Elements of Geometry and Trigonometry |
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Page 20
... follow , that the side EF must be less than BC : but EF is 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 ...
... follow , that the side EF must be less than BC : but EF is 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 ...
Page 21
... follows , from what has just been proved , that AB AC ; which is contrary to the hypothesis . If the angle CB , then the side AB = AC ( Prop . XII . ) ; which is also contrary to the supposition . Therefore , when AB > AC , the angle C ...
... follows , from what has just been proved , that AB AC ; which is contrary to the hypothesis . If the angle CB , then the side AB = AC ( Prop . XII . ) ; which is also contrary to the supposition . Therefore , when AB > AC , the angle C ...
Page 32
... follows that the angle A is equal to the angle C ; and also that the angle ADC com- posed of the two ADB , BDC , is equal to ABC , composed of the two equal angles DBC , ABD : hence the opposite angles of a parallelogram are also equal ...
... follows that the angle A is equal to the angle C ; and also that the angle ADC com- posed of the two ADB , BDC , is equal to ABC , composed of the two equal angles DBC , ABD : hence the opposite angles of a parallelogram are also equal ...
Page 33
... therefore equal : whence it follows that the angles AEB , BEC , are equal , and therefore , that the two diagonals of a rhombus cut each other at right angles . BOOK II . OF RATIOS AND PROPORTIONS . Definitions . 5 BOOK I. 33.
... therefore equal : whence it follows that the angles AEB , BEC , are equal , and therefore , that the two diagonals of a rhombus cut each other at right angles . BOOK II . OF RATIOS AND PROPORTIONS . Definitions . 5 BOOK I. 33.
Page 34
... follows , that magnitudes may be rep- resented by numbers to any degree of exactness , or they will differ from their numerical representatives by less than any assignable quantity . Therefore , of two magnitudes , A and B , we may ...
... follows , that magnitudes may be rep- resented by numbers to any degree of exactness , or they will differ from their numerical representatives by less than any assignable quantity . Therefore , of two magnitudes , A and B , we may ...
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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