Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Results 1-5 of 28
Page 56
... results will be proportional to the quantities themselves . We have , Prop . VII . , A : B :: mA : mB . If we make m = 1 ± p > 9 in which P is any fraction , we shall have , A : B :: A ± 2oA : B ± p -B ; q q which was to be proved ...
... results will be proportional to the quantities themselves . We have , Prop . VII . , A : B :: mA : mB . If we make m = 1 ± p > 9 in which P is any fraction , we shall have , A : B :: A ± 2oA : B ± p -B ; q q which was to be proved ...
Page 58
... 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 be proportional . Cor . 2. If the principle of the proposition be ...
... 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 be proportional . Cor . 2. If the principle of the proposition be ...
Page 142
... resulting figure will be a regular inscribed pentagon . Scholium 1. If the arcs subtended by the sides of any regular inscribed polygon be bisected , and chords of the semi- arcs be drawn , the resulting figure will be a regular ...
... resulting figure will be a regular inscribed pentagon . Scholium 1. If the arcs subtended by the sides of any regular inscribed polygon be bisected , and chords of the semi- arcs be drawn , the resulting figure will be a regular ...
Page 144
... resulting figure will be a regular inscribed polygon similar to the given polygon . Cor . 2. The sum of the lines HT and HN is equal to the sum of HT and TG , or to HG ; that is , to one of the sides of the circumscribed polygon . Cor ...
... resulting figure will be a regular inscribed polygon similar to the given polygon . Cor . 2. The sum of the lines HT and HN is equal to the sum of HT and TG , or to HG ; that is , to one of the sides of the circumscribed polygon . Cor ...
Page 9
... result will be the required mantissa . It is to be observed that when the decimal part of the product just spoken of is equal to or exceeds .5 , we add 1 to the entire part , otherwise the decimal part is rejected . EXAMPLE . 1. To find ...
... result will be the required mantissa . It is to be observed that when the decimal part of the product just spoken of is equal to or exceeds .5 , we add 1 to the entire part , otherwise the decimal part is rejected . EXAMPLE . 1. To find ...
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Common terms and phrases
ABČ 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