Elements of Geometry: And the First Principles of Modern GeometrySheldon & Company, 1878 - 209 páginas |
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Página 35
... 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 radii drawn to its extremities ; as , BOC . II . Theorem . A diameter divides the circle and ...
... 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 radii drawn to its extremities ; as , BOC . II . Theorem . A diameter divides the circle and ...
Página 44
... segment less than a semicircle is an obtuse angle ; and an angle inscribed in a segment greater than a semicircle is an acute angle . COR . 4. In an inscribed quadrilat- eral , ABCD , two opposite angles , A and C , are together equal ...
... segment less than a semicircle is an obtuse angle ; and an angle inscribed in a segment greater than a semicircle is an acute angle . COR . 4. In an inscribed quadrilat- eral , ABCD , two opposite angles , A and C , are together equal ...
Página 46
... segment ACB , the angles EAB and ACB have the same numerical measure as half the arc AB : therefore EAB = ACB ; that is , the angle formed by a tan- gent and chord meeting at the point of contact , is equal to the angle in- scribed in ...
... segment ACB , the angles EAB and ACB have the same numerical measure as half the arc AB : therefore EAB = ACB ; that is , the angle formed by a tan- gent and chord meeting at the point of contact , is equal to the angle in- scribed in ...
Página 61
... is no solution . XXXVI . Problem . Upon a given line to construct a segment that shall contain a given angle . Let AB be the given line , and A the given angle . H SOLUTION . At the point A construct the angle BOOK II . ] 61 THE CIRCLE .
... is no solution . XXXVI . Problem . Upon a given line to construct a segment that shall contain a given angle . Let AB be the given line , and A the given angle . H SOLUTION . At the point A construct the angle BOOK II . ] 61 THE CIRCLE .
Página 62
... segment required . : PROOF . AD is a tangent , since it is perpendicular to the radius CA ( 11 , Cor . 7 ) hence any angle in the seg- ment AFB = BAD = A ; for they have the same numerical measure , arc AGB ( 11 , Cor . 10 ) . If the ...
... segment required . : PROOF . AD is a tangent , since it is perpendicular to the radius CA ( 11 , Cor . 7 ) hence any angle in the seg- ment AFB = BAD = A ; for they have the same numerical measure , arc AGB ( 11 , Cor . 10 ) . If 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.