Elements of Geometry and Trigonometry |
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Page 4
... Ratios and Proportions , has been partly adopted from the Encyclopedia Metropolitana , and will , it is believed , supply a deficiency in the original work . Very considerable alterations have also been made in the manner of treating ...
... Ratios and Proportions , has been partly adopted from the Encyclopedia Metropolitana , and will , it is believed , supply a deficiency in the original work . Very considerable alterations have also been made in the manner of treating ...
Page 5
... Ratios and Proportions , 34 BOOK III . The Circle and the Measurement of Angles , Problems relating to the First and Third Books , BOOK IV . The Proportions of Figures and the Measurement of Areas , - Problems relating to the Fourth ...
... Ratios and Proportions , 34 BOOK III . The Circle and the Measurement of Angles , Problems relating to the First and Third Books , BOOK IV . The Proportions of Figures and the Measurement of Areas , - Problems relating to the Fourth ...
Page 33
... and are therefore equal : whence it follows that the angles AEB , BEC , are equal , and therefore , that the two diagonals of a rhombus cut each other at right angles . BOOK II . OF RATIOS AND PROPORTIONS . Definitions . 5 BOOK I. 33.
... and are therefore equal : whence it follows that the angles AEB , BEC , are equal , and therefore , that the two diagonals of a rhombus cut each other at right angles . BOOK II . OF RATIOS AND PROPORTIONS . Definitions . 5 BOOK I. 33.
Page 34
... Ratio is the quotient arising from dividing one quantity by another quantity of the same kind . Thus , if A and B rep- resent quantities of the same kind , the ratio of A ... ratio of any other 34 GEOMETRY . BOOK II Ratios and Proportions,
... Ratio is the quotient arising from dividing one quantity by another quantity of the same kind . Thus , if A and B rep- resent quantities of the same kind , the ratio of A ... ratio of any other 34 GEOMETRY . BOOK II Ratios and Proportions,
Page 35
... ratio will be the same as that of P to Q. 2. If there be four magnitudes A , B , C , and D , having suen then A is said to have the same ratio B values that is equal to A D C ' to B , that C has to D , or the ratio of A to B is equal to the ...
... ratio will be the same as that of P to Q. 2. If there be four magnitudes A , B , C , and D , having suen then A is said to have the same ratio B values that is equal to A D C ' to B , that C has to D , or the ratio of A to B is equal to the ...
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Common terms and phrases
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
Popular passages
Page 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.
Page 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.
Page 232 - ... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.
Page 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.
Page 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.
Page 169 - The convex surface of a cylinder is equal to the circumference of its base multiplied by its altitude, Fig.
Page 20 - In an isosceles triangle the angles opposite the equal sides are equal.
Page 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'.
Page 225 - B) = cos A cos B — sin A sin B, (6a) cos (A — B) = cos A cos B + sin A sin B...
Page 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.