Elements of Geometry: And the First Principles of Modern GeometrySheldon & Company, 1878 - 209 páginas |
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... INSCRIBED AND CIRCUMSCRIBED POLYGONS 48 50 PROBLEMS . 52 . BOOK III . RATIO AND PROPORTION AREAS · PROPORTIONAL LINES SIMILAR POLYGONS TRANSVERSALS LINES ON THE CIRCLE PROBLEMS CERR 63 67 79 83 90 93 97 BOOK IV . REGULAR POLYGONS , AND ...
... INSCRIBED AND CIRCUMSCRIBED POLYGONS 48 50 PROBLEMS . 52 . BOOK III . RATIO AND PROPORTION AREAS · PROPORTIONAL LINES SIMILAR POLYGONS TRANSVERSALS LINES ON THE CIRCLE PROBLEMS CERR 63 67 79 83 90 93 97 BOOK IV . REGULAR POLYGONS , AND ...
Página 42
... inscribed when its sides are chords , and its vertex is in the circumference ; as , ZABC . 2. A poly- D gon is inscribed C when all its angles are in- scribed . The circle is said to be cir- cumscribed about the polygon . 3. A secant is ...
... inscribed when its sides are chords , and its vertex is in the circumference ; as , ZABC . 2. A poly- D gon is inscribed C when all its angles are in- scribed . The circle is said to be cir- cumscribed about the polygon . 3. A secant is ...
Página 43
... inscribed in the polygon . XI . Theorem . The angle at the centre of a circle is double the inscribed angle upon the same arc . HYPOTH . BCD is an angle at the centre , and BAD an inscribed angle upon the same arc , BD . There may be ...
... inscribed in the polygon . XI . Theorem . The angle at the centre of a circle is double the inscribed angle upon the same arc . HYPOTH . BCD is an angle at the centre , and BAD an inscribed angle upon the same arc , BD . There may be ...
Página 44
... inscribed in the same segment , are equal ; for they have the same arc , ACB , F included between A their sides ... inscribed in a semicircle is a right angle ; an angle inscribed in a segment less than a semicircle is an obtuse angle ...
... inscribed in the same segment , are equal ; for they have the same arc , ACB , F included between A their sides ... inscribed in a semicircle is a right angle ; an angle inscribed in a segment less than a semicircle is an obtuse angle ...
Página 46
... inscribed angle in the 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 ...
... inscribed angle in the 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 ...
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.