Elements of Geometry: And the First Principles of Modern GeometrySheldon & Company, 1878 - 209 páginas |
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... locus , " which is frequently used to shorten and generalize a demonstration . An angle is supposed to be generated by the revolution of a side about the vertex ; and is defined as the differ- ence of direction of two lines drawn from ...
... locus , " which is frequently used to shorten and generalize a demonstration . An angle is supposed to be generated by the revolution of a side about the vertex ; and is defined as the differ- ence of direction of two lines drawn from ...
Página 24
... locus , of those points . DEF . A locus is a line or surface that 24 [ BOOK I. ELEMENTS OF GEOMETRY .
... locus , of those points . DEF . A locus is a line or surface that 24 [ BOOK I. ELEMENTS OF GEOMETRY .
Página 25
... locus of all the points within the angle that are equally distant from the sides . HYPOTH 1. BD bisects the angle ABC . From any point , E , in the line BD , the lines EF and EG are drawn per- pendicular to the sides , and measure its ...
... locus of all the points within the angle that are equally distant from the sides . HYPOTH 1. BD bisects the angle ABC . From any point , E , in the line BD , the lines EF and EG are drawn per- pendicular to the sides , and measure its ...
Página 34
... locus of all the points of a plane that are equally distant from a given point . COR . 3. Circles with equal radii are congruent ; for , if we apply the centres to each other , the circumferences will coin- 34 cide : otherwise some ...
... locus of all the points of a plane that are equally distant from a given point . COR . 3. Circles with equal radii are congruent ; for , if we apply the centres to each other , the circumferences will coin- 34 cide : otherwise some ...
Página 36
... locus of all the points equally distant from A and B ; EF is the locus of all the points equally distant from B and C : consequently their intersection , F , is equally distant from A , B , and C , and is the only point . Hence the ...
... locus of all the points equally distant from A and B ; EF is the locus of all the points equally distant from B and C : consequently their intersection , F , is equally distant from A , B , and C , and is the only point . Hence the ...
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.