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 páginas |
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Página 12
... , in the abstract , with which the mind should be made conversant , and too much pains cannot be taken to exclude the idea that we are dealing with material things . ELEMENTS OF GEOMETRY . BOOK I. DEFINITIONS . * 1. 12 GEOMETRY .
... , in the abstract , with which the mind should be made conversant , and too much pains cannot be taken to exclude the idea that we are dealing with material things . ELEMENTS OF GEOMETRY . BOOK I. DEFINITIONS . * 1. 12 GEOMETRY .
Página 18
... taken from A ; and A - B + C , or A + C - B , sig- nifies that A and C are to be added together , and that B is to be subtracted from their sum . 6. The sign X indicates multiplication : thus AXB re- presents the product of A and B. The ...
... taken from A ; and A - B + C , or A + C - B , sig- nifies that A and C are to be added together , and that B is to be subtracted from their sum . 6. The sign X indicates multiplication : thus AXB re- presents the product of A and B. The ...
Página 19
... taken from equals , the remainders will be equal . 4. If equals be added to unequals , the wholes will be unequal . 5. If equals be taken from unequals , the remainders will be unequal . 6. Things which are doubles of equal things , are ...
... taken from equals , the remainders will be equal . 4. If equals be added to unequals , the wholes will be unequal . 5. If equals be taken from unequals , the remainders will be unequal . 6. Things which are doubles of equal things , are ...
Página 42
... taken as many times as there are triangles in the figure ; that is , as many times as there are sides , less two . But this pro- duct is equal to twice as many right angles as the figure has sides , less four right angles . Cor . 1. The ...
... taken as many times as there are triangles in the figure ; that is , as many times as there are sides , less two . But this pro- duct is equal to twice as many right angles as the figure has sides , less four right angles . Cor . 1. The ...
Página 49
... taken for unity , the line AB would be 13 ; if AB were taken for unity , CD would be 5 5. What has been shown , in respect to the straight lines , CD and AB , is equally true of any two magnitudes , A and B. For , we may conceive A to ...
... taken for unity , the line AB would be 13 ; if AB were taken for unity , CD would be 5 5. What has been shown , in respect to the straight lines , CD and AB , is equally true of any two magnitudes , A and B. For , we may conceive A to ...
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Términos y frases comunes
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
Pasajes populares
Página 27 - If two triangles have two sides of the one equal to two sides of the...
Página 227 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Página 256 - The logarithm of . the quotient of two numbers, is equal to the logarithm of the dividend diminished by the logarithm of the divisor.
Página 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.
Página 26 - The sum of any two sides of a triangle is greater than the third side.
Página 271 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees...
Página 93 - The area of a parallelogram is equal to the product of its base and altitude.
Página 358 - CUBIC MEASURE 1728 cubic inches = 1 cubic foot 27 cubic feet = 1 cubic yard...
Página 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.
Página 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.