Elements of Geometry and Trigonometry |
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Page 15
... draw the line CF , making with AC the right angle ACF . Now , since ACD is a straight line , the angle FCD will be a right angle ( Prop . I. Cor . 1. ) ; and since ACE is a straight line , the angle FCE will likewise be a right angle ...
... draw the line CF , making with AC the right angle ACF . Now , since ACD is a straight line , the angle FCD will be a right angle ( Prop . I. Cor . 1. ) ; and since ACE is a straight line , the angle FCE will likewise be a right angle ...
Page 18
... drawn to the extremities of either side , their sum will be less than the sum of the two other sides of the triangle . Let any point , as O , be taken within the ... draw CG . The C F triangle GAC is equal to DEF , since , by 18 GEOMETRY .
... drawn to the extremities of either side , their sum will be less than the sum of the two other sides of the triangle . Let any point , as O , be taken within the ... draw CG . The C F triangle GAC is equal to DEF , since , by 18 GEOMETRY .
Page 21
... draw CD . Now , in the two triangles BDC , BAC , we have BD - AC , by construction ; the angle B equal to the angle ACB , by hypothesis ; B and the side BC common : therefore , the two triangles , BDC , BAC , have two sides and the ...
... draw CD . Now , in the two triangles BDC , BAC , we have BD - AC , by construction ; the angle B equal to the angle ACB , by hypothesis ; B and the side BC common : therefore , the two triangles , BDC , BAC , have two sides and the ...
Page 22
... drawn to that line . Let A be the point , and DE the given line . A B E Let us suppose that we can draw two perpendiculars , AB , AC . Produce either of them , as AB , till BF is equal to AB , and D draw FC . Then , the two triangles ...
... drawn to that line . Let A be the point , and DE the given line . A B E Let us suppose that we can draw two perpendiculars , AB , AC . Produce either of them , as AB , till BF is equal to AB , and D draw FC . Then , the two triangles ...
Page 23
... draw FC , FD . First . The triangle BCF , is equal to the triangle BCA , for they have the right angle CBF CBA , the ... drawn ; for , if there could be more , we should have at least two equal oblique lines on the same side of the ...
... draw FC , FD . First . The triangle BCF , is equal to the triangle BCA , for they have the right angle CBF CBA , the ... drawn ; for , if there could be more , we should have at least two equal oblique lines on the same side of the ...
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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