Elements of Geometry and TrigonometryWiley & Long, 1836 - 359 σελίδες |
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Σελίδα 5
... Regular Polygons and the Measurement of the Circle , 109 BOOK VI . Planes and Solid Angles , 126 BOOK VII . Polyedrons , 142 BOOK VIII . The three round bodies , 19 166 BOOK IX . Of Spherical Triangles and Spherical Polygons , The regular ...
... Regular Polygons and the Measurement of the Circle , 109 BOOK VI . Planes and Solid Angles , 126 BOOK VII . Polyedrons , 142 BOOK VIII . The three round bodies , 19 166 BOOK IX . Of Spherical Triangles and Spherical Polygons , The regular ...
Σελίδα 108
... these two lines are to each other :: √2 : 1 ( Prop . XI . Cor . 4. ) , but which acquires a greater degree of clearness by the geometrical investigation . BOOK V. REGULAR POLYGONS , AND THE MEASUREMENT OF THE 108 GEOMETRY .
... these two lines are to each other :: √2 : 1 ( Prop . XI . Cor . 4. ) , but which acquires a greater degree of clearness by the geometrical investigation . BOOK V. REGULAR POLYGONS , AND THE MEASUREMENT OF THE 108 GEOMETRY .
Σελίδα 109
... regular polygon . Regular polygons may have any number of sides : the equi- lateral triangle is one of three sides ; the square is one of four . PROPOSITION I. THEOREM . Two regular polygons of the same number of sides are similar ...
... regular polygon . Regular polygons may have any number of sides : the equi- lateral triangle is one of three sides ; the square is one of four . PROPOSITION I. THEOREM . Two regular polygons of the same number of sides are similar ...
Σελίδα 110
Adrien Marie Legendre David Brewster, Charles Davies. PROPOSITION II . THEOREM . Any regular polygon may be inscribed in a circle , and circum scribed about one . Let ABCDE & c . be a regular poly- gon : describe a circle through the ...
Adrien Marie Legendre David Brewster, Charles Davies. PROPOSITION II . THEOREM . Any regular polygon may be inscribed in a circle , and circum scribed about one . Let ABCDE & c . be a regular poly- gon : describe a circle through the ...
Σελίδα 111
... regular polygon . PROPOSITION III . PROBLEM . To inscribe a square in a given circle . Draw two diameters AC , BD , cut- ting each other at right angles ; join their extremities A , B , C , D : the figure ABCD will be a square . For the ...
... regular polygon . PROPOSITION III . PROBLEM . To inscribe a square in a given circle . Draw two diameters AC , BD , cut- ting each other at right angles ; join their extremities A , B , C , D : the figure ABCD will be a square . For the ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
adjacent altitude angle ACB ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone consequently convex surface cosine Cotang 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 greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular perpendicular let fall plane MN polyedron polygon ABCDE PROBLEM PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment side BC similar sine slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex
Δημοφιλή αποσπάσματα
Σελίδα 241 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.
Σελίδα 18 - If two triangles have two sides of the one equal to two sides of the...
Σελίδα 233 - It is, indeed, evident, that the negative characteristic will always be one greater than the number of ciphers between the decimal point and the first significant figure.
Σελίδα 168 - The radius of a sphere is a straight line drawn from the centre to any point of the surface ; the diameter or axis is a line passing through this centre, and terminated on both sides by the surface.
Σελίδα 18 - America, but know that we are alive, that two and two make four, and that the sum of any two sides of a triangle is greater than the third side.
Σελίδα 225 - B) = cos A cos B — sin A sin B, (6a) cos (A — B) = cos A cos B + sin A sin B...
Σελίδα 20 - In an isosceles triangle the angles opposite the equal sides are equal.
Σελίδα 86 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Σελίδα 159 - S-o6c be the smaller : and suppose Aa to be the altitude of a prism, which having ABC for its base, is equal to their difference. Divide the altitude AT into equal parts Ax, xy, yz, &c. each less than Aa, and let k be one of those parts ; through the points of division...
Σελίδα 168 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.