## Elements of Geometry and Trigonometry |

### From inside the book

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**radius**or semidiam- F H eter ; every line which , like AB , passes through the centre , and is terminated on both sides by the circumference , is called a diameter . From the definition of a circle , it follows that all the radii are ... Page 44

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**radius**CD will fall on the**radius**OG , and the point D on the point G ; therefore the arc AMD is equal to the arc ENG . PROPOSITION V. THEOREM . In the same circle , or in equal circles , a greater arc is subtended by a greater chord ... Page 45

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**radius**which is perpendicular to a chord , 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 ... Page 46

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**radius**OB , will pass through the three given points A , B , C. We have now shown that one circumference can always be made to pass through three given points , not in the same straight line : we say farther , that but one can be ... Page 47

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**radius**, at its extremity , is a tangent to the circumference . Let BD be perpendicular to the B**radius**CA , at its extremity A ; then will it be tangent to the circumfe- rence . For , every oblique line CE , is longer than the ...### 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