## Elements of Geometry and Trigonometry |

### From inside the book

Results 1-5 of 18

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**equal**( Prop . V. Cor . ) . But ABF , being a straight line , is shorter than ACF , which is a broken line ( Def . 3. ) ; therefore , AB , the**half**of ABF , is shorter than AC , the**half**of ACF ; hence , the per- pendicular is shorter ... Page 54

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**measured by half**the arc included between its sides . Let BAD be an inscribed angle , and let us first suppose that ... measured by the arc BE ; hence BAC will be measured by the half of BE . For a like reason , the angle CAD will be ... Page 55

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**equal**; because they are all**measured**by the**half**of the same arc BOC . B Cor . 2. Every angle BAD , inscribed in a semicircle is a right angle ; because it is mea- sured by**half**the semicircumference BOD , that is , by the fourth part ... Page 56

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**measured by half**of AC + DB . Draw AF parallel to DC : then will the arc DF be equal to AC ( Prop . X. ) ; and the angle FAB equal to the angle DEB ( Book I. Prop . XX . Cor . 3. ) . But F the angle FAB is**measured by half**the arc FDB ... Page 57

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**measured by half**the semicircumference AMD ; the angle DAC is measured by the half of DČ : hence , BAD + DAC , or BAC , is measured by the half of AMD plus the half of DC , or by half the whole arc AMDC . E It might be shown , by taking ...### 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 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