A Course of Mathematics: In Three Volumes : Composed for the Use of the Royal Military Academy ...J. Johnson, 1811 |
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Page 36
... known , the Greatest is that which may be Inscribed in a Semicircle whose Diameter is that Unknown Side . For , if you suppose the contrary to be the case , then when- ever the figure made with the sides given , and the side un- known ...
... known , the Greatest is that which may be Inscribed in a Semicircle whose Diameter is that Unknown Side . For , if you suppose the contrary to be the case , then when- ever the figure made with the sides given , and the side un- known ...
Page 54
... known terms , the value of each of the unknown quantities , the others being exterminated by the usual pro- cesses . Each of these general methods has its peculiar ad- vantages . The geometrical method carries conviction at every step ...
... known terms , the value of each of the unknown quantities , the others being exterminated by the usual pro- cesses . Each of these general methods has its peculiar ad- vantages . The geometrical method carries conviction at every step ...
Page 55
... known . 4. It has been shown in the 2d vol . ( pa . 6 ) , that the tan- gent is a fourth proportional to the cosine , sine , and radius ; the secant , a third proportional to the cosine and radius ; the cotangent , a fourth proportional ...
... known . 4. It has been shown in the 2d vol . ( pa . 6 ) , that the tan- gent is a fourth proportional to the cosine , sine , and radius ; the secant , a third proportional to the cosine and radius ; the cotangent , a fourth proportional ...
Page 57
... known terms , they may be represented by the same character ; suppose K : then shall we have 2K 2K sin . A = 2K bc · • sin . B = sin . c = ... ab ac ( iii . ) Hence we may immediately deduce a very important theo- rem : for , the first ...
... known terms , they may be represented by the same character ; suppose K : then shall we have 2K 2K sin . A = 2K bc · • sin . B = sin . c = ... ab ac ( iii . ) Hence we may immediately deduce a very important theo- rem : for , the first ...
Page 64
... known , to half . For , substituting for cos A its value 2 sin A ( R2- sin ? a ) there will arise sin 2A = R it will be find that of its / ( R2 — Sin2 - A ) , - This squared gives R2 sin2 2A = 4R2 Sin2 A 4 sin A. Here taking sin A for ...
... known , to half . For , substituting for cos A its value 2 sin A ( R2- sin ? a ) there will arise sin 2A = R it will be find that of its / ( R2 — Sin2 - A ) , - This squared gives R2 sin2 2A = 4R2 Sin2 A 4 sin A. Here taking sin A for ...
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A Course of Mathematics: In Three Volumes: Composed for the Use of the Royal ... Charles Hutton No preview available - 2016 |
A Course of Mathematics: In Three Volumes: Composed for the Use of the Royal ... Charles Hutton No preview available - 2016 |
Common terms and phrases
abscissas altitude ANHG asymptotes axis ball base beam becomes bisect CA² CE² centre circle circumscribed coefficients cone conic section consequently Corol cosine cubic equation curve cylinder denote determine diameter distance divided draw drawn equa equal equation expression feet find the fluent fluxion force greatest Hence horizontal hyperbola inches length logarithm manner measured meridian motion nearly 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 trapezium velocity vertical weight whence whole
Popular passages
Page 65 - 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 116 - Since the exterior angle of a triangle is equal to the sum of the two interior opposite angles (th.
Page 249 - 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 82 - 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 335 - ... 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 166 - 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 164 - ... 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 74 - 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 261 - 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 74 - 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.
Bibliographic information
| Title | A Course of Mathematics: In Three Volumes : Composed for the Use of the Royal Military Academy ... Volume 3 of A Course of Mathematics: In Three Volumes : Composed for the Use of the Royal Military Academy, Charles Hutton |
| Author | Charles Hutton |
| Edition | 6 |
| Publisher | J. Johnson, 1811 |
| Original from | the New York Public Library |
| Digitized | 2 May 2006 |
| Export Citation | BiBTeX EndNote RefMan |