Elements of Geometry: And the First Principles of Modern GeometrySheldon & Company, 1878 - 209 páginas |
Dentro del libro
Resultados 1-5 de 43
Página 34
... radius is a line drawn from the centre to the circumference ; as , OC or OA . 5. A diameter is a line passing through the centre , and terminated each way by the circumference ; as , AB . COR . 1. A radius is one - half a diameter : all ...
... radius is a line drawn from the centre to the circumference ; as , OC or OA . 5. A diameter is a line passing through the centre , and terminated each way by the circumference ; as , AB . COR . 1. A radius is one - half a diameter : all ...
Página 35
... radius . 6. A chord is a line joining any two points of the cir- cumference ; as , DE . 7. A segment is the part of the circle included between an arc and its chord ; as , DFE . 8. A sector is the figure included between an arc and the ...
... radius . 6. A chord is a line joining any two points of the cir- cumference ; as , DE . 7. A segment is the part of the circle included between an arc and its chord ; as , DFE . 8. A sector is the figure included between an arc and the ...
Página 36
... radius FA = FB = FC , will pass through the points A , B , and C , and is the only one that can be drawn through those points . = COR . The centre of a circle lies in the perpendicular drawn from the middle of a chord . Hence the ...
... radius FA = FB = FC , will pass through the points A , B , and C , and is the only one that can be drawn through those points . = COR . The centre of a circle lies in the perpendicular drawn from the middle of a chord . Hence the ...
Página 37
... radius passing through that point . VI . Theorem . In the same or equal circles : 1. To equal angles at the centre belong equal chords and equal arcs . 2. To equal chords belong equal angles at the centre , and equal arcs . 3. To equal ...
... radius passing through that point . VI . Theorem . In the same or equal circles : 1. To equal angles at the centre belong equal chords and equal arcs . 2. To equal chords belong equal angles at the centre , and equal arcs . 3. To equal ...
Página 38
... radius OA lie upon O'A ' , the circumferences will coincide ( 1 Cor . 3 ) , the triangle AOB will fall upon A'O'B ' , the point B upon B ' , and the arc AB will coincide with A'B ' . Hence arc AB A'B ' . = HYPOTH . 2. Chord AB = A'B ...
... radius OA lie upon O'A ' , the circumferences will coincide ( 1 Cor . 3 ) , the triangle AOB will fall upon A'O'B ' , the point B upon B ' , and the arc AB will coincide with A'B ' . Hence arc AB A'B ' . = HYPOTH . 2. Chord AB = A'B ...
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.