Elements of Geometry and Trigonometry |
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Page 7
... Prop . 27 Prop . 26 Prop . 15 33 30 28 5 Prop . 4 Prop . 5 34 28 29 5 11 Book IV . Cor . of 5 Cor . of 11 Cor . 2 . 6 12 35 1 31 18 & 3 . 8 10 36 1 Book IV . 13 1 37 Cor . 2. of 2 38 Cor . 2. of 2 35 28 4 2 36 30 47 11 Book VI . 4 Cor ...
... Prop . 27 Prop . 26 Prop . 15 33 30 28 5 Prop . 4 Prop . 5 34 28 29 5 11 Book IV . Cor . of 5 Cor . of 11 Cor . 2 . 6 12 35 1 31 18 & 3 . 8 10 36 1 Book IV . 13 1 37 Cor . 2. of 2 38 Cor . 2. of 2 35 28 4 2 36 30 47 11 Book VI . 4 Cor ...
Page 15
... ( Prop . I. Cor . 1. ) ; and since ACE is a straight line , the angle FCE will likewise be a right angle . Hence , the angle FCD is equal to the angel FCE ( Ax . 10. ) ; which can only be the case when the lines CD and CE coincide : there ...
... ( Prop . I. Cor . 1. ) ; and since ACE is a straight line , the angle FCE will likewise be a right angle . Hence , the angle FCD is equal to the angel FCE ( Ax . 10. ) ; which can only be the case when the lines CD and CE coincide : there ...
Page 19
... ( 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 it . First Case . The straight line GC < GI + IC ...
... ( 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 it . First Case . The straight line GC < GI + IC ...
Page 21
... ( Prop . V. ) . But the part cannot be equal to the whole ( Ax . 8. ) ; hence , there is no inequality between the sides BA , AC ; therefore , the triangle BAC is isosceles . PROPOSITION XIII . THEOREM . The greater side of every triangle ...
... ( Prop . V. ) . But the part cannot be equal to the whole ( Ax . 8. ) ; hence , there is no inequality between the sides BA , AC ; therefore , the triangle BAC is isosceles . PROPOSITION XIII . THEOREM . The greater side of every triangle ...
Page 22
... ( Prop . V. Cor . ) . But the angle ACB is a right angle , by hypothesis ; therefore , BCF must likewise be a right angle . But if the adja- cent angles BCA , BCF , are together equal to two right angles , ACF must be a straight line ( Prop ...
... ( Prop . V. Cor . ) . But the angle ACB is a right angle , by hypothesis ; therefore , BCF must likewise be a right angle . But if the adja- cent angles BCA , BCF , are together equal to two right angles , ACF must be a straight line ( Prop ...
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone convex surface Cosine cylinder diagonal diameter dicular distance divided draw drawn equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular perpendicular let fall plane MN polyedron polygon ABCDE PROBLEM proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment similar Sine Cotang slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex