Elements of GeometryGinn and Heath, 1881 - 250 σελίδες |
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Σελίδα 74
... inscribed in a circle when its sides are chords of the circle , as A ABC , Fig . 1 . A circle is inscribed in a polygon when the circumference touches the sides of the polygon but does not intersect them , as in Fig . 4 . 174. DEF . A ...
... inscribed in a circle when its sides are chords of the circle , as A ABC , Fig . 1 . A circle is inscribed in a polygon when the circumference touches the sides of the polygon but does not intersect them , as in Fig . 4 . 174. DEF . A ...
Σελίδα 93
... equal parts called min- utes , denoted by the symbol ( ) .- A minute is subdivided into sixty equal parts called sec- onds , denoted by the symbol ( " ) . PROPOSITION XIV . THEOREM . 203. An inscribed angle is MEASUREMENT OF ANGLES . 93.
... equal parts called min- utes , denoted by the symbol ( ) .- A minute is subdivided into sixty equal parts called sec- onds , denoted by the symbol ( " ) . PROPOSITION XIV . THEOREM . 203. An inscribed angle is MEASUREMENT OF ANGLES . 93.
Σελίδα 94
... inscribed angle B. We are to prove ZB is measured by arc P A. Draw CA. ― CA CB , ( being radii of the same O ) . .L B = ZA , ( being opposite equal sides ) . L PC A = ZB + ZA . § 112 $ 105 ( the exterior of a △ is equal to the sum of ...
... inscribed angle B. We are to prove ZB is measured by arc P A. Draw CA. ― CA CB , ( being radii of the same O ) . .L B = ZA , ( being opposite equal sides ) . L PC A = ZB + ZA . § 112 $ 105 ( the exterior of a △ is equal to the sum of ...
Σελίδα 95
... inscribed in a semicircle is a right angle , for it is measured by one - half a semi - circumfer- ence , or by 90 ° . 205. COR . 2. An angle inscribed in a segment greater than a semicircle is an acute angle ; for it is measured by an ...
... inscribed in a semicircle is a right angle , for it is measured by one - half a semi - circumfer- ence , or by 90 ° . 205. COR . 2. An angle inscribed in a segment greater than a semicircle is an acute angle ; for it is measured by an ...
Σελίδα 96
... inscribed is measured by the intercepted arc ) ; and A is measured by arc BD , $ 203 ..ZCOA is measured by arc A C + 1 arc B D. Q. E. D. Ex . Show that the least chord that can be drawn through a given point in a circle is perpendicular ...
... inscribed is measured by the intercepted arc ) ; and A is measured by arc BD , $ 203 ..ZCOA is measured by arc A C + 1 arc B D. Q. E. D. Ex . Show that the least chord that can be drawn through a given point in a circle is perpendicular ...
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A B C AABC AACB ABCD acute adjacent angles alt.-int altitude apothem arc A B BC² bisect centre chord A B circumference circumscribed coincide COROLLARY describe an arc diagonals diameter divided Draw equal arcs equal distances equal respectively equiangular polygon equilateral equilateral polygon equivalent exterior angles figure given line given point given polygon greater homologous sides hypotenuse Iden isosceles triangle Let A B limit line A B measured by arc middle point number of sides parallelogram perimeter perpendicular plane PROBLEM prove Q. E. D. PROPOSITION quadrilateral radii radius equal ratio rect rectangles regular inscribed regular polygon required to construct rhombus right angles right triangle SCHOLIUM segment sides of equal sides of similar similar polygons subtend tangent THEOREM third side triangle ABC variable vertex vertices