## Elements of Geometry and Trigonometry |

### From inside the book

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**intersection**A is the vertex of the A4 angle , and the lines AB , AC , are its sides .. -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

... and the same straight line . PROPOSITION IV . THEOREM . When two straight lines

... and the same straight line . PROPOSITION IV . THEOREM . When two straight lines

**intersect**each other , the opposite or ver- tical angles , which they form , are equal . Let AB and DE be two straight lines , intersecting BOOK I. 15. Page 16

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**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

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**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

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**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 be erected from the middle of this chord , it will ...### Other editions - View all

### 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