Elements of Geometry and Trigonometry: From the Works of A.M. Legendre |
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Page 93
... ALTITUDE OF A TRIANGLE , is the perpendicular distance from the vertex of either an- gle to the opposite side , or the opposite side produced . The vertex of the angle from which the distance is measured , is called the vertex of the ...
... ALTITUDE OF A TRIANGLE , is the perpendicular distance from the vertex of either an- gle to the opposite side , or the opposite side produced . The vertex of the angle from which the distance is measured , is called the vertex of the ...
Page 94
... altitudes : then will the parallelograms be equal . For , let them be so placed that their lower bases shall coincide ; then , because they have the same altitude , their upper bases will be in the same line DG , parallel to AB HAA The ...
... altitudes : then will the parallelograms be equal . For , let them be so placed that their lower bases shall coincide ; then , because they have the same altitude , their upper bases will be in the same line DG , parallel to AB HAA The ...
Page 95
... altitude . Let the triangle ABC , and the parallelogram ABFD , have equal bases and equal altitudes : then will the triangle be equal to one - half of the parallelogram . For , let them be so placed that the base of D E F the triangle ...
... altitude . Let the triangle ABC , and the parallelogram ABFD , have equal bases and equal altitudes : then will the triangle be equal to one - half of the parallelogram . For , let them be so placed that the base of D E F the triangle ...
Page 96
... altitudes , are proportional to their bases . There may be two cases : the bases may be commensu- rable , or they may be incommensurable . 1o . Let ABCD and HEFK , be two rectangles whose altitudes AD and HK are equal , and whose bases ...
... altitudes , are proportional to their bases . There may be two cases : the bases may be commensu- rable , or they may be incommensurable . 1o . Let ABCD and HEFK , be two rectangles whose altitudes AD and HK are equal , and whose bases ...
Page 97
... be equal to AE : hence , ABCD : AEFD :: AB AE ; which was to be proved . Cor . If rectangles have equal bases , they are to each other as their altitudes . PROPOSITION IV . THEOREM . Any two rectangles are to 7 300K IV . 97.
... be equal to AE : hence , ABCD : AEFD :: AB AE ; which was to be proved . Cor . If rectangles have equal bases , they are to each other as their altitudes . PROPOSITION IV . THEOREM . Any two rectangles are to 7 300K IV . 97.
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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.