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, 1857 - 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. EXTENSION 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. EXTENSION 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 ...
... 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 ...
Página 19
... taken three times ; A signifies the half of the angle A. 3 8. The square of the line AB is designated by AB its cube ... taken from equals , the remainders will be equal . 4. If equals be added to unequals , the wholes will be unequal ...
... taken three times ; A signifies the half of the angle A. 3 8. The square of the line AB is designated by AB its cube ... taken from equals , the remainders will be equal . 4. If equals be added to unequals , the wholes will be unequal ...
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. 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 be ...
... taken for unity , the line AB would be 13 ; if AB were taken for unity , CD would be 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 be ...
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Términos y frases comunes
altitude angle ACB angle BAD bisect centre chord circ circumference circumscribed common comp cone consequently convex surface cos² cosine Cotang cubes 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 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 similar triangles sin² sine slant height solidity sphere spherical polygon spherical triangle square described straight line Tang tangent THEOREM three angles triangle ABC triangular prism triedral angles vertex vertices
Pasajes populares
Página 227 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Página 34 - If two right-angled triangles have the hypothenuse and a side of the one, equal to the hypothenuse and a side of the other, each to each, the triangles are equal. Let...
Página 271 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees...
Página 278 - In any triangle, the sum of the two sides containing either angle, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of half their difference.
Página 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.
Página 1 - O's, points or dots are introduced instead of the 0's through the rest of the line, to catch the eye, and to indicate that from thence the annexed first two figures of the Logarithm in the second column stand in the next lower line. N'.
Página 43 - BtSL hence the sum of all the interior and exterior angles, is equal to twice as many right angles as the polygon has sides.
Página 119 - The angle formed by a tangent and a chord is measured by half the intercepted arc.
Página 30 - B : hence the 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 : hence, the two triangles are equal (Th.
Página 97 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.