Elements of Geometry: And the First Principles of Modern GeometrySheldon & Company, 1878 - 209 páginas |
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Página 134
... 2nR ( 30 ) hence S < 2nR . S > 2nR - 4R . Also P < 4R ( 29 ) ; hence XXXII . Theorem . If two trihedrals have two face angles of the one equal to two face angles of the other , each 134 [ Book V. ELEMENTS OF GEOMETRY .
... 2nR ( 30 ) hence S < 2nR . S > 2nR - 4R . Also P < 4R ( 29 ) ; hence XXXII . Theorem . If two trihedrals have two face angles of the one equal to two face angles of the other , each 134 [ Book V. ELEMENTS OF GEOMETRY .
Página 135
... trihedrals have two dihedrals of the one equal to two dihedrals of the other , each to each , and the in- cluded face angles equal , the two trihedrals will be congruent , or symmetrical . ( Proof similar to the last . ) XXXIV . Theorem ...
... trihedrals have two dihedrals of the one equal to two dihedrals of the other , each to each , and the in- cluded face angles equal , the two trihedrals will be congruent , or symmetrical . ( Proof similar to the last . ) XXXIV . Theorem ...
Página 136
... trihedrals are equal each to each , being supplements of the equal dihedrals . ( 30 ) ; hence the dihedrals of the polar trihedrals are also equal ( 34 ) ; and the face angles of the given trihedrals are equal , being supplements of ...
... trihedrals are equal each to each , being supplements of the equal dihedrals . ( 30 ) ; hence the dihedrals of the polar trihedrals are also equal ( 34 ) ; and the face angles of the given trihedrals are equal , being supplements of ...
Página 160
... trihedrals ( poly- hedrals ) formed by planes passing through the arcs of polar triangles ( polygons ) will be polar trihedrals ( polyhedrals ) , whose vertices are at the centre of the sphere . For , since A is the pole of the arc B'C ...
... trihedrals ( poly- hedrals ) formed by planes passing through the arcs of polar triangles ( polygons ) will be polar trihedrals ( polyhedrals ) , whose vertices are at the centre of the sphere . For , since A is the pole of the arc B'C ...
Página 161
... trihedral is greater A B XVII . Hence ( 12 , Cor . 1 ; 16 , Cor . ) , The sum of any two sides of a spherical triangle is ... trihedrals have two face angles of the one 14 * BOOK VII . ] 161 THE THREE ROUND BODIES . Reciprocal Theorems ·
... trihedral is greater A B XVII . Hence ( 12 , Cor . 1 ; 16 , Cor . ) , The sum of any two sides of a spherical triangle is ... trihedrals have two face angles of the one 14 * BOOK VII . ] 161 THE THREE ROUND BODIES . Reciprocal Theorems ·
Términos y frases comunes
AB² ABCD AC² adjacent angles altitude angles are equal anharmonic ratio bisect called centre chord circle circumference circumscribed polygon cone congruent construct cylinder diagonals diameter dihedrals distance divided draw equal altitudes equal bases equally distant equations equiangular EXERCISE exterior angle face angles formed frustum Geometry harmonically hence homologous HYPOTH infinite number inscribed angle intersection lateral edges line joining lines drawn locus middle point number of sides Olney's opposite sides P₁ parallel lines parallelogram parallelopiped pass perpendicular plane angle point of contact polar pole polyhedral polyhedron prism Problem PROOF proportional PROVED pyramid quadrilateral radical axis radii radius rectangle regular polygon right angles SCHOLIUM segments solid angle sphere spherical excess spherical polygon spherical triangle square straight line symmetrical tangent Theorem triangle ABC trihedrals vertex vertices
Pasajes populares
Página 19 - IF two triangles have two sides of the one equal to two sides of the...
Página 34 - A Circle is a plane figure bounded by a curved line every point of which is equally distant from a point within called the center.
Página 14 - A Polygon of three sides is called a triangle ; one of four sides, a quadrilateral; one of five sides, a pentagon; one of six sides, a hexagon; one of seven sides, a heptagon; one of eight sides, an octagon ; one of ten sides, a decagon ; one of twelve sides, a dodecagon, &c.
Página 75 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.
Página 170 - Two prisms are to each other as the products of their bases by their altitudes ; prisms having equivalent bases are to each other as their altitudes; prisms having equal altitudes are to each other as their bases ; prisms having equivalent bases and equal altitudes are equivalent.
Página 69 - Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing those angles proportional, are similar.