Elements of Geometry and Trigonometry |
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Page 10
... intersection A is the vertex of the angle , and the lines AB , AC , are its sides . A -B The angle is sometimes designated simply by the letter at the vertex A ; sometimes by the three letters BAC , or CAB , the letter at the vertex ...
... intersection A is the vertex of the angle , and the lines AB , AC , are its sides . A -B The angle is sometimes designated simply by the letter at the vertex A ; sometimes by the three letters BAC , or CAB , the letter at the vertex ...
Page 15
... CB , form one and the same straight li .. PROPOSITION IV . THEOREM . When two straight lines intersect each other , the oppor ver- tical angles , which they form , are equal . Let AB and DE be two straight A lines , BOOK I. 15.
... CB , form one and the same straight li .. PROPOSITION IV . THEOREM . When two straight lines intersect each other , the oppor ver- tical angles , which they form , are equal . Let AB and DE be two straight A lines , BOOK I. 15.
Page 16
... intersect each other , are together equal to four right angles : for the sum of the two angles ACE , ECB , is equal to two right angles ; and the sum of the other two , ACD , DCB , is also equal to two right angles : therefore , the sum ...
... intersect each other , are together equal to four right angles : for the sum of the two angles ACE , ECB , is equal to two right angles ; and the sum of the other two , ACD , DCB , is also equal to two right angles : therefore , the sum ...
Page 17
... intersection A : hence , the two triangles EDF , BAC , coincide with each other , and are therefore equal ( Ax . 13. ) . Cor . Whenever , in two triangles , these three things are equal , namely , the angle E = B , the angle F - C , and ...
... intersection A : hence , the two triangles EDF , BAC , coincide with each other , and are therefore equal ( Ax . 13. ) . Cor . Whenever , in two triangles , these three things are equal , namely , the angle E = B , the angle F - C , and ...
Page 49
... intersection , and will divide it into two equal parts . For , let the line AB join the points of intersection . It will be a common chord to the two circles . Now if a perpendicular B be erected from the middle of this chord , it will ...
... intersection , and will divide it into two equal parts . For , let the line AB join the points of intersection . It will be a common chord to the two circles . Now if a perpendicular B be erected from the middle of this chord , it will ...
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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