A Course of Mathematics, Volume 2Longman Rees, 1837 - Mathematics |
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Page 4
... ratio of 2 to 1. But this is foreign to the present inquiry . THEOREM IV . Of all triangles in which two sides are given in magnitude , the greatest is that in which the two given sides are perpendicular to each other . For , assuming ...
... ratio of 2 to 1. But this is foreign to the present inquiry . THEOREM IV . Of all triangles in which two sides are given in magnitude , the greatest is that in which the two given sides are perpendicular to each other . For , assuming ...
Page 6
... ratios in both these proportions , are equal , the consequents are proportional : that is , surf . P : surf . P ' :: perim . P : perim P ' . Q. E. D. * This theorem , together with the analogous ones respecting bodies circumscribing ...
... ratios in both these proportions , are equal , the consequents are proportional : that is , surf . P : surf . P ' :: perim . P : perim P ' . Q. E. D. * This theorem , together with the analogous ones respecting bodies circumscribing ...
Page 8
... ratio of the perimeters , or of the surfaces , of figures similar to them , and both circumscribed about one and the same circle . And that the perimeters of equal rectilineal figures , each circumscribable about a circle , are ...
... ratio of the perimeters , or of the surfaces , of figures similar to them , and both circumscribed about one and the same circle . And that the perimeters of equal rectilineal figures , each circumscribable about a circle , are ...
Page 9
... ratio of figures similar to them circumscribed about the same circle . And ( theor . 15 ) these latter are smaller when their number of sides is greater : therefore , on the contrary , the former become greater as they have more sides ...
... ratio of figures similar to them circumscribed about the same circle . And ( theor . 15 ) these latter are smaller when their number of sides is greater : therefore , on the contrary , the former become greater as they have more sides ...
Page 11
... ratios will obtain , viz . C P surf . C : surf . P : base C : base P base C base P'C ' : P : surf . C ' surf . P ' . Then , 1st : when CC . Since C : P : C ' : P ' , it follows that P = P ' ; and therefore ( theer 25 ) surf P surf P But ...
... ratios will obtain , viz . C P surf . C : surf . P : base C : base P base C base P'C ' : P : surf . C ' surf . P ' . Then , 1st : when CC . Since C : P : C ' : P ' , it follows that P = P ' ; and therefore ( theer 25 ) surf P surf P But ...
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