Elements of Geometry and Trigonometry |
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Page 57
... radius , or , semidiameter . Every line which passes through the centre , and is terminated , on both sides , by the circumference , is called a diameter . From the definition of a circle , it follows , that all the radii are equal ...
... radius , or , semidiameter . Every line which passes through the centre , and is terminated , on both sides , by the circumference , is called a diameter . From the definition of a circle , it follows , that all the radii are equal ...
Page 58
... in the poly- gon . POSTULATE . 12. Let it be granted that the circumference of a circle may be described from any centre , and with any radius . PROPOSITION I. THEOREM . Every diameter divides the circle and 58 GEOMETRY .
... in the poly- gon . POSTULATE . 12. Let it be granted that the circumference of a circle may be described from any centre , and with any radius . PROPOSITION I. THEOREM . Every diameter divides the circle and 58 GEOMETRY .
Page 60
... radius AC may fall on the equal radius EO . Then , since the angle ACD is equal to the angle EOG , the radius CD will fall on OG , and the sector AMDC will coincide with the sector ENGO , and the arc AMD with the are ENG : therefore ...
... radius AC may fall on the equal radius EO . Then , since the angle ACD is equal to the angle EOG , the radius CD will fall on OG , and the sector AMDC will coincide with the sector ENGO , and the arc AMD with the are ENG : therefore ...
Page 61
... radius which is perpendicular to a chord , bisects the chord , and bisects also the subtended arc of the chord . Let AB be any chord , and CG a radius perpendicu- lar to it : then will AD be equal to DB , and the arc AG to the arc GB ...
... radius which is perpendicular to a chord , bisects the chord , and bisects also the subtended arc of the chord . Let AB be any chord , and CG a radius perpendicu- lar to it : then will AD be equal to DB , and the arc AG to the arc GB ...
Page 62
... radius CG , at right G angles to the chord AB , divides the arc subtended by that chord into two equal parts . Scholium . The centre C , the middle point D of the chord AB , and the middle point & of the subtended arc , are three points ...
... radius CG , at right G angles to the chord AB , divides the arc subtended by that chord into two equal parts . Scholium . The centre C , the middle point D of the chord AB , and the middle point & of the subtended arc , are three points ...
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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 base ABCD bisect centre chord circ circumference circumscribed common comp cone consequently convex surface Cosine Cotang cube cylinder diagonal diameter distance divided draw drawn edges equations equivalent feet figure find the area find the solidity frustum given angle given line greater hence homologous homologous sides hypothenuse inches inscribed circle intersect less Let ABCD let fall logarithm magnitudes middle point number of sides opposite parallel parallelogram parallelopipedon pendicular perimeter perpendicular plane MN polyedral angle proportional PROPOSITION pyramid quadrant radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar sine slant height sphere spherical polygon spherical triangle square described straight line Tang tangent THEOREM triangle ABC triangular prism triedral angles upper base vertex vertices
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...