A Course of Mathematics, Volume 2Longman Rees, 1837 - Mathematics |
From inside the book
Results 1-5 of 32
Page 12
... cones : therefore the surfaces and solidities are proportional . THEOREM XXX . THE surface or the solidity of a right cone circumscribed about a sphere is directly as the square of the cone's altitude , and inversely as the excess of ...
... cones : therefore the surfaces and solidities are proportional . THEOREM XXX . THE surface or the solidity of a right cone circumscribed about a sphere is directly as the square of the cone's altitude , and inversely as the excess of ...
Page 13
... cone , is triple the radius of the sphere . Cor . 2. Hence also , the side of such cone is triple the radius of its base . THEOREM XXXII . THE whole surface of a right cone being given , the inscribed sphere is the greatest when the ...
... cone , is triple the radius of the sphere . Cor . 2. Hence also , the side of such cone is triple the radius of its base . THEOREM XXXII . THE whole surface of a right cone being given , the inscribed sphere is the greatest when the ...
Page 14
... cone being given , the inscribed sphere is the greatest when the side of the cone is triple the radius of its base . For the capacities of such cones vary as their surfaces ( theor . 29 ) . THEOREM XXXIII . Or all right cones of equal ...
... cone being given , the inscribed sphere is the greatest when the side of the cone is triple the radius of its base . For the capacities of such cones vary as their surfaces ( theor . 29 ) . THEOREM XXXIII . Or all right cones of equal ...
Page 15
... cone whose base is equal to the surface of the sphere , and altitude equal to its radius . Consequently , the ... cone , be equal to a sphere either in capacity , or in surface ; in the first case , the surface of the sphere is less than ...
... cone whose base is equal to the surface of the sphere , and altitude equal to its radius . Consequently , the ... cone , be equal to a sphere either in capacity , or in surface ; in the first case , the surface of the sphere is less than ...
Page 16
... cone , and of its circumscribed cylinder . Ex . 11. The surface of a sphere is 28-274337 , and of an irregular polyhedron circumscribed about it 35 : what are their respective solidities ? Ex . 12. The solidity of a sphere , equilateral ...
... cone , and of its circumscribed cylinder . Ex . 11. The surface of a sphere is 28-274337 , and of an irregular polyhedron circumscribed about it 35 : what are their respective solidities ? Ex . 12. The solidity of a sphere , equilateral ...
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