An Elementary Geometry and TrigonometryThompson, Bigelow, and Brown, 1872 - 238 σελίδες |
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Σελίδα 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 . In 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 . In 52.
Σελίδα 53
... inscribed in the polygon . 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. Draw the radius CA , and ...
... inscribed in the polygon . 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. Draw the radius CA , and ...
Σελίδα 54
... inscribed in the same segment are equal ; for each is measured by half the arc A E C 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 A E C 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 ) ...
Σελίδα 57
... inscribed in a circle . A B Draw the radii CA and C B ; CAB is an equilateral , and therefore an equiangu- lar ... inscribed in the circle ( 12 and 24 ) . 34. Corollary . The chord of half the arc A B would be the side of a regular ...
... inscribed in a circle . A B Draw the radii CA and C B ; CAB is an equilateral , and therefore an equiangu- lar ... inscribed in the circle ( 12 and 24 ) . 34. Corollary . The chord of half the arc A B would be the side of a regular ...
Σελίδα 59
... inscribed in the circle is one half ( 33 ) , and the perimeter of the hexagon is 6 X 13 . 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 13 . 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 ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
A B C ABCDEF acute angle adjacent altitude angle BCD apothem arc or angle bisect centre chord circumference comp cone construct the triangle convex surface Corollary cosec decr diagonals diameter distance divided draw equiangular equilateral equivalent feet Find the Log frustum Geom given angle given line given point given side hypothenuse included angle incr inscribed internal angles isosceles triangle lines A B Logarithm M.
M. Sine multiplied number of sides opposite side parallelogram parallelopiped perimeter perpendicular PLANE GEOMETRY plane triangle PLANE TRIGONOMETRY prism PROBLEM quadrilateral radii radius ratio rectangle regular polygon right angle right pyramid right triangle right-angled triangle Scholium secant segment side opposite similar triangles slant height sphere square straight line Tang tangent THEOREM THEOREM VII trapezoid triangle ABC TRIGONOMETRY vertex
Δημοφιλή αποσπάσματα
Σελίδα 30 - Hence -,- = -76" dn that is a" : b" = c" : dn THEOREM IX. 23 1 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...
Σελίδα 49 - A circle is a plane figure bounded by a curved line, called the circumference, every point of which is equally distant from a point within called the center.
Σελίδα 96 - Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle.
Σελίδα 12 - In an isosceles triangle the angles opposite the equal sides are equal.
Σελίδα 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.
Σελίδα 23 - If two triangles have two sides of one respectively equal to two sides of the other, and the angles contained by those sides supplementary, the triangles are equal in area.
Σελίδα 20 - ... polygon, is equal to twice as many right angles as the polygon has sides minus two.
Σελίδα 71 - The convex surface of a right prism is equal to the perimeter of its base multiplied by its altitude.
Σελίδα 40 - At a point 200 feet from, and on a level with the base of a tower, the angle of elevation of the top of the tower is observed to be 60° : what is the height of the tower?
Σελίδα 23 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.