A Course of Mathematics, Volume 2Longman Rees, 1837 - Mathematics |
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Page 2
... 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 triangles of the same base , the isosceles triangle has the smallest perimeter ...
... 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 triangles of the same base , the isosceles triangle has the smallest perimeter ...
Page 4
... consequently in this case also BAC is less than DCG . Q. E. D. Cor . If PM and PN be drawn parallel to CB and CA respectively , the two triangles PAM , PBN , will be equal , and these two taken together ( since AM = PNMC ) will be equal ...
... consequently in this case also BAC is less than DCG . Q. E. D. Cor . If PM and PN be drawn parallel to CB and CA respectively , the two triangles PAM , PBN , will be equal , and these two taken together ( since AM = PNMC ) will be equal ...
Page 5
... Consequently , one at least of these two figures is smaller than the corresponding part of the figure APBCDEFG ( theor . 5 ) . Therefore the figure APBCDEFG is greater than the figure apbcdefg : and if from these there be taken away the ...
... Consequently , one at least of these two figures is smaller than the corresponding part of the figure APBCDEFG ( theor . 5 ) . Therefore the figure APBCDEFG is greater than the figure apbcdefg : and if from these there be taken away the ...
Page 6
... consequently ( theor . 8 ) all its angles are equal : that is , it is regular . Q. E. D. Cor . Hence we see that regular polygons possess the property of a maximum of surface , when compared with any other figures of the same name , and ...
... consequently ( theor . 8 ) all its angles are equal : that is , it is regular . Q. E. D. Cor . Hence we see that regular polygons possess the property of a maximum of surface , when compared with any other figures of the same name , and ...
Page 8
... consequently these angles are aş n and n + 1 : and hence , the angle may be conceived divided into n + 1 equal parts , of which BCD is one . Consequently ( cor . to the lemma ) , ( n + 1 ) BD > AD . Taking , then , unequal quantities ...
... consequently these angles are aş n and n + 1 : and hence , the angle may be conceived divided into n + 1 equal parts , of which BCD is one . Consequently ( cor . to the lemma ) , ( n + 1 ) BD > AD . Taking , then , unequal quantities ...
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