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viii

CONTENTS

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I. Definitions of Geometric Magnitudes.

66. Right angle defined .

13

34. Geometry defined

8 67. A perpendicular defined

13

35. A solid defined

8 68. Complement defined

13

36. A surface defined

8 69. Acute angle defined.

13

37. A line defined.

8 70. Obtuse angle defined

13

38. A point defined

8

71. Perigon defined

13

39. A magnitude defined

8 72. Sum of angles about a point is a

40-43. Point, line, surface, solid, de-

perigon

14

fined, using motion.

8 73. Reflex angle defined

14

44. Why space is called tri-dimensional, 9 74. Oblique angles and lines defined

14

45. Straight line defined

9 75. Vertical angles defined.

14

46. A curve defined

9 76. Bisector defined

14

47. Line henceforth means straight 77. A trace defined

14

line
9 78. A triangle defined

15
48. A sect defined.
9 79. Vertices defined

15

49. A plane defined

9

80. Sides defined

15

50. Plane defined, using motion
9 81. Interior angle defined

15

51. A figure defined .

9 82. Exterior angle defined .

15

52. A plane figure defined

9 83. Congruent defined

15

53. Circle and center defined

84. Equivalent defined

15

54. Radius defined
55. Diameter defined.

II. Properties of Distinct Things.
56. Arc defined .

85-93. The so-called axioms of arith-

57. Parallel lines defined

metic,

58. Angle, vertex, arms, defined .
59. Explement defined

III. Some Geometrical Assumptions about

60. Equal angles defined

Euclid's Space.

61. Adjacent angles and their sum de-
fined

94-99. The so-called geometric axioms, 16

62. Straight angle defined .

IV. The Assumed Constructions.

63. When two adjacent angles equal a

straight angle .

12 100-103. The so-called postulates.

17

64. Supplement defined.

65. Supplemental adjacent angles 12 | Table of symbols used

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PRIMARY RELATIONS OF LINES, ANGLES, AND TRIANGLES.

ARTICLE

PAGE

20, 21

22

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.

II. Angles at the Center.

VI. Problems.

360. Angles subtended by arcs 128

361, 362, Sector .

To bisect a given arc. . . 148

363. Angle subtended by a sect.

Circumscribed polygon and in-

364. Inscribed angle.

128

scribed circle

148

365.

Corresponding arcs, angles, 414.

Escribed circle defined

148

sectors, chords .

129 | 415-417. Problems,

149, 150

128 412.

128 413.

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