Elements of Geometry and Trigonometry |
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Page 56
... results will be proportional to the quantities themselves . We have , Prop . VII . , A : B :: mA : mB . If we make m = ± in which p is any fraction , 9 9 we shall have , Ρ A B :: : A ± A : BB ; 9 which was to be proved . PROPOSITION X ...
... results will be proportional to the quantities themselves . We have , Prop . VII . , A : B :: mA : mB . If we make m = ± in which p is any fraction , 9 9 we shall have , Ρ A B :: : A ± A : BB ; 9 which was to be proved . PROPOSITION X ...
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 IIN 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 IIN 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 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 to the entire part , otherwise the decimal part is rejected . EXAMPLE . 1. To find ...
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Common terms and phrases
ABCD AC² adjacent angles altitude angle ACB apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin logarithm lower base mantissa mean proportional measured by half middle point number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROBLEM PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment side BC similar sine slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence