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 18
... scholium is a remark on one or several preceding propositions , which tends to point out their connection , their use , their restriction , or their extension . 9. A hypothesis is a supposition , made either in the enunciation of a ...
... scholium is a remark on one or several preceding propositions , which tends to point out their connection , their use , their restriction , or their extension . 9. A hypothesis is a supposition , made either in the enunciation of a ...
Página 21
... F A * In the references , A. stands for Axiom - D . for Definition - B . for Book -- P . for Proposition - C . for Corollary - S . for Scholium , and Prob . for Problem . PROPOSITION II . THEOREM . Two straight lines , which BOOK I. 21.
... F A * In the references , A. stands for Axiom - D . for Definition - B . for Book -- P . for Proposition - C . for Corollary - S . for Scholium , and Prob . for Problem . PROPOSITION II . THEOREM . Two straight lines , which BOOK I. 21.
Página 23
... In a similar manner it may be proved that ACE is equal to DCB . Scholium . The four angles formed about a point by two straight lines , which intersect each other , are together equal to four right angles . For , the sum of BOOK I. 23.
... In a similar manner it may be proved that ACE is equal to DCB . Scholium . The four angles formed about a point by two straight lines , which intersect each other , are together equal to four right angles . For , the sum of BOOK I. 23.
Página 25
... Scholium . Two triangles which being applied to each other , coincide in all their parts , are equal ( A. 14 ) . The like parts are those which coincide with each other ; hence , they are also equal each to each . The converse of this ...
... Scholium . Two triangles which being applied to each other , coincide in all their parts , are equal ( A. 14 ) . The like parts are those which coincide with each other ; hence , they are also equal each to each . The converse of this ...
Página 29
... Scholium . It may be observed , that when two triangles are equal to each other , the equal angles lie opposite the equal sides , and consequently , the equal sides opposite the equal angles : thus , the equal angles D and A , lie ...
... Scholium . It may be observed , that when two triangles are equal to each other , the equal angles lie opposite the equal sides , and consequently , the equal sides opposite the equal angles : thus , the equal angles D and A , lie ...
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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.