Elements of Geometry and Trigonometry |
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Page iv
... inscribed and circumscribed polygons , the demonstrations in Book V. have been much simplified ; and the same principle is made the basis of several im- portant demonstrations in Book VIII . The subjects of Plane and Spherical ...
... inscribed and circumscribed polygons , the demonstrations in Book V. have been much simplified ; and the same principle is made the basis of several im- portant demonstrations in Book VIII . The subjects of Plane and Spherical ...
Page 57
... two arcs , and consequently , also to two segments : but the smaller one is always meant , unless the contrary is expressed . 6. A STRAIGHT LINE is said to be inscribed in BOOK III The Circle, and the Measurement of Angles,
... two arcs , and consequently , also to two segments : but the smaller one is always meant , unless the contrary is expressed . 6. A STRAIGHT LINE is said to be inscribed in BOOK III The Circle, and the Measurement of Angles,
Page 58
... inscribed angle is one which has its vertex in the circumference , and is included by two chords of the circle . 7. An inscribed triangle is one which has the vertices of its three angles in the circumference . And generally , a polygon ...
... inscribed angle is one which has its vertex in the circumference , and is included by two chords of the circle . 7. An inscribed triangle is one which has the vertices of its three angles in the circumference . And generally , a polygon ...
Page 59
... inscribed in a circle is a diameter . PROPOSITION III . THEOREM . A straight line cannot meet the circumference of a circle in more than two points . For , if it could meet it in three , those three points would be equally distant from ...
... inscribed in a circle is a diameter . PROPOSITION III . THEOREM . A straight line cannot meet the circumference of a circle in more than two points . For , if it could meet it in three , those three points would be equally distant from ...
Page 73
... inscribed angle is measured by half the arc included between its sides . Let BAD be an inscribed angle , and let us first sup- pose the centre of the circle to lie within the angle BAD . Draw the diameter ACE , and the radii CB , CD ...
... inscribed angle is measured by half the arc included between its sides . Let BAD be an inscribed angle , and let us first sup- pose the centre of the circle to lie within the angle BAD . Draw the diameter ACE , and the radii CB , CD ...
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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...