A Course of Mathematics: In Three Volumes : Composed for the Use of the Royal Military Academy ...J. Johnson, 1811 |
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Page 23
... half the constant inscribed parallelogram GK . And therefore the whole triangle CTs , which is composed of the two smaller triangles and the parallelogram , is equal to double the constant inscribed parallelogram GK . Q. E. D. THEOREM ...
... half the constant inscribed parallelogram GK . And therefore the whole triangle CTs , which is composed of the two smaller triangles and the parallelogram , is equal to double the constant inscribed parallelogram GK . Q. E. D. THEOREM ...
Page 35
... half ABC , but less than half DGC . From which it follows ( consistently with both the algebraical and geometrical solution of prob . 8 , Application of Algebra to Geometry ) , that a parallelogram is always less than half a triangle in ...
... half ABC , but less than half DGC . From which it follows ( consistently with both the algebraical and geometrical solution of prob . 8 , Application of Algebra to Geometry ) , that a parallelogram is always less than half a triangle in ...
Page 39
... half the corresponding side AB , BC , & c : and consequently , the area of the polygon ABCD , circumscribing the circle , will be equal to the rectangle of the radius of the circle and half the perimeter of the polygon . But , the sur ...
... half the corresponding side AB , BC , & c : and consequently , the area of the polygon ABCD , circumscribing the circle , will be equal to the rectangle of the radius of the circle and half the perimeter of the polygon . But , the sur ...
Page 41
... of Sides shall have the Smallest Pe- rimeter . Let CA be the radius of a circle , and AB , AD , the half sides of two regular polygons circumscribed about that circle , of which n + 1 1 and the th A which the SURFACES . 41.
... of Sides shall have the Smallest Pe- rimeter . Let CA be the radius of a circle , and AB , AD , the half sides of two regular polygons circumscribed about that circle , of which n + 1 1 and the th A which the SURFACES . 41.
Page 42
... half side is AB is smaller than the semiperimeter of the polygon whose half side is AD : whence the proposition is manifest . Cor . Hence , augmenting successively by unity the num- ber of sides , it follows generally , that the ...
... half side is AB is smaller than the semiperimeter of the polygon whose half side is AD : whence the proposition is manifest . Cor . Hence , augmenting successively by unity the num- ber of sides , it follows generally , that the ...
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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 |