Elements of Geometry and Trigonometry |
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Page 16
... that the point E shall fall upon B , and the side ED on the equal side BA ; then , since the angle D is equal to the angle A , the side DF will take the direction AC . But DF is equal to AC ; therefore , the point 16 GEOMETRY .
... that the point E shall fall upon B , and the side ED on the equal side BA ; then , since the angle D is equal to the angle A , the side DF will take the direction AC . But DF is equal to AC ; therefore , the point 16 GEOMETRY .
Page 17
... falling at the same time in the two straight lines BA and CA , must fall at their intersection A : hence , the two triangles EDF , BAC , coincide with each other , and are therefore equal ( Ax . 13. ) . Cor . Whenever , in two triangles ...
... falling at the same time in the two straight lines BA and CA , must fall at their intersection A : hence , the two triangles EDF , BAC , coincide with each other , and are therefore equal ( Ax . 13. ) . Cor . Whenever , in two triangles ...
Page 19
... falls without the triangle ABC , or upon its base BC , or within it . First Case . The straight line GC < GI + IC ... fall within the triangle BAC , we shall have , by the preceding theorem , AG + GC < AB + BC ; and , taking AG from ...
... falls without the triangle ABC , or upon its base BC , or within it . First Case . The straight line GC < GI + IC ... fall within the triangle BAC , we shall have , by the preceding theorem , AG + GC < AB + BC ; and , taking AG from ...
Page 22
... fall on the line , and oblique lines be drawn to different points : 1st , The perpendicular will be shorter than any oblique line . 2d , Any two oblique lines , drawn on different sides of the perpen- dicular , cutting off equal ...
... fall on the line , and oblique lines be drawn to different points : 1st , The perpendicular will be shorter than any oblique line . 2d , Any two oblique lines , drawn on different sides of the perpen- dicular , cutting off equal ...
Page 25
... fall from the same point on the same straight line ; which is impossible ( Prop . XIV . ) . PROPOSITION XIX . THEOREM . If two straight lines meet a third line , making the sum of the interior angles on the same side of the line met ...
... fall from the same point on the same straight line ; which is impossible ( Prop . XIV . ) . PROPOSITION XIX . THEOREM . If two straight lines meet a third line , making the sum of the interior angles on the same side of the line met ...
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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