Elements of Geometry and TrigonometryA. S. Barnes and Company, 1852 - 432 sider |
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Side 87
... homologous angles : and the sides which are like situated , in respect to the . equal angles , are called homologous sides . 3. AREA , denotes the superficial contents of a figure . The area of a figure is expressed numerically by the ...
... homologous angles : and the sides which are like situated , in respect to the . equal angles , are called homologous sides . 3. AREA , denotes the superficial contents of a figure . The area of a figure is expressed numerically by the ...
Side 105
... AFC ; consequently , AF is equal to AC . But , since FC is parallel to the base AD , hence , E A F B BD : DC AB AF ; : BD : DC : AB : AC . : PROPOSITION XVIII . THEOREM . Equiangular triangles have their homologous BOOK IV . 105.
... AFC ; consequently , AF is equal to AC . But , since FC is parallel to the base AD , hence , E A F B BD : DC AB AF ; : BD : DC : AB : AC . : PROPOSITION XVIII . THEOREM . Equiangular triangles have their homologous BOOK IV . 105.
Side 106
... homologous sides will be proportional , viz .: BA : :: B A F CD :: AC : DE . D E BC : CE Place the homologous sides BC , CE in the same straight line ; and prolong the sides BA , ED , till they meet in F. Since BCE is a straight line ...
... homologous sides will be proportional , viz .: BA : :: B A F CD :: AC : DE . D E BC : CE Place the homologous sides BC , CE in the same straight line ; and prolong the sides BA , ED , till they meet in F. Since BCE is a straight line ...
Side 107
... homologous to DC ; in like manner AC and DE are homologous , be- cause opposite to the equal angles ABC , DCE . PROPOSITION XIX . THEOREM . Conversely : Triangles , which have their sides proportional , are equiangular and similar . If ...
... homologous to DC ; in like manner AC and DE are homologous , be- cause opposite to the equal angles ABC , DCE . PROPOSITION XIX . THEOREM . Conversely : Triangles , which have their sides proportional , are equiangular and similar . If ...
Side 110
... homologous sides are the parallel ones : in the case of their being perpendicular , the homologous sides are the perpen- dicular ones . Thus , in the latter case , DE is homologous with BA , DF with AC , and EF with BC . The case of the ...
... homologous sides are the parallel ones : in the case of their being perpendicular , the homologous sides are the perpen- dicular ones . Thus , in the latter case , DE is homologous with BA , DF with AC , and EF with BC . The case of the ...
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Elements of Geometry and Trigonometry: From the Works of A. M. Legendre Adrien Marie Legendre,Charles Davies Ingen forhåndsvisning tilgjengelig - 2016 |
Vanlige uttrykk og setninger
adjacent angles altitude angle ACB angle BAD bisect centre chord circ circumference circumscribed common comp cone consequently convex surface cos² Cosine Cosine D Cotang cylinder diagonal diameter distance divided draw drawn equations equivalent feet figure find the area frustum given angle given line 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 parallel 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 sin² sine slant height solidity sphere spherical polygon spherical triangle square described straight line Tang tangent THEOREM triangle ABC triangular prism triedral angles vertex vertices ΙΟ
Populære avsnitt
Side 24 - If 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, the two triangles will be equal.
Side 38 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Side 227 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Side 271 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees...
Side 43 - Hence, the interior angles plus four right angles, is equal to twice as many right angles as the polygon has sides, and consequently, equal to the sum of the interior angles plus the sum of the exterior angles.
Side 215 - The surface of a sphere is equal to the product of its diameter by the circumference of a great circle.
Side 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.
Side 93 - The area of a parallelogram is equal to the product of its base and altitude.
Side 231 - The angles of spherical triangles may be compared together, by means of the arcs of great circles described from their vertices as poles and included between their sides : hence it is easy to make an angle of this kind equal to a given angle.
Side 232 - F, be respectively poles of the sides BC, AC, AB. For, the point A being the pole of the arc EF, the distance AE is a 'quadrant ; the point C being the pole of the arc DE, the distance CE is likewise a quadrant : hence the point E is...