An Elementary Geometry |
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Page 52
... Inscribed Angle is one whose vertex is in the circum- ference and whose sides are chords ; as DA B. 19. An Inscribed Polygon is one whose sides are chords . Thus ABCDEF is inscribed in the outer circle . the 52 PLANE GEOMETRY .
... Inscribed Angle is one whose vertex is in the circum- ference and whose sides are chords ; as DA B. 19. An Inscribed Polygon is one whose sides are chords . Thus ABCDEF is inscribed in the outer circle . the 52 PLANE GEOMETRY .
Page 53
... inscribed in the polygon . B In this case C O E F D THEOREM V. 21. An inscribed angle is measured by half the arc included by its sides . 1st . When one of the sides BD is a diameter ; then the angle B is measured by half the arc A D ...
... inscribed in the polygon . B In this case C O E F D THEOREM V. 21. An inscribed angle is measured by half the arc included by its sides . 1st . When one of the sides BD is a diameter ; then the angle B is measured by half the arc A D ...
Page 54
... inscribed in the same segment are equal ; for each is measured by half the arc AEC . 23. Cor . 2. Every angle inscribed in a semicircle is a right angle ; for it is measured by half a semi - circumference , or by a quadrant ( 15 ) ...
... inscribed in the same segment are equal ; for each is measured by half the arc AEC . 23. Cor . 2. Every angle inscribed in a semicircle is a right angle ; for it is measured by half a semi - circumference , or by a quadrant ( 15 ) ...
Page 59
... inscribed in the circle is one half ( 33 ) , and the perimeter of the hexagon is 6 X = 3 . As the diameter is unity , and the side of the inscribed hexa- gon one half , we can find the side of the regular inscribed dodec- agon from the ...
... inscribed in the circle is one half ( 33 ) , and the perimeter of the hexagon is 6 X = 3 . As the diameter is unity , and the side of the inscribed hexa- gon one half , we can find the side of the regular inscribed dodec- agon from the ...
Page 60
... inscribed in a circle whose area is a square metre ? 10. What is the area of a regular hexagon inscribed in a circle whose area is 567 square feet . 11. If a rope an inch in diameter will support 1,000 pounds , what must be the diameter ...
... inscribed in a circle whose area is a square metre ? 10. What is the area of a regular hexagon inscribed in a circle whose area is 567 square feet . 11. If a rope an inch in diameter will support 1,000 pounds , what must be the diameter ...
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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.