Elements of GeometryGinn, Heath & Company, 1884 |
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Σελίδα 15
... Q. E. D. 50. COROLLARY . If two straight lines cut one another , the four angles which they make at the point of intersection are together equal to four right angles . PROPOSITION II . THEOREM . 51. When the sum of PERPENDICULAR AND ...
... Q. E. D. 50. COROLLARY . If two straight lines cut one another , the four angles which they make at the point of intersection are together equal to four right angles . PROPOSITION II . THEOREM . 51. When the sum of PERPENDICULAR AND ...
Σελίδα 16
George Albert Wentworth. PROPOSITION II . THEOREM . 51. When the sum of two adjacent angles is equal to two right angles , their exterior sides ... Q. E. D. PROPOSITION III . THEOREM . 52. A perpendicular measures the 16 BOOK Í . GEOMETRY .
George Albert Wentworth. PROPOSITION II . THEOREM . 51. When the sum of two adjacent angles is equal to two right angles , their exterior sides ... Q. E. D. PROPOSITION III . THEOREM . 52. A perpendicular measures the 16 BOOK Í . GEOMETRY .
Σελίδα 17
George Albert Wentworth. PROPOSITION III . THEOREM . 52. A perpendicular measures the shortest distance from a point to a straight line ... Q. E. D. PROPOSITION IV . THEOREM . 53. Two oblique lines drawn PERPENDICULAR AND OBLIQUE LINES . 17.
George Albert Wentworth. PROPOSITION III . THEOREM . 52. A perpendicular measures the shortest distance from a point to a straight line ... Q. E. D. PROPOSITION IV . THEOREM . 53. Two oblique lines drawn PERPENDICULAR AND OBLIQUE LINES . 17.
Σελίδα 18
... ) . Point A will fall upon point 0 , ( FA = FO , by hyp . ) . ... line CA = line CO , ( their extremities being the same points ) . § 18 Q. E. D. PROPOSITION V. THEOREM . 54. The sum of two lines 18 GEOMETRY . BOOK I.
... ) . Point A will fall upon point 0 , ( FA = FO , by hyp . ) . ... line CA = line CO , ( their extremities being the same points ) . § 18 Q. E. D. PROPOSITION V. THEOREM . 54. The sum of two lines 18 GEOMETRY . BOOK I.
Σελίδα 19
... OA + OE + O B. Substitute for CE + BE its equal C B , and take away O E from each side of the inequality . We have CA + CBOA + O B. § 18 $ 18 Q. E. D. PROPOSITION VI . THEOREM . 55. Of two oblique lines PERPENDICULAR AND OBLIQUE LINES . 19.
... OA + OE + O B. Substitute for CE + BE its equal C B , and take away O E from each side of the inequality . We have CA + CBOA + O B. § 18 $ 18 Q. E. D. PROPOSITION VI . THEOREM . 55. Of two oblique lines PERPENDICULAR AND OBLIQUE LINES . 19.
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A B C AABC ABCD adjacent angles alt.-int altitude apothem arc A B bisect centre 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 isosceles triangle Let A B Let ABC limit line A B Mailing price measured by arc middle point number of sides parallelogram perimeter perpendicular PHILLIPS EXETER ACADEMY 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 vertex vertices Wentworth