Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Page 46
... corresponding exterior angle , is equal D \ B Cle to two right angles ( P. I. ) : hence , the sum of all the inte rior and exterior angles is equal to two right angles taken as many times as the polygon has sides . But 46 GEOMETRY .
... corresponding exterior angle , is equal D \ B Cle to two right angles ( P. I. ) : hence , the sum of all the inte rior and exterior angles is equal to two right angles taken as many times as the polygon has sides . But 46 GEOMETRY .
Page 49
... corresponding sides of the other ; they are , therefore , equal : hence , the angles AEB , BEC , are equal , and therefore , the two diagonals bisect each other at right angles . BOOK II . RATIOS AND PROPORTIONS . DEFINITIONS . 1. BOOK ...
... corresponding sides of the other ; they are , therefore , equal : hence , the angles AEB , BEC , are equal , and therefore , the two diagonals bisect each other at right angles . BOOK II . RATIOS AND PROPORTIONS . DEFINITIONS . 1. BOOK ...
Page 57
... corresponding consequent . From the definition of a continued proportion ( D. 3 ) , A : B :: C : D :: E : F :: G : H , & c . , hence , В 34 B A 34 34 B A B 314 Α = B = whence , BA = AB ; Α AP EN D ; whence , BC = AD ; F whence , BE = AF ...
... corresponding consequent . From the definition of a continued proportion ( D. 3 ) , A : B :: C : D :: E : F :: G : H , & c . , hence , В 34 B A 34 34 B A B 314 Α = B = whence , BA = AB ; Α AP EN D ; whence , BC = AD ; F whence , BE = AF ...
Page 58
... corresponding terms of two proportions are equal , each term of the resulting proportion will be the square of the corresponding term in either of the given pro- portions hence , If four quantities are proportional , their squares will ...
... corresponding terms of two proportions are equal , each term of the resulting proportion will be the square of the corresponding term in either of the given pro- portions hence , If four quantities are proportional , their squares will ...
Page 75
... corresponding angles at the centre , as may be shown by changing the order of the couplets in . the above proportion . PROPOSITION XVII . THEOREM . In equal circles , incommensurable angles are proportional to their intercepted arcs ...
... corresponding angles at the centre , as may be shown by changing the order of the couplets in . the above proportion . PROPOSITION XVII . THEOREM . In equal circles , incommensurable angles are proportional to their intercepted arcs ...
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Common terms and phrases
AB² ABCD altitude apothem Applying logarithms centre chord circle circumference cone consequently convex surface cosec Cosine Cotang cylinder demonstrated in Book denote diameter distance divided draw edges Equation feet find the area Find the logarithmic following RULE frustum given angle greater hence homologous hypothenuse included angle inscribed intersection less Let ABC linear units log cot log sin lower base lune mantissa multiplied number of sides opposite parallel parallelogram parallelopipedon perpendicular plane MN polar triangle polyedral angle polyedron principle demonstrated prism proportional PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium segment similar six right slant height solution sphere spherical angle spherical excess spherical polygon spherical triangle square straight line subtracting Tang tangent THEOREM triangle ABC triangular prism upper base vertex volume whence write the following