Elements of Geometry: And the First Principles of Modern GeometrySheldon & Company, 1878 - 209 σελίδες |
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Σελίδα 2
... figure is a combination of points , lines , surfaces , or solids , formed under certain conditions . A plane figure is a combination of points and lines which are confined to one and the same plane . 15. A rectilinear figure is one ...
... figure is a combination of points , lines , surfaces , or solids , formed under certain conditions . A plane figure is a combination of points and lines which are confined to one and the same plane . 15. A rectilinear figure is one ...
Σελίδα 26
... . The sum of all the angles of a polygon is equal to twice as many right angles as the figure has sides less two . HYPOTH . The polygon , ABCDE , has n sides . • TO BE PRoved . ABC BCD + CDE + . 26 [ Воок І. ELEMENTS OF GEOMETRY .
... . The sum of all the angles of a polygon is equal to twice as many right angles as the figure has sides less two . HYPOTH . The polygon , ABCDE , has n sides . • TO BE PRoved . ABC BCD + CDE + . 26 [ Воок І. ELEMENTS OF GEOMETRY .
Σελίδα 27
... figure has sides less two , or ( n - 2 ) triangles . The sum of the angles of the triangles is the same as that of the polygon ; and the angles of each triangle together 2R . Hence the sum of the angles of the polygon , ABC + BCD + CDE ...
... figure has sides less two , or ( n - 2 ) triangles . The sum of the angles of the triangles is the same as that of the polygon ; and the angles of each triangle together 2R . Hence the sum of the angles of the polygon , ABC + BCD + CDE ...
Σελίδα 30
... figure is a parallelogram . A B HYPOTH . AB = CD , and AD = BC . x D TO BE PROVED . AB || CD and AD || BC . PROOF . Draw the diagonal AC . Then AABC≈ CDA ( 24 ) ; op , hence AB || CD ( 11 , 2 ) ; that is and x = = y , hence AD || BC ...
... figure is a parallelogram . A B HYPOTH . AB = CD , and AD = BC . x D TO BE PROVED . AB || CD and AD || BC . PROOF . Draw the diagonal AC . Then AABC≈ CDA ( 24 ) ; op , hence AB || CD ( 11 , 2 ) ; that is and x = = y , hence AD || BC ...
Σελίδα 35
... figure included between an arc and the radii drawn to its extremities ; as , BOC . II . Theorem . A diameter divides the circle and its circum- ference into two congruent parts . HYPOTH . AB is a diameter of the circumference ACBD . TO ...
... figure included between an arc and the radii drawn to its extremities ; as , BOC . II . Theorem . A diameter divides the circle and its circum- ference into two congruent parts . HYPOTH . AB is a diameter of the circumference ACBD . TO ...
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.