Elements of Geometry: And the First Principles of Modern GeometrySheldon & Company, 1878 - 209 páginas |
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... manner , that few will desire to do so . A complete classification has been made ; and each subject is treated by itself as distinctly as possible . It has been my object to make the definitions and demonstrations short and concise ...
... manner , that few will desire to do so . A complete classification has been made ; and each subject is treated by itself as distinctly as possible . It has been my object to make the definitions and demonstrations short and concise ...
Página 11
... manner , we may prove the other pairs of alternate angles equal . TO BE PROVED . 3. 26 + 8 = 2R . . PROOF . 28 ( Case 1 ) , < 6 + 2 = 2R ( 4 ) : hence , by substitution , 6 + 8 = 2R . COR . If 6 is a right angle , ≤8 will be a right ...
... manner , we may prove the other pairs of alternate angles equal . TO BE PROVED . 3. 26 + 8 = 2R . . PROOF . 28 ( Case 1 ) , < 6 + 2 = 2R ( 4 ) : hence , by substitution , 6 + 8 = 2R . COR . If 6 is a right angle , ≤8 will be a right ...
Página 20
... manner , it may be proved that B = E , and C = F . XXV . Theorem . The angles opposite the equal sides of an isos- celes triangle are equal . A HYPOTH . ABAC . TO BE PROVED . PROOF . Bisect B = C . BAC by the line AD ; B and hence then ...
... manner , it may be proved that B = E , and C = F . XXV . Theorem . The angles opposite the equal sides of an isos- celes triangle are equal . A HYPOTH . ABAC . TO BE PROVED . PROOF . Bisect B = C . BAC by the line AD ; B and hence then ...
Página 22
... manner , it may be shown that EF is not less than BC : hence BC EF and △ ABC DEF ( 20 or 24 ) . COR . Two right - angled triangles are congruent when any two sides of the one are equal to two similarly 22 [ BOOK I. ELEMENTS OF GEOMETRY .
... manner , it may be shown that EF is not less than BC : hence BC EF and △ ABC DEF ( 20 or 24 ) . COR . Two right - angled triangles are congruent when any two sides of the one are equal to two similarly 22 [ BOOK I. ELEMENTS OF GEOMETRY .
Página 31
... manner it may be proved that AB || DC . XLI . Theorem . The diagonals of a parallelogram bisect each other . HYPOTH . AC and BD are diagonals of A the parallelogram ABCD . TO BE PROVED . AE = EC , and BE = ED . PROOF . In the triangles ...
... manner it may be proved that AB || DC . XLI . Theorem . The diagonals of a parallelogram bisect each other . HYPOTH . AC and BD are diagonals of A the parallelogram ABCD . TO BE PROVED . AE = EC , and BE = ED . PROOF . In the triangles ...
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.