Elements of Geometry and Trigonometry |
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Page 21
... common : therefore , the two triangles , BDC , BAC , have two sides and the included angle in the one , equal to two sides and the included angle in the other , each to each : hence they are equal ( Prop . V. ) . But the part cannot be ...
... common : therefore , the two triangles , BDC , BAC , have two sides and the included angle in the one , equal to two sides and the included angle in the other , each to each : hence they are equal ( Prop . V. ) . But the part cannot be ...
Page 22
... common , and the side AB equal to BF , by construction ; there- fore , the triangles are equal , and the angle ACB = BCF ( Prop . V. Cor . ) . But the angle ACB is a right angle , by hypothesis ; therefore , BCF must likewise be a right ...
... common , and the side AB equal to BF , by construction ; there- fore , the triangles are equal , and the angle ACB = BCF ( Prop . V. Cor . ) . But the angle ACB is a right angle , by hypothesis ; therefore , BCF must likewise be a right ...
Page 23
... common , and the D 19 B F side BF = BA ; hence the third sides , CF and CA are equal ( Prop . V. Cor . ) . But ABF , being a straight line , is shorter than ACF , which is a broken line ( Def . 3. ) ; therefore , AB , the half of ABF ...
... common , and the D 19 B F side BF = BA ; hence the third sides , CF and CA are equal ( Prop . V. Cor . ) . But ABF , being a straight line , is shorter than ACF , which is a broken line ( Def . 3. ) ; therefore , AB , the half of ABF ...
Page 28
... common side , and two adjacent angles in each equal ; hence these triangles are equal ( Prop . VI . ) ; therefore , the side EG , which measures the distance of the parallels AB and CD at the point E , is equal to the side FH , which ...
... common side , and two adjacent angles in each equal ; hence these triangles are equal ( Prop . VI . ) ; therefore , the side EG , which measures the distance of the parallels AB and CD at the point E , is equal to the side FH , which ...
Page 30
... common vertex , and for bases , the several sides of the polygon , excepting the two sides which form the angle A. It is evident , also , that the sum of all the angles in these triangles does not differ from the sum of all the angles ...
... common vertex , and for bases , the several sides of the polygon , excepting the two sides which form the angle A. It is evident , also , that the sum of all the angles in these triangles does not differ from the sum of all the angles ...
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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