Elements of Geometry and Trigonometry |
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Page 19
... triangle ABC , or upon its base BC , or within it . First Case . The straight line GC < GI + IC , and the straight line AB < AI + IB ; therefore , GC + AB GI + AI + IC + IB , or , which is the same thing , GC + AB < AG + BC . Take away ...
... triangle ABC , or upon its base BC , or within it . First Case . The straight line GC < GI + IC , and the straight line AB < AI + IB ; therefore , GC + AB GI + AI + IC + IB , or , which is the same thing , GC + AB < AG + BC . Take away ...
Page 20
... triangle is likewise equiangular , that is to say , has all its angles equal . Scholium . The equality of the triangles BAD , DAC , proves also that the angle BAD , is equal to DAC , and BDA to ADC , hence the latter two are right ...
... triangle is likewise equiangular , that is to say , has all its angles equal . Scholium . The equality of the triangles BAD , DAC , proves also that the angle BAD , is equal to DAC , and BDA to ADC , hence the latter two are right ...
Page 21
... triangle BAC is isosceles . PROPOSITION XIII . THEOREM . The greater side of every triangle is opposite to the greater an- gle ; and conversely , the greater angle is opposite to the greater side . First , Let the angle C be greater ...
... triangle BAC is isosceles . PROPOSITION XIII . THEOREM . The greater side of every triangle is opposite to the greater an- gle ; and conversely , the greater angle is opposite to the greater side . First , Let the angle C be greater ...
Page 23
... triangle BCF , is equal to the triangle BCA , for they have the right angle CBF = CBA , the side CB common , and the D A BE F side BF BA ; hence the third sides , CF and CA are equal ( Prop . V. Cor . ) . But ABF , being a straight line ...
... triangle BCF , is equal to the triangle BCA , for they have the right angle CBF = CBA , the side CB common , and the D A BE F side BF BA ; hence the third sides , CF and CA are equal ( Prop . V. Cor . ) . But ABF , being a straight line ...
Page 29
... triangle the sum of the three angles is equal to two right angles . Let ABC be any triangle : then will the an- gle C + A + B be equal to two right angles . A D For , produce the side CA towards D , and at the point A , draw AE parallel ...
... triangle the sum of the three angles is equal to two right angles . Let ABC be any triangle : then will the an- gle C + A + B be equal to two right angles . A D For , produce the side CA towards D , and at the point A , draw AE parallel ...
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Common terms and phrases
adjacent altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone convex surface cosine cotangent cylinder diagonal diameter dicular distance divided draw drawn equal angles 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 measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular 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 slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex