Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Revised and Adapted to the Course of Mathematical Instruction in the United StatesA.S. Barnes & Company, 1854 - 432 Seiten |
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Seite 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 ...
Seite 58
... 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 .
... 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 .
Seite 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 arc 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 arc ENG : therefore ...
Seite 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 ...
Seite 62
... radius CG , at right 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 G of the subtended arc , are three points ...
... radius CG , at right 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 G of the subtended arc , are three points ...
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Häufige Begriffe und Wortgruppen
adjacent angles altitude angle ACB angle BAD base ABCD bisect centre chord circ circumference circumscribed common comp cone consequently convex surface cosine Cotang cylinder diagonal diameter distance divided draw drawn edges equations equivalent feet figure find the area frustum given angle given line given point 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 oblique lines opposite 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 sine slant height solidity sphere spherical polygon spherical triangle square described straight line Tang tangent THEOREM triangle ABC triangular prism triedral angles vertex vertices
Beliebte Passagen
Seite 27 - If two triangles have two sides of the one equal to two sides of the...
Seite 227 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Seite 256 - The logarithm of . the quotient of two numbers, is equal to the logarithm of the dividend diminished by the logarithm of the divisor.
Seite 97 - The square described on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares described on the other two sides.
Seite 26 - The sum of any two sides of a triangle is greater than the third side.
Seite 271 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees...
Seite 93 - The area of a parallelogram is equal to the product of its base and altitude.
Seite 358 - CUBIC MEASURE 1728 cubic inches = 1 cubic foot 27 cubic feet = 1 cubic yard...
Seite 323 - 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.
Seite 64 - Two equal chords are equally distant from the centre ; and of two unequal chords, the less is at the greater distance from the centre.