Elements of Geometry and Trigonometry: From the Works of A.M. Legendre |
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Page iii
... figure , that figure being taken to represent any one of the class to which it belongs . By this arrangement , the difficulty experienced by beginners in comprehending abstract truths , is lessened , without in any manner impairing the ...
... figure , that figure being taken to represent any one of the class to which it belongs . By this arrangement , the difficulty experienced by beginners in comprehending abstract truths , is lessened , without in any manner impairing the ...
Page v
... Figures - Measurement of Areas , Problems relating to the Fourth Book , ..... PAGE . 13 20 50 60 59 82 93 129 BOOK V. Regular Polygons - Measurement of the Circle , 136 BOOK VI . Planes , and Polyedral Angles , 157 BOOK VII . Polyedrons ...
... Figures - Measurement of Areas , Problems relating to the Fourth Book , ..... PAGE . 13 20 50 60 59 82 93 129 BOOK V. Regular Polygons - Measurement of the Circle , 136 BOOK VI . Planes , and Polyedral Angles , 157 BOOK VII . Polyedrons ...
Page 15
... FIGURE is a portion of a plane bounded by lines , either straight or curved . 18. A POLYGON is a plane figure bounded by straight lines . The The bounding lines are called sides of the polygon . broken line , made up of all the sides of ...
... FIGURE is a portion of a plane bounded by lines , either straight or curved . 18. A POLYGON is a plane figure bounded by straight lines . The The bounding lines are called sides of the polygon . broken line , made up of all the sides of ...
Page 46
... figure has sides , less four right angles , divided by the number of angles . PROPOSITION XXVII . THEOREM . The sum of the exterior angles of a polygon is equal to four right angles . Let the sides of the polygon ABCDE be prolonged , in ...
... figure has sides , less four right angles , divided by the number of angles . PROPOSITION XXVII . THEOREM . The sum of the exterior angles of a polygon is equal to four right angles . Let the sides of the polygon ABCDE be prolonged , in ...
Page 48
... figure is a parallelogram ( D. 28 ) ; which was to be proved . PROPOSITION XXX . THEOREM . If two sides of a quadrilateral are equal and parallel , the figure is a parallelogram . In the quadrilateral ABCD , let AB D be equal and ...
... figure is a parallelogram ( D. 28 ) ; which was to be proved . PROPOSITION XXX . THEOREM . If two sides of a quadrilateral are equal and parallel , the figure is a parallelogram . In the quadrilateral ABCD , let AB D be equal and ...
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Common terms and phrases
AB² ABCD AC² adjacent angles altitude 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 difference distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given straight line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin lower base mantissa measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment semi-circumference side BC similar sine slant height sphere spherical polygon spherical triangle square subtracted Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence
Popular passages
Page 126 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Page 59 - A'B'C', and applying the law of cosines, we have cos a' = cos b' cos c' + sin b' sin c' cos A'. Remembering the relations a' = 180° -A, b' = 180° - B, etc. (this expression becomes cos A = — cos B cos C + sin B sin C cos a.
Page 18 - The circumference of every circle is supposed to be divided into 360 equal parts called degrees, and each degree into 60 equal parts called minutes, and each minute into 60 equal parts called seconds, and these into thirds, fourths, &c.
Page 104 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.
Page 6 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 28 - If two triangles have two sides of the one equal to two sides of the...
Page 46 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 99 - The area of a parallelogram is equal to the product of its base and altitude.
Page 172 - If two planes are perpendicular to 'each other, a straight line drawn in one of them, perpendicular to their intersection, will be perpendicular to the other.
Page 214 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.