Elements of Geometry and Trigonometry |
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Page 17
... equal to the triangle BAC ( Ax . 13. ) . Cor . When two triangles have these three things equal , namely , the side ED = BA , the side DF - AC , and the angle D = A , the remaining three are also respectively equal , namely , the side ...
... equal to the triangle BAC ( Ax . 13. ) . Cor . When two triangles have these three things equal , namely , the side ED = BA , the side DF - AC , and the angle D = A , the remaining three are also respectively equal , namely , the side ...
Page 18
Adrien Marie Legendre Charles Davies. to each , are equal ; for they may be applied to each other , and the equal parts will mutually coincide . PROPOSITION VII . THEOREM . The sum of any two sides of a triangle , is greater than the ...
Adrien Marie Legendre Charles Davies. to each , are equal ; for they may be applied to each other , and the equal parts will mutually coincide . PROPOSITION VII . THEOREM . The sum of any two sides of a triangle , is greater than the ...
Page 19
... equal angle in each , contained by equal sides , ( Prop . V. ) ; therefore CG is equal to EF . Now , there may be three cases in the proposition , according as the point G falls without the triangle ABC , or upon its base BC , or within ...
... equal angle in each , contained by equal sides , ( Prop . V. ) ; therefore CG is equal to EF . Now , there may be three cases in the proposition , according as the point G falls without the triangle ABC , or upon its base BC , or within ...
Page 20
... equal to BC , by hypothesis ; therefore , the angle D can neither be greater nor less than A ; therefore it must be equal to it . In the same manner it may be shown that the angle E is equal to B , and the angle F to C : hence the two ...
... equal to BC , by hypothesis ; therefore , the angle D can neither be greater nor less than A ; therefore it must be equal to it . In the same manner it may be shown that the angle E is equal to B , and the angle F to C : hence the two ...
Page 21
... equal to either of the other two . PROPOSITION XII . THEOREM . Conversely , if two angles of a triangle are equal , the sides oppo- site them are also equal , and the triangle is isosceles . Let the angle ABC be equal to the angle ACB ...
... equal to either of the other two . PROPOSITION XII . THEOREM . Conversely , if two angles of a triangle are equal , the sides oppo- site them are also equal , and the triangle is isosceles . Let the angle ABC be equal to the angle ACB ...
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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 consequently convex surface cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equation equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides 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 solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex