Elements of Geometry |
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Page 15
... PROPOSITION I. THEOREM . 15 49. When one straight line crosses another ... Q. E. D. 50. COROLLARY . If two straight lines cut one another , the four ... PROPOSITION II . THEOREM . 51. When the sum of PERPENDICULAR AND OBLIQUE LINES.
... PROPOSITION I. THEOREM . 15 49. When one straight line crosses another ... Q. E. D. 50. COROLLARY . If two straight lines cut one another , the four ... PROPOSITION II . THEOREM . 51. When the sum of PERPENDICULAR AND OBLIQUE LINES.
Page 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 I. 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 I. GEOMETRY . -
Page 18
... 2 ) . 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 BOOK I. GEOMETRY . ―
... 2 ) . 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 BOOK I. GEOMETRY . ―
Page 20
... Q. E. D. 56. COROLLARY . Only two equal straight lines can be drawn from a point to a straight line ; and of two unequal lines , the greater cuts off the greater distance from the foot of the perpen- dicular . + I PROPOSITION VII ...
... Q. E. D. 56. COROLLARY . Only two equal straight lines can be drawn from a point to a straight line ; and of two unequal lines , the greater cuts off the greater distance from the foot of the perpen- dicular . + I PROPOSITION VII ...
Page 21
... of these oblique lines must be more remote from the 1 , and .. greater than the other ; which is contrary to the hypothesis . $ 55 .. FE FK . = Q. E. D. PROPOSITION VIII . THEOREM . 58. If at the middle PERPENDICULAR AND OBLIQUE LINES . 21.
... of these oblique lines must be more remote from the 1 , and .. greater than the other ; which is contrary to the hypothesis . $ 55 .. FE FK . = Q. E. D. PROPOSITION VIII . THEOREM . 58. If at the middle PERPENDICULAR AND OBLIQUE LINES . 21.
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Common terms and phrases
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