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 18
... scholium is a remark on one or several preceding ropositions , 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 ropositions , 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
... , 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 Propositions,
... , 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 Propositions,
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
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.