Elements of Geometry and TrigonometryA. S. Barnes and Company, 1838 - 269 σελίδες |
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Σελίδα 3
... figures . The method of enunciating them by the aid of particu- lar diagrams seems to have been adopted to avoid the difficulty which beginners experience in comprehend- ing abstract propositions . But in avoiding this diffi- culty ...
... figures . The method of enunciating them by the aid of particu- lar diagrams seems to have been adopted to avoid the difficulty which beginners experience in comprehend- ing abstract propositions . But in avoiding this diffi- culty ...
Σελίδα 5
... Figures and the Measurement of Areas , - Problems relating to the Fourth Book , 41 57 98 8888888 68 BOOK V. Regular Polygons and the Measurement of the Circle , 109 BOOK VI . Planes and Solid Angles , 126 BOOK VII . Polyedrons , 142 ...
... Figures and the Measurement of Areas , - Problems relating to the Fourth Book , 41 57 98 8888888 68 BOOK V. Regular Polygons and the Measurement of the Circle , 109 BOOK VI . Planes and Solid Angles , 126 BOOK VII . Polyedrons , 142 ...
Σελίδα 10
... figure is a plane terminated on all sides by lines , either straight or curved . A If the lines are straight , the space they enclose is called a rectilineal figure , or polygon , and the lines themselves , taken together , form the ...
... figure is a plane terminated on all sides by lines , either straight or curved . A If the lines are straight , the space they enclose is called a rectilineal figure , or polygon , and the lines themselves , taken together , form the ...
Σελίδα 30
... figure has sides . Let ABCDEFG be the proposed polygon . If from the vertex of any one angle A , diagonals B AC , AD , AE , AF , be drawn to the vertices of all the opposite angles , it is plain that the poly- gon will be divided into ...
... figure has sides . Let ABCDEFG be the proposed polygon . If from the vertex of any one angle A , diagonals B AC , AD , AE , AF , be drawn to the vertices of all the opposite angles , it is plain that the poly- gon will be divided into ...
Σελίδα 31
... sides ( Prop . XXVI . ) ; that is , equal to twice as many right angles as the figure has sides , wanting four right angles . Hence , the interior angles plus four right angles , is equal to twice as many right angles BOOK I. 31.
... sides ( Prop . XXVI . ) ; that is , equal to twice as many right angles as the figure has sides , wanting four right angles . Hence , the interior angles plus four right angles , is equal to twice as many right angles BOOK I. 31.
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Συχνά εμφανιζόμενοι όροι και φράσεις
adjacent altitude angle ACB angle BAC 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 equal angles equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm number of sides opposite parallel parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE PROBLEM proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment 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 19 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Σελίδα 232 - ... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.
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 169 - The convex surface of a cylinder is equal to the circumference of its base multiplied by its altitude, Fig.
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 225 - B) = cos A cos B — sin A sin B, (6a) cos (A — B) = cos A cos B + sin A sin B...
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.