A Course of Mathematics, Volume 2Longman Rees, 1837 - Mathematics |
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Page 2
... less than AC + C'D ( theor . 10 , Geom . ) , or than its equal AC ' + C ́B . And consequently , AB + BC + AC is less than AB + BC ' + AC . Q. E. D. Cor . 1. Of all triangles of the same base and the same altitude , or of all equal ...
... less than AC + C'D ( theor . 10 , Geom . ) , or than its equal AC ' + C ́B . And consequently , AB + BC + AC is less than AB + BC ' + AC . Q. E. D. Cor . 1. Of all triangles of the same base and the same altitude , or of all equal ...
Page 3
... less perimeter : whence the corollary is manifest . Scholium . To illustrate the second corollary above , the student may proceed thus : assum- ing an isosceles triangle whose base is not equal to either of the two sides , and then ...
... less perimeter : whence the corollary is manifest . Scholium . To illustrate the second corollary above , the student may proceed thus : assum- ing an isosceles triangle whose base is not equal to either of the two sides , and then ...
Page 4
... less or greater than PAG , according as CG is greater or less than CA. In the former case , let PACD , which is common , be added to both ; then will BAC be less than DGC ( ax . 4 , Geom . ) In the latter case , if PGCB be added , DCG ...
... less or greater than PAG , according as CG is greater or less than CA. In the former case , let PACD , which is common , be added to both ; then will BAC be less than DGC ( ax . 4 , Geom . ) In the latter case , if PGCB be added , DCG ...
Page 7
... less than the sum of the two tangents drawn from its extremities and produced till they meet . The first part of this corollary is evident , because a right line is the shortest distance between two given points . The second part ...
... less than the sum of the two tangents drawn from its extremities and produced till they meet . The first part of this corollary is evident , because a right line is the shortest distance between two given points . The second part ...
Page 10
... less than the base of the prism P. For , let P " be a prism of equal altitude , and whose base is equal to that of the prism P ' and similar to that of the prism P. Then , the lateral surface of the prism P " is smaller than the lateral ...
... less than the base of the prism P. For , let P " be a prism of equal altitude , and whose base is equal to that of the prism P ' and similar to that of the prism P. Then , the lateral surface of the prism P " is smaller than the lateral ...
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