Elements of Geometry: And the First Principles of Modern GeometrySheldon & Company, 1878 - 209 σελίδες |
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Σελίδα
... given in a distinct form . Exercises and numerical examples are inserted in numbers sufficiently great to fix the truth of the proposition in the mind of the student , without materially increasing the amount of work to be done . In ...
... given in a distinct form . Exercises and numerical examples are inserted in numbers sufficiently great to fix the truth of the proposition in the mind of the student , without materially increasing the amount of work to be done . In ...
Σελίδα 9
... given line , CD ; for any other line , AE , A must have a different direction from C AB , and , consequently , from CD also . E B D COR . 2. If a straight line cuts one of two parallel lines , it will cut the other also , if ...
... given line , CD ; for any other line , AE , A must have a different direction from C AB , and , consequently , from CD also . E B D COR . 2. If a straight line cuts one of two parallel lines , it will cut the other also , if ...
Σελίδα 13
... given F angle ; DCL AC , and EBL AB . TO BE PROVED . DC and EB will meet , if produced . PROOF . Through the ver- tex A , draw AF || CD , and AG || BE . Then FAC = R , since AF || CD , and CDAC : B G E D F G A C B D E hence FAB < or > R ...
... given F angle ; DCL AC , and EBL AB . TO BE PROVED . DC and EB will meet , if produced . PROOF . Through the ver- tex A , draw AF || CD , and AG || BE . Then FAC = R , since AF || CD , and CDAC : B G E D F G A C B D E hence FAB < or > R ...
Σελίδα 16
... given , the third may be found by subtracting their sum from two right angles . COR . 2. If two angles of one triangle are respectively equal to two angles of another triangle , the third angles are also equal , and the triangles are ...
... given , the third may be found by subtracting their sum from two right angles . COR . 2. If two angles of one triangle are respectively equal to two angles of another triangle , the third angles are also equal , and the triangles are ...
Σελίδα 34
... 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 points would be at a greater BOOK II THE CIRCLE.
... 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 points would be at a greater BOOK II THE CIRCLE.
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 19 - IF two triangles have two sides of the one equal to two sides of the...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.