Elements of Geometry and Trigonometry |
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Page 41
... 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 ...
... 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
... 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 ...
... 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
... 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 ...
... 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
... 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 ...
... 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
... 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 ...
... 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 ...
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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