Elements of Geometry and Trigonometry |
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Page 18
... sides of a triangle , is greater than the third side . Let ABC be a triangle : then will the sum of two of its sides , as AC , CB , be greater than the third side AB . For , the line AB is the shortest dis- tance between the points A ...
... sides of a triangle , is greater than the third side . Let ABC be a triangle : then will the sum of two of its sides , as AC , CB , be greater than the third side AB . For , the line AB is the shortest dis- tance between the points A ...
Page 19
... sides BA , AC , of the triangle BAC , are equal to the two ED , DF , of the triangle EDF , each to each , while the third side BC of the first triangle is greater than the third side EF of the second ; then will the an- gle BAC of the ...
... sides BA , AC , of the triangle BAC , are equal to the two ED , DF , of the triangle EDF , each to each , while the third side BC of the first triangle is greater than the third side EF of the second ; then will the an- gle BAC of the ...
Page 20
Adrien Marie Legendre Charles Davies. Let the side ED = BA , the side EF - BC , and the side DF - AC ; then will the ... sides : thus , the equal angles D and A , lie op- posite the equal sides EF and BC . PROPOSITION XI . THEOREM . In ...
Adrien Marie Legendre Charles Davies. Let the side ED = BA , the side EF - BC , and the side DF - AC ; then will the ... sides : thus , the equal angles D and A , lie op- posite the equal sides EF and BC . PROPOSITION XI . THEOREM . In ...
Page 21
... sides oppo- site them are also equal , and the triangle is isosceles . Let the angle ABC be equal to the angle ACB ; then will the side AC be equal to the side AB . D For , if these sides are not equal , suppose AB to be the greater ...
... sides oppo- site them are also equal , and the triangle is isosceles . Let the angle ABC be equal to the angle ACB ; then will the side AC be equal to the side AB . D For , if these sides are not equal , suppose AB to be the greater ...
Page 23
... side CB common , and the = D A BE F side BF = BA ; hence the third sides , CF and CA are equal ( Prop . V. Cor . ) . But ABF , being a straight line , is shorter than ACF , which is a broken line ( Def . 3. ) ; therefore , AB , the half ...
... side CB common , and the = D A BE F side BF = BA ; hence the third sides , CF and CA are equal ( Prop . V. Cor . ) . But ABF , being a straight line , is shorter than ACF , which is a broken line ( Def . 3. ) ; therefore , AB , the half ...
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book centre chord circ circumference circumscribed common cone convex surface Cosine Cotang cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides oblique lines opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE prism proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant secant line segment side BC similar sine solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex