Practical geometry for the architect, engineer, surveyor and mechanic - Edward Wyndham Tarn - Google Books

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CONTENTS.

THE STRAIGHT LINE.

PAGE

1. Definitions of a point, a line, a surface, a plane, a circumference,

an angle, a perpendicular

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-

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

6. From the longer of two unequal right-lines to cut off a part

equal to the shorter

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

11. From two given points to draw two right-lines meeting a given

right-line in the same point and making equal angles there-

12. Definition of parallel lines.

13. To draw a right-line through a given point and parallel to a

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

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-

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. 18

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.

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

36. To construct a square which shall be equal in area to a given

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-

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

length of a side being given.

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

length of a side being given.

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

47. Definitions of a curve, circle, tangent, chord, arc, segment,

sector, semicircle, quadrant, inscribed circles, concentric

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

•

50. To describe a circle through three given points which are not in

the same right-line

51. From a given point outside a given circle to draw tangents

52. To find any number of points upon an arc of a circle, the middle

point and two extremities of the arc being given

53. To draw an arc of a circle by continuous motion, when the

centre is not available.

54. On a given right-line to describe a segment of a circle that shall

contain a given angle

55. From the extremities of a given right-line to draw two other

lines in any directions meeting at right-angles to each other.

35

56. To lay out an arc of a circle as a railway curve of given radius,

by finding points on the circumference.

PAGE

57. To find arithmetically the radius of an arc of a circle of which

the chord and height are given

59. To describe a circle touching a given circle, and also a given

right-line outside of it in a given point

60. To describe a circle of given radius which shall touch two given

61. To describe a circle through two given points and touching a

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

58. To describe a circle touching a given right-line and passing

through two given points.

64. To describe a circle touching a given circle, and also two given

right-lines which are not parallel .

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

[blocks in formation]

71. In any regular polygon to inscribe a circle

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

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