## Elements of Geometry and Trigonometry |

### From inside the book

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Page 120

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**circ**. CA ; and its area , by area CA : it is then to be shown that**circ**. CA**circ**. OB area CA CA : OB , and that area OB :: CA2 : OB2 . B E M P T L K Inscribe within the circles two regular polygons of the same number of sides . Then ... Page 121

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**circ**. OA . For , inscribe in the circle any E regular polygon , and draw OF perpendicular to one of its sides . Then the area of the polygon will be equal to OF , multiplied by the perimeter ( Prop . IX . ) . F C ind D Now , let the ... Page 122

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**circ**. CA , there- fore**circ**. CA = 2CA . Multiply both terms by CA ; we have CAx**circ**. CA = л × CA2 , or area СA = л × CA2 : hence the area of a circle is equal to the product of the square of its radius by the constant number π ... Page 169

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**circ**. CA , we are to show that the convex surface of H the cylinder is equal to**circ**, CA x H. Inscribe in the circle any regular polygon , BDEFGA , and construct on this polygon a right : G F C E B D prism having its altitude equal to ... Page 170

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**circ**. CA ( Book V. Prop . VIII . Cor . 1 . & 2. ) ; the inscribed prism then coincides with the cylinder , since their altitudes are equal , and their convex surfaces per- pendicular to the common base : hence the two solids will be ...### 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