A Treatise on Special Or Elementary Geometry: Including an Elementary, and Also, in Part III, a Higher Course, in Plane, Solid, and Spherical Geometry; and Plane and Spherical Trigonometry, with the Necessary TablesSheldon, 1879 - 440 Seiten |
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Seite 175
... Diedral Angle , or simply a Diedral , is the opening between two intersecting planes . 422. A Polyedral Angle , called also simply a Polyedral , is the opening between three or more planes which intersect so as to have one common point ...
... Diedral Angle , or simply a Diedral , is the opening between two intersecting planes . 422. A Polyedral Angle , called also simply a Polyedral , is the opening between three or more planes which intersect so as to have one common point ...
Seite 176
... diedral in ( a ) may be designated as AB , or as C - AB - D . In ( b ) we have a Triedral ( angle The edges are SA , SB , and SC ; the faces ASB , BSC , and ASC : the facial angies are ASB , ASC , and BSC ; and S is the vertex . Such an ...
... diedral in ( a ) may be designated as AB , or as C - AB - D . In ( b ) we have a Triedral ( angle The edges are SA , SB , and SC ; the faces ASB , BSC , and ASC : the facial angies are ASB , ASC , and BSC ; and S is the vertex . Such an ...
Seite 177
... diedral is right . Thus , if MO is perpendicular to the plane DB , C - AB - D is a right diedral . For MO is perpendicular to every line of DB passing through its foot ( ? ) ; and hence is perpendicular to ON , drawn at right angles to ...
... diedral is right . Thus , if MO is perpendicular to the plane DB , C - AB - D is a right diedral . For MO is perpendicular to every line of DB passing through its foot ( ? ) ; and hence is perpendicular to ON , drawn at right angles to ...
Seite 178
... diedral angles . A 血 B FIG . 275 . ILL'S . The corner of a cube is a Trirectangular triedral , as S - ADC . Conceive the upper portion of the cube removed by the plane ASEF ; then the angle at S , i . e . , S - AEC is a Birectangular ...
... diedral angles . A 血 B FIG . 275 . ILL'S . The corner of a cube is a Trirectangular triedral , as S - ADC . Conceive the upper portion of the cube removed by the plane ASEF ; then the angle at S , i . e . , S - AEC is a Birectangular ...
Seite 180
... diedral A - SC - B , equals angle acb , measuring the diedral a - sc - b , these diedrals are equal , and can be applied to each other . Applying these diedrals , since angle ASC asc , and BSC = bsc , the edges AS and as coincide , as ...
... diedral A - SC - B , equals angle acb , measuring the diedral a - sc - b , these diedrals are equal , and can be applied to each other . Applying these diedrals , since angle ASC asc , and BSC = bsc , the edges AS and as coincide , as ...
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Häufige Begriffe und Wortgruppen
ABCD adjacent altitude angle or arc bisect centre chord circle circumference coincide common point conceive construct cosec cosine cotangent DEM.-Let diagonals diameter dicular diedral distance divided draw drawn edge equal angles equiangular equilateral equivalent exterior angle facial angles figure frustum Geometry given line given point greater Hence hypotenuse included angle inscribed intersect isosceles less let fall locus logarithms lune measured middle point opposite sides parallel parallelogram parallelopiped passing pendicular perpen perpendicular plane triangle prism Prob Prob.-To project the triangle PROP PROPOSITION pyramid quadrant quadrilateral radii radius rectangle regular polygon revolve right angled triangle secant secant line similar similar triangles sine solid solution sphere spherical angle spherical triangle square straight line student SUG's surface symmetrical tangent Theorem.-The triangle ABC triedral trigonometrical functions vertex vertices whence
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Seite 232 - 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.
Seite 41 - The homologous sides of similar triangles are to each other as the square roots of their areas. This theorem is involved in the theorem that the areas of similar triangles are to each other as the squares of their homologous sides.
Seite 203 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Seite 131 - Theorem. — The area of a trapezoid is equal to the product of its altitude...
Seite 217 - If two semicircumferences of great circles intersect on the surface of a hemisphere, the sum of the two opposite triangles thus formed is equivalent to a lune whose angle is that included by the semicircumferences. DEM. — Let the semicircumferences CEB and DEA intersect at E on the surface of the...
Seite 34 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Seite 128 - Theorem — Two triangles are equal when the three sides of the one are respectively equal to the three sides of the other.
Seite 276 - Find the locus of a point the sum of whose distances from two fixed intersecting lines is constant, ie, is equal to a given line.
Seite 96 - The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.
Seite 206 - 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 in all their parts." Axiom 1. "Things which are equal to the same thing, are equal to each other.