Elements of Geometry and Trigonometry |
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Page 70
... contained 7 times in the angle ACB , and 4 ᎪᎷ . C น 4 ' S B { X E У Z times in DCE . The seven partial angles ACm , mCn , nếp , & c . , into which ACB is divided , are each equal to any of the four partial angles into which DCE is ...
... contained 7 times in the angle ACB , and 4 ᎪᎷ . C น 4 ' S B { X E У Z times in DCE . The seven partial angles ACm , mCn , nếp , & c . , into which ACB is divided , are each equal to any of the four partial angles into which DCE is ...
Page 80
... contain , being given , to describe the triangle . Let the lines B and C be equal to the given sides , and A the given angle . Having drawn the indefinite line DF , make at the point D , the angle FDE equal to the given angle A ; then ...
... contain , being given , to describe the triangle . Let the lines B and C be equal to the given sides , and A the given angle . Having drawn the indefinite line DF , make at the point D , the angle FDE equal to the given angle A ; then ...
Page 84
... contain a given angle ; that is to say , a segment such , that any angle inscribed in it shall be equal to a given angle . Let AB be the given straight line , and C the given angle . E M M E A G B D A -D 84 GEOMETRY .
... contain a given angle ; that is to say , a segment such , that any angle inscribed in it shall be equal to a given angle . Let AB be the given straight line , and C the given angle . E M M E A G B D A -D 84 GEOMETRY .
Page 90
... contain seven partial rectangles , while AEFD will contain four : hence , the rectangle ABCD : AEFD :: 7 : 4 , or as AB : AE . The same reasoning may be applied to any other ratio equally with that of 7 to 4 : hence , whatever be the ...
... contain seven partial rectangles , while AEFD will contain four : hence , the rectangle ABCD : AEFD :: 7 : 4 , or as AB : AE . The same reasoning may be applied to any other ratio equally with that of 7 to 4 : hence , whatever be the ...
Page 92
... contained in the base of any rectangle , and also , how many times it is contained in the altitude : then , the product of these two ratios may be assumed as the measure of the rectangle . For example , if the base of the rectangle A ...
... contained in the base of any rectangle , and also , how many times it is contained in the altitude : then , the product of these two ratios may be assumed as the measure of the rectangle . For example , if the base of the rectangle A ...
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Elements of Geometry and Trigonometry: From the Works of A. M. Legendre Adrien Marie Legendre,Charles Davies No preview available - 2016 |
Common terms and phrases
adjacent angles altitude angle ACB angle BAD bisect centre chord circ circumference circumscribed common comp cone consequently convex surface cos² Cosine Cosine D Cotang cylinder diagonal diameter distance divided draw drawn equations equivalent feet figure find the area frustum given angle given line gles greater hence homologous homologous sides hypothenuse included angle inscribed circle intersect less Let ABC let fall logarithm magnitudes measured by half middle point number of sides opposite parallel parallelogram parallelopipedon pendicular perimeter perpendicular plane MN polyedral angle polyedron PROBLEM PROPOSITION pyramid quadrant radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar sin² sine slant height solidity sphere spherical polygon spherical triangle square described straight line Tang tangent THEOREM triangle ABC triangular prism triedral angles vertex vertices ΙΟ
Popular passages
Page 24 - If two triangles have two sides and the included angle of the one, equal to two sides and the included angle of the other, each to each, the two triangles will be equal.
Page 38 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Page 227 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Page 271 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees...
Page 43 - Hence, the interior angles plus four right angles, is equal to twice as many right angles as the polygon has sides, and consequently, equal to the sum of the interior angles plus the sum of the exterior angles.
Page 215 - The surface of a sphere is equal to the product of its diameter by the circumference of a great circle.
Page 107 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Page 93 - The area of a parallelogram is equal to the product of its base and altitude.
Page 231 - The angles of spherical triangles may be compared together, by means of the arcs of great circles described from their vertices as poles and included between their sides : hence it is easy to make an angle of this kind equal to a given angle.
Page 232 - F, be respectively poles of the sides BC, AC, AB. For, the point A being the pole of the arc EF, the distance AE is a 'quadrant ; the point C being the pole of the arc DE, the distance CE is likewise a quadrant : hence the point E is...