An Elementary Geometry |
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Page 49
... Tangent ( in geometry ) is a line which touches , but does not , though produced , cut the circumference ; as GD . 1 A tangent is often considered as terminating at one 3 D BOOK III THE CIRCLE.
... Tangent ( in geometry ) is a line which touches , but does not , though produced , cut the circumference ; as GD . 1 A tangent is often considered as terminating at one 3 D BOOK III THE CIRCLE.
Page 50
... tangent . THEOREM I. 11. In the same circle , or equal circles , equal angles at the cen- tre are subtended by equal arcs ; and , conversely , equal arcs sub- tend equal angles at the centre . Let B and E be equal angles at the centres ...
... tangent . THEOREM I. 11. In the same circle , or equal circles , equal angles at the cen- tre are subtended by equal arcs ; and , conversely , equal arcs sub- tend equal angles at the centre . Let B and E be equal angles at the centres ...
Page 53
... tangents . Thus ABCDEF is circumscribed about the inner circle . In this case the circle is said to be inscribed in the polygon . A B C F E D THEOREM V. 21. An inscribed angle is measured by half the arc included by its sides . 1st ...
... tangents . Thus ABCDEF is circumscribed about the inner circle . In this case the circle is said to be inscribed in the polygon . A B C F E D THEOREM V. 21. An inscribed angle is measured by half the arc included by its sides . 1st ...
Page 61
... tangent to the circumference . Draw CB . ( Ι . 51. ) 48. The lines joining the extremities of two diameters are parallel . B A D C 49. If the extremities of two chords are joined , the triangles thus 50. If two circumferences cut each ...
... tangent to the circumference . Draw CB . ( Ι . 51. ) 48. The lines joining the extremities of two diameters are parallel . B A D C 49. If the extremities of two chords are joined , the triangles thus 50. If two circumferences cut each ...
Page 62
... tangent at the point of contact . ( 47. ) 52. The distance between the centres of two circles whose cir- cumferences cut one another , is less than the sum , but greater than the difference , of their radii . 53. Every angle inscribed ...
... tangent at the point of contact . ( 47. ) 52. The distance between the centres of two circles whose cir- cumferences cut one another , is less than the sum , but greater than the difference , of their radii . 53. Every angle inscribed ...
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Common terms and phrases
ABC and DEF ABCD adjacent altitude angle ABC apothem base and altitude bisect centre chord circ circumference coincide cone construct the triangle convex surface Corollary cube cylinder diameter distance divided dodecagon EATON'S equal altitudes equally distant equiangular equilateral feet frustum given angle given circle given line given point given side given square given triangle half the arc hexagon homologous sides hypothenuse included angle infinite number inscribed internal angles intersection isosceles triangle Let ABCDEF line joining mean proportional measured by half number of sides opposite sides parallel planes parallelogram parallelopiped perimeter perpendicular plane parallel propositions quadrilateral radii radius ratio rectangle regular polygon respectively equal rhombus right angles right prism right pyramid right triangle Scholium secant segment similar triangles slant height sphere tangent THEOREM VIII trapezoid triangle ABC vertex
Popular passages
Page 25 - Four quantities are in proportion when the ratio of the first to the second is equal to the ratio of the third to the fourth.
Page 30 - If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d = e :f Now ab = ab (1) and by Theorem I.
Page 27 - If the product of two quantities is equal to the product of two others, the...
Page 43 - The area of a regular polygon is equal to half the product of its perimeter and apothem.
Page 11 - If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to each, the two triangles are equal in all respects.
Page 23 - If two triangles have two sides of one respectively equal to two sides of the other, but the third sides unequal...
Page 20 - ... polygon, is equal to twice as many right angles as the polygon has sides minus two.
Page 49 - 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.
Page 70 - A right cylinder is a solid described by the revolution of a rectangle about one of its sides.
Page 64 - DEFINITIONS. 1 . A straight line is perpendicular to a plane, when it is perpendicular to every straight line of the plane which it meets.