Elements of Geometry: And the First Principles of Modern GeometrySheldon & Company, 1878 - 209 σελίδες |
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Σελίδα 8
... supplements of equal angles are equal to each other . VI . Theorem . If the sum of two contiguous angles is equal to ... supplement of COB ( 5 , 2 ) . * But the angle which CO makes with the prolongation of BO is also the supplement of ...
... supplements of equal angles are equal to each other . VI . Theorem . If the sum of two contiguous angles is equal to ... supplement of COB ( 5 , 2 ) . * But the angle which CO makes with the prolongation of BO is also the supplement of ...
Σελίδα 13
... supplements of each other . XIII . Theorem . Two perpendiculars erected on the sides of an angle ( not an extended angle ) will meet , if sufficiently produced . HYPOTH . BAC is the given F angle ; DCL AC , and EBL AB . TO BE PROVED ...
... supplements of each other . XIII . Theorem . Two perpendiculars erected on the sides of an angle ( not an extended angle ) will meet , if sufficiently produced . HYPOTH . BAC is the given F angle ; DCL AC , and EBL AB . TO BE PROVED ...
Σελίδα 16
... . TO BE PROVED . CBD = A + C . PROOF . CBD and ZA + C are each supplements of the same angle , ABC ( 4 and 17 ) : hence DCBD A + C ( 5 Cor . ) . A B = COR . 1. The exterior angle of a triangle is 16 [ BOOK I. ELEMENTS OF GEOMETRY .
... . TO BE PROVED . CBD = A + C . PROOF . CBD and ZA + C are each supplements of the same angle , ABC ( 4 and 17 ) : hence DCBD A + C ( 5 Cor . ) . A B = COR . 1. The exterior angle of a triangle is 16 [ BOOK I. ELEMENTS OF GEOMETRY .
Σελίδα 27
... supplements of each other ( 5 , 2 ) . If ZA + C = 2R , then ≤B + D = 2R ; A that is , B and D are supplements of each other . COR . 5. From Cor . 4 it follows , that , if two angles have their sides perpendicular each to each , they ...
... supplements of each other ( 5 , 2 ) . If ZA + C = 2R , then ≤B + D = 2R ; A that is , B and D are supplements of each other . COR . 5. From Cor . 4 it follows , that , if two angles have their sides perpendicular each to each , they ...
Σελίδα 28
... supplement of BA'C , or its equal , DA'E : hence and CA'E , being supplements of BA'C , are equal to A. QUADRILATERALS . XXXVI . DEFINITIONS . 1. Quadrilaterals are of three kinds : parallelograms , trape- zoids , and trapeziums . 2. A ...
... supplement of BA'C , or its equal , DA'E : hence and CA'E , being supplements of BA'C , are equal to A. QUADRILATERALS . XXXVI . DEFINITIONS . 1. Quadrilaterals are of three kinds : parallelograms , trape- zoids , and trapeziums . 2. A ...
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 19 - IF two triangles have two sides of the one equal to two sides of the...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.