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
... chord , or subtense of the arc . * 4. A SEGMENT is the part of a circle included between an arc and its chord . 5. A SECTOR is the part of the circle included between an arc , and the two radii drawn to the extremities of the arc . * In ...
... chord , or subtense of the arc . * 4. A SEGMENT is the part of a circle included between an arc and its chord . 5. A SECTOR is the part of the circle included between an arc , and the two radii drawn to the extremities of the arc . * In ...
Seite 58
... 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 is said to be inscribed in a circle , when the vertices of all its angles are in the ...
... 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 is said to be inscribed in a circle , when the vertices of all its angles are in the ...
Seite 59
... chord is less than a diameter . Let AD be any chord . Draw the radii CA , CD , to its extremities . We shall then have ( B. I. , P. 7 ) * AD < AC + CD , but AC plus CD is equal to AB ; hence , AD AB . B Ө A Cor . Hence , the greatest ...
... chord is less than a diameter . Let AD be any chord . Draw the radii CA , CD , to its extremities . We shall then have ( B. I. , P. 7 ) * AD < AC + CD , but AC plus CD is equal to AB ; hence , AD AB . B Ө A Cor . Hence , the greatest ...
Seite 60
... chords : and conversely , equal chords subtend equal arcs . Let C and O be the centres of two equal circles , and suppose the arc AMD equal to the arc ENG : then will the chord AD be equal to the chord EG . For , since the diam- eters ...
... chords : and conversely , equal chords subtend equal arcs . Let C and O be the centres of two equal circles , and suppose the arc AMD equal to the arc ENG : then will the chord AD be equal to the chord EG . For , since the diam- eters ...
Seite 61
... chord which subtends the greater arc is the greater . Conversely : If the chord AH is greater than AD , the arc ADH will be greater than the arc AD . For , if ADH were equal to AD , the chord AH would be equal to the chord AD ( P. 4 ) ...
... chord which subtends the greater arc is the greater . Conversely : If the chord AH is greater than AD , the arc ADH will be greater than the arc AD . For , if ADH were equal to AD , the chord AH would be equal to the chord AD ( P. 4 ) ...
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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.