A Course of Mathematics, Volume 2Longman Rees, 1837 - Mathematics |
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Page 2
... common base of a series of triangles ABC ' , ABC , & c . , whose vertices C ́ , C , fall in the right line LM , given in position , then is the triangle of least perimeter that whose sides AC , BC , are inclined to the line LM in equal ...
... common base of a series of triangles ABC ' , ABC , & c . , whose vertices C ́ , C , fall in the right line LM , given in position , then is the triangle of least perimeter that whose sides AC , BC , are inclined to the line LM in equal ...
Page 3
... common , we have C'E < CE * . Q. E. D. Cor . Of all isoperimetrical figures , of which the number of sides is given , that which is the greatest has all its sides equal . And in particular , of all isoperi- metrical triangles , that ...
... common , we have C'E < CE * . Q. E. D. Cor . Of all isoperimetrical figures , of which the number of sides is given , that which is the greatest has all its sides equal . And in particular , of all isoperi- metrical triangles , that ...
Page 4
... common , be added to both ; then will BAC be less than DGC ( ax . 4 , Geom . ) In the latter case , if PGCB be added , DCG will be greater than BAC ; and consequently in this case also BAC is less than DCG . Q. E. D. Cor . If PM and PN ...
... common , be added to both ; then will BAC be less than DGC ( ax . 4 , Geom . ) In the latter case , if PGCB be added , DCG will be greater than BAC ; and consequently in this case also BAC is less than DCG . Q. E. D. Cor . If PM and PN ...
Page 5
... common summit the centre of the circle . Consequently , the magnitude of the polygon , that is , of the assemblage of these triangles , does not at all depend on their disposition , or arrangement around the common centre . Q. E. D. ...
... common summit the centre of the circle . Consequently , the magnitude of the polygon , that is , of the assemblage of these triangles , does not at all depend on their disposition , or arrangement around the common centre . Q. E. D. ...
Page 15
... common altitude the radius of the sphere . Hence , the sum of all these pyramids , or the whole circumscribing solid , is equal to a pyramid or a cone whose base is equal to the whole surface of that solid , and altitude equal to the ...
... common altitude the radius of the sphere . Hence , the sum of all these pyramids , or the whole circumscribing solid , is equal to a pyramid or a cone whose base is equal to the whole surface of that solid , and altitude equal to the ...
Other editions - View all
A Course of Mathematics: For the Use of Academies ... as Well as Private Tuition Charles Hutton No preview available - 2015 |
A Course of Mathematics: For the Use of Academies ... As Well As Private Tuition Charles Hutton No preview available - 2022 |
A Course of Mathematics: For the Use of Academies, as Well as Private Tuition Charles Hutton No preview available - 2015 |
Common terms and phrases
abscisses altitude asymptotes Ax² axis ball base becomes bisected body Ca² centre of gravity chord circle circumscribed co-ordinates coefficients cone conic section conjugate conjugate hyperbolas consequently Corol cosec cosine curve denoted determine diameter difference differential direction distance divided draw drawn ellipse equal equation equilibrium expression feet figure find the fluent fluid fluxion force function Geom given Hence horizontal hyperbola inches intersection length logarithm motion ordinate parabola parallel parallelogram pendulum perpendicular plane polygon pressure produced PROP proportional quantity radius ratio rectangle respectively right angles SCHOLIUM sides similar triangles sine solid angles specific gravity sphere spherical triangle square Suppose surface tangent theor theorem transverse trigonometrical variable velocity vertex vertical weight whence