## Elements of Geometry and Trigonometry |

### From inside the book

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**bisect**each other . Let ABCD be a parallelogram , AC and DB its diagonals , intersecting at E , then will AE EC , and DE = EB . Comparing the triangles ADE , CEB , we find the side AD = CB ( Prop . XXVIII . ) , the angle ADE = CBE , and ... Page 45

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**bisects**the chord , and**bisects**also the subtended arc of the chord . Let AB be a chord , and CG the ra- dius perpendicular to it : then will AD = DB , and the arc AG - GB . For , draw the radii CA , CB . Then the two right angled ... Page 46

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**bisect**these straight lines by the perpendiculars DE , FG : we say first , that DE and FG , will meet in some point O. For , they must necessarily cut A each other , if they are not parallel . E -К Now , if they were parallel , the line ... Page 47

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**Bisect**these chords by the per- pendiculars CF , CG , and draw the radii CA , CD . In the right angled triangles CAF , DCG , the hypothenuses CA , CD , are equal ; and the side AF , the half of AB , is equal to the side DG , the half of ... Page 49

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**bisect**the chord at right angles . PROPOSITION XII . THEOREM . If the distance between the centres of two circles is less than the sum of the radii , the greater radius being at the same time less than the sum of the smaller and the ...### Other editions - View all

### Common terms and phrases

adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone convex surface Cosine cylinder diagonal diameter dicular distance divided draw drawn 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 number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular perpendicular let fall 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 Cotang slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex