Elements of Geometry and Trigonometry |
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Page 11
... equiangular polygon , one which has all its angles equal . 20. Two polygons are mutually equilateral , when they have their sides equal each to each , and placed in the same order ; that is to say , when following their perimeters in ...
... equiangular polygon , one which has all its angles equal . 20. Two polygons are mutually equilateral , when they have their sides equal each to each , and placed in the same order ; that is to say , when following their perimeters in ...
Page 20
... 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 angles ; therefore , the ...
... 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 angles ; therefore , the ...
Page 30
... equiangular . Cor . 3. In any triangle there can be but one right angle ; for if there were two , the third angle must be nothing . Still less , can a triangle have more than one obtuse angle . Cor . 4. In every right angled triangle ...
... equiangular . Cor . 3. In any triangle there can be but one right angle ; for if there were two , the third angle must be nothing . Still less , can a triangle have more than one obtuse angle . Cor . 4. In every right angled triangle ...
Page 31
... equiangular , each angle is equal to the fifth part of six right angles , or to of one right angle . Cor . 3. The sum of the angles of a hexagon is equal to 2 × ( 6—2 , ) or eight right angles ; hence in the equiangular hexagon , each ...
... equiangular , each angle is equal to the fifth part of six right angles , or to of one right angle . Cor . 3. The sum of the angles of a hexagon is equal to 2 × ( 6—2 , ) or eight right angles ; hence in the equiangular hexagon , each ...
Page 83
... gle ACE AEC , and consequently AE - AC ( Book I. Prop . XII . ) . In place of AE in the above proportion , substitute AC , and we shall have BD DC : AB : AC . : PROPOSITION XVIII . THEOREM . Two equiangular triangles have their BOOK IV .
... gle ACE AEC , and consequently AE - AC ( Book I. Prop . XII . ) . In place of AE in the above proportion , substitute AC , and we shall have BD DC : AB : AC . : PROPOSITION XVIII . THEOREM . Two equiangular triangles have their BOOK IV .
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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