BCA , we take the arcs CN , CM , each equal 90 ° , and through the radii GN , GM ( figure to art . 7 ) draw the plane NGM , it is manifest ... angle BCA ; though it is customary suring SPHERICAL TRIGONOMETRY . 79.
Page 80
... spherical angle be a right angle , the arcs of the great circles which form it , will pass mutually through the poles of each other : and that , if the planes of two great circles contain each the axis of the other , or pass through ...
... spherical angle be a right angle , the arcs of the great circles which form it , will pass mutually through the poles of each other : and that , if the planes of two great circles contain each the axis of the other , or pass through ...
Page 81
... spherical angle at B ; consequently the spherical angle at B is greater than the angle at B made by the chords AB , CB . like manner , the spherical angles at A and c , are greater than the respective angles made by the chords meeting ...
... spherical angle at B ; consequently the spherical angle at B is greater than the angle at B made by the chords AB , CB . like manner , the spherical angles at A and c , are greater than the respective angles made by the chords meeting ...
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Common terms and phrases
abscissas altitude ANHG asymptotes axis ball base beam becomes bisect CA² CD² CE² centre circle circumscribed coefficients cone conic section consequently Corol cosine CR² cubic equation curve cylinder denote determine diameter distance divided draw drawn equa equal equation expression feet find the fluent fluxion force gives greatest Hence horizontal hyperbola inches length logarithm manner measured meridian motion nearly negative ordinates parabola parallel perimeter perp perpendicular plane polygon prism prob PROBLEM proportional quadrant quantity radius rectangle resistance right angles right line roots Scholium sides sin² sine solid angle sphere spherical angle spherical excess spherical triangle spherical trigonometry square suppose surf surface tangent theor THEOREM theref tion velocity vertical weight whence whole
Popular passages
Page 63 - In any plane triangle, the sum of any two sides is to their difference, as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page 112 - Since the exterior angle of a triangle is equal to the sum of the two interior opposite angles (th.
Page 247 - Or, by art. 3 14 of the same, the pressure is equal to the weight of a column of the fluid, •whose base is equal to the surface pressed, and...
Page 78 - A solid angle is that which is made by the meeting of more than two plane angles, which are not in the same plane, in one point. X. ' The tenth definition is omitted for reasons given in the notes.
Page 333 - ... to secure uniformity, his trees were all felled in the same season of the year, were squared the day after, and the experiments tried the 3d day.
Page 164 - Cor. 3. An equation will want its third term, if the sum of the products of the roots taken two and two, is partly positive, partly negative, and these mutually destroy each other. Remark.
Page 162 - ... preceding equation is only of the fourth power or degree ; but it is manifest that the above remark applies to equations of higher or lower dimensions : viz. that in general an equation of any degree whatever has as many roots as there are units in the exponent of the highest power of the unknown quantity, and that each root has the property of rendering, by its substitution in place of the unknown quantity, the aggregate of all the terms of the equation equul to nothing.
Page 72 - Prove that, in any plane triangle, the base is to the difference of the other two sides, as the sine of half the sum of the angles at the base, to the sine of half their difference : also, that the...
Page 259 - And when this is compared with the proportion of the velocity and length of gun in the last paragraph, it is evident that we gain extremely little in the range by a great increase in the length of the gun, with the same charge of powder. In fact the range is nearly as the 5th root of the length of the bore ; which is so small an increase, as to amount only to about a...
Page 72 - Prob. 12. How must three trees, A, B, C, be planted, so that the angle at A may be double the angle at B, the angle at B double the angle at C, and a line of 400 yards may just go round them ? Ans.