An Elementary Geometry |
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Page 49
... chord ; as the space included by the arc A FB and the chord A B. 8. A Sector is the part of a circle included by two radii and the intercepted arc ; as the space B C D. 9. A Tangent ( in geometry ) is a line which touches , but does not ...
... chord ; as the space included by the arc A FB and the chord A B. 8. A Sector is the part of a circle included by two radii and the intercepted arc ; as the space B C D. 9. A Tangent ( in geometry ) is a line which touches , but does not ...
Page 51
... chords subtend equal arcs ; and , conversely , equal arcs are subtended by equal chords . Let A B C and DEF be two equal circles ; if the arcs AB and DE are equal , the chords AB A B Ꭰ . E and DE are C F equal ; and conversely , if the ...
... chords subtend equal arcs ; and , conversely , equal arcs are subtended by equal chords . Let A B C and DEF be two equal circles ; if the arcs AB and DE are equal , the chords AB A B Ꭰ . E and DE are C F equal ; and conversely , if the ...
Page 52
... chord bisects the chord and the arc subtended by the chord . Let CE be a radius perpendicular to the chord AB ; it bisects the chord A B , and also the arc A E B. Draw the radii CA and CB and the chords AE and EB . As equal oblique A ...
... chord bisects the chord and the arc subtended by the chord . Let CE be a radius perpendicular to the chord AB ; it bisects the chord A B , and also the arc A E B. Draw the radii CA and CB and the chords AE and EB . As equal oblique A ...
Page 54
... chord coincides with its arc . Let A B be an infinitely small chord ; it coincides with the arc AD B. Draw the diameter CD perpendicu- lar to the chord AB 54 PLANE GEOMETRY .
... chord coincides with its arc . Let A B be an infinitely small chord ; it coincides with the arc AD B. Draw the diameter CD perpendicu- lar to the chord AB 54 PLANE GEOMETRY .
Page 55
... chord would coincide with its arc ( 25 ) , the polygon would be the circle itself . 27. Scholium . It might be supposed that although the dif- ference between each chord and its arc is infinitesimal , yet as there is an infinite number ...
... chord would coincide with its arc ( 25 ) , the polygon would be the circle itself . 27. Scholium . It might be supposed that although the dif- ference between each chord and its arc is infinitesimal , yet as there is an infinite number ...
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Common terms and phrases
A B C ABCD adjacent altitude angle ABC apothem arcs A B base and altitude bisect centre chord circ circumference cone construct the triangle convex surface Corollary cube cylinder diagonals 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 half the arc hexagon homologous sides hypothenuse included angle infinite number inscribed internal angles intersection isosceles triangle Let ABCDEF line joining lines A B measured by half number of sides opposite sides parallel planes parallelogram parallelopiped perimeter perpendicular plane parallel 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 VII 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.