Elements of Geometry and Trigonometry: From the Works of A.M. Legendre |
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Page 76
... similar manner , it may be shown that the fourth term cannot be less than AD : hence , it must be equal to AD ; therefore , we have , angle ACB : angle ACD :: arc AB • arc AD which was to be proved . Cor . 1. The intercepted arcs are ...
... similar manner , it may be shown that the fourth term cannot be less than AD : hence , it must be equal to AD ; therefore , we have , angle ACB : angle ACD :: arc AB • arc AD which was to be proved . Cor . 1. The intercepted arcs are ...
Page 93
... SIMILAR ARCS , SECTORS , or SEGMENTS , in different circles , are those which correspond to equal angles at the centre . Thus , if the angles A and O are A equal , the arcs BFC and DGE are similar , the sectors BAC and DOE are similar ...
... SIMILAR ARCS , SECTORS , or SEGMENTS , in different circles , are those which correspond to equal angles at the centre . Thus , if the angles A and O are A equal , the arcs BFC and DGE are similar , the sectors BAC and DOE are similar ...
Page 113
... similar . Let the triangles ABC and DEF have the angle A equal to the angle D , the angle B to the angle E , and the angle C to the angle F : then will they be similar . For , place the triangle DEF upon the triangle ABC , so that the ...
... similar . Let the triangles ABC and DEF have the angle A equal to the angle D , the angle B to the angle E , and the angle C to the angle F : then will they be similar . For , place the triangle DEF upon the triangle ABC , so that the ...
Page 114
... similar ( D. 1 ) ; which was to be proved . Cor . If two triangles have two angles in one , equel to two angles in the other , each to each , they will be similar ( B. L. , P. XXV . , C. 2 ) . PROPOSITION XIX . THEOREM . Triangles which ...
... similar ( D. 1 ) ; which was to be proved . Cor . If two triangles have two angles in one , equel to two angles in the other , each to each , they will be similar ( B. L. , P. XXV . , C. 2 ) . PROPOSITION XIX . THEOREM . Triangles which ...
Page 115
... similar . For , on BA lay off BG equal to ED ; on BC lay off BH equal to EF , and draw GH . Then , because BG is equal to A D DE , and BH to EF , we have , B E BA : BG :: BC : BH ; hence , GH is parallel to AC ( P. XVI . ) ; and ...
... similar . For , on BA lay off BG equal to ED ; on BC lay off BH equal to EF , and draw GH . Then , because BG is equal to A D DE , and BH to EF , we have , B E BA : BG :: BC : BH ; hence , GH is parallel to AC ( P. XVI . ) ; and ...
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Common terms and phrases
ABē ABCD ACē 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.