Докладніше про цю книгу
Моя бібліотека
Книги в Google Play
CONTENTS.
CHAPTER I.
THE STRAIGHT LINE.
LINES.
PAGE
1. Definitions of a point, a line, a surface, a plane, a circumference,
an angle, a perpendicular
1
2. To divide a right-line of given length into two or more equal
3. From a given point in a given right-line to erect a perpendi-
cular
3
4. To draw a perpendicular to a given right-line from a given
point outside of it.
5. From a given point to draw a right-line equal in length to a
given line
6. From the longer of two unequal right-lines to cut off a part
equal to the shorter
4
5
ANGLES.
7. To construct an angle equal to a given angle
8. To divide a given rectilinear angle into two or more equal angles. 5
9. To divide a right-angle into three or more equal angles
10. To divide a right-angle into five or fifteen equal parts
6
7
11. From two given points to draw two right-lines meeting a given
right-line in the same point and making equal angles there-
with
8.
PARALLELS.
12. Definition of parallel lines.
8
13. To draw a right-line through a given point and parallel to a
PROPORTION.
14. Definitions of multiple, equi-multiple, ratio, proportionals, ex-
treme and mean ratio, sum, difference
15. To find a third-proportional to two given right-lines
16. To find a fourth-proportional to three given right-lines
17. To find a mean-proportional between two given right-lines
18. To divide a right-line of given length into any number of parts
19. To divide a given finite right-line in extreme and mean ratio
20. To produce a given finite right-line so that the whole line thus
produced shall be divided in extreme and mean ratio by the
end of the given line next the produced part
21. Harmonical division of a line.
22. To divide a given right-line harmonically
RECTILINEAR FIGURES.
23. Definitions of figure, perimeter, triangle, quadrilateral, trape- zium, parallelogram, rhomboid, rhombus, rectangle, square, regular polygon, similar figures
24. To construct an isosceles triangle, of which two unequal sides
are given
25. To construct an isosceles triangle in which each angle at the
base is double that at the vertex
26. To construct an equilateral triangle upon a given finite right-
line.
10
11
27. To construct a right-angled triangle of which two sides are given.
28. To construct a triangle whose three sides are of given lengths
29. To construct a triangle of which two sides and the included
angle are given.
30. To construct a triangle of which two angles and a side are given
31. To construct a triangle of which two sides and an angle not in-
cluded are given.
32. To construct a square upon a given right-line
33. In a given triangle to inscribe a square
17
34. To construct a parallelogram of given sides and given angle
35. To construct a square equal in area to the sum of the areas of
two given squares
21
36. To construct a square which shall be equal in area to a given
parallelogram
. 21
37. Upon a given right-line to construct a rectangle equal in area to
a given rectangle.
38. To construct a rectangle equal in area to a given irregular recti-
linear figure
22
39. To construct a rectilinear figure of a given irregular form
40. To divide a given finite right-line into two parts, so that the
rectangle under the whole line and one of the parts shall be
equal in area to the square upon the other part
41. To produce a given right-line so that the rectangle under the
whole produced line and the part produced shall be equal in
area to the square upon the given line .
42. To construct a regular pentagon, or figure of five sides, the
length of a side being given.
43. To construct a regular decagon, or figure of ten sides, the
44. To construct a regular hexagon, or figure of six sides, the length
of a side being given
45. To construct a regular octagon, or figure of eight sides, the
23
24
46. To construct a dodecagon, or figure of twelve sides, the length
of a side being given. Also a quindecagon, and polygons of
sixteen and of twenty sides.
26
CHAPTER II.
THE CIRCLE.
47. Definitions of a curve, circle, tangent, chord, arc, segment,
sector, semicircle, quadrant, inscribed circles, concentric
circles
48. To draw a tangent at a given point of a given circle
49. To describe a circle of given radius touching a given circle in a
given point
50. To describe a circle through three given points which are not in
the same right-line
31
51. From a given point outside a given circle to draw tangents
thereto
52. To find any number of points upon an arc of a circle, the middle
point and two extremities of the arc being given
33
53. To draw an arc of a circle by continuous motion, when the
centre is not available.
34
54. On a given right-line to describe a segment of a circle that shall
contain a given angle.
35
55. From the extremities of a given right-line to draw two other
lines in any directions meeting at right-angles to each other
56. To lay out an arc of a circle as a railway curve of given radius,
by finding points on the circumference.
57. To find arithmetically the radius of an arc of a circle of which
the chord and height are given
36
.
58. To describe a circle touching a given right-line and passing
through two given points
37
59. To describe a circle touching a given circle, and also a given
right-line outside of it in a given point
38
60. To describe a circle of given radius which shall touch two given
39
61. To describe a circle through two given points and touching a
given circle
62. To draw geometrical tracery in a Gothic arch
63. To describe a circle which shall touch a given circle and a given
right-line, and shall also have its centre on another given
line
64. To describe a circle touching a given circle, and also two given
right-lines which are not parallel .
41
43
45
46
INSCRIBED AND CIRCUMSCRIBED CIRCLES.
65. To inscribe three circles in an equilateral Gothic arch
66. To inscribe three circles in an equilateral triangle
67. To inscribe three circles in a given isosceles triangle
68. In a given triangle to inscribe a circle
69. In an equilateral triangle to inscribe a circle
49
70. In a given square to inscribe a circle
50
71. In any regular polygon to inscribe a circle
51
72. In a given square to inscribe four equal circles.
73. In any given regular polygon to inscribe as many equal circles
as the figure has sides.
74. In a given circle to inscribe three equal circles
75. To inscribe six equal circles in a given circle
76. To inscribe twelve equal circles in a given circle
77. To inscribe four equal circles in a given circle .
78. To inscribe eight equal circles in a given circle.
79. In a given circle to inscribe five equal circles
80. In a given circle to inscribe ten equal circles
81. In a given circle to inscribe (approximately) seven equal circles.
82. To circumscribe a circle about a given triangle.
83. To circumscribe a circle about any given regular polygon