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# Geometrical Drawing and Design [J. Humphrey Spanton]

Submitted by mgmay281 on Sun, 12/31/2017 - 07:07

No known copyright restrictions on the source work from J. Humphrey Spanton. For verification of copyright status, see the following document from the Internet Archive in September 2014:

Internet Archive Documentation

Internet Archive ID for Source Material: geometricaldrawi00span

- Figure 028: To bisect a given straight line AB
- Figure 029: To bisect a given arc AB
- Figure 030: To draw a line parallel to a given line AB through a given point C
- Figure 031: To draw a line parallel to a given line AB at a given distance from it
- Figure 032: From a point C in a given line AB, to draw a line perpendicular to AB.
- Figure 033: To draw a perpendicular to AB from a point at, or near, the end of the given line.
- Figure 034: To draw a line perpendicular to a given line, from a point which is without the line.
- Figure 035: To draw a perpendicular to AB from a point opposite, or nearly-opposite, to one end of the line.
- Figure 036: To divide a given line AB into any number of equal parts. Take five for example.
- Figure 037: Another Method
- Figure 038: From a given point B, in a given line AB, to construct an angle equal to a given angle C.
- Figure 039: To bisect a given angle ABC.
- Figure 040: To trisect a right angle.
- Figure 041: To trisect any angle ABC.
- Figure 042: To construct an equilateral triangle on a given line AB.
- Figure 043: On a given base AB to construct an isosceles triangle, the angle at vertex to be equal to given angle C.
- Figure 044: On a given base AB, to construct an isosceles triangle, its altitude to be equal to a given line CD.
- Figure 045: To construct a triangle, the three sides A, B, and C being given.
- Figure 046: To construct a triangle with two sides equal to given lines A and B, and the included angle equal to C.
- Figure 047: To construct a triangle with a perpendicular height equal to AB, and the two sides forming the vertex equal to the given lines C and D.
- Figure 057: 30. To draw a line bisecting the angle between two given converging lines AB and CD, when the angular point is inaccessible.
- Figure 058: 31. Through the given point A, to draw a line which would, if produced, meet at the same point as the given lines BC and DE produced.
- Figure 059: 32. To find the centre of a circle.
- Figure 060: 33. To draw a circle through three given points A, B, C.
- Figure 061: 36. At the given equidistant poihtS A, B, C, D; etc.. on a given arc, to draw a numher of radial lines, the centre of the circle being inaccessible.
- Figure 062: 37. To draw the arc of a circle through three given points A, B, C, the centre of the circle being inaccessible.
- Figure 075: *** Fix Content 39. To inscribe any regular polygon in a given circle; for example, a heptagon.
- Figure 076: 38. To inscribe in a circle, a triangle, square, pentagon, hexagon, octagon, decagon, or duodecagon.
- Figure 077: *** Fix content
- Figure 078: 40. To inscribe any regular polygon in a given circle (second method) ; for example, a nonagon.
- Figure 079: 41. On a given line AB, to describe a regular polygon; for example, a heptagon.
- Figure 080: 42. On a given line AB, to describe a regular polygon (second method) ; for example, a pentagon.
- Figure 081: 43. On a given straight line AB, to construct a regular pentagon. (True construction.)
- Figure 082: 44. On a given straight line AB, to construct a regular hexagon.
- Figure 083: 45. In a given circle to inscribe a regular heptagon (approximately).
- Figure 084: 46. On a given line AB, to construct a regular heptagon (approximately).
- Figure 085: 47. On a given line AB, to construct a regular octagon.
- Figure 086: 48. In a given circle to inscribe a nonagon.
- Figure 087: 49. In a given circle to inscribe a regular undecagon.
- Figure 089: 50, To inscribe an equilateral triangle in a given circle ABC.
- Figure 090: 52. To inscribe a circle in a given triangle ABC.
- Figure 091: 53. To describe a circle about a given triangle ABC. Bisect the two sides AB and AC perpendicularly by lines meeting in D. With D as centre, and DA as radius, describe the required circle.
- Figure 092: 54. To describe an equilateral triangle about a given square ABDC.
- Figure 093: *** Need Figure 55. In a given triangle ABC, to inscribe an oblong having one of its sides equal to the given line D.
- Figure 094: 56. To inscribe a square in a given circle. - 57. To describe a square about a given circle.
- Figure 095: 58. To inscribe a circle in a given square. - 59. To describe a circle about a given square.
- Figure 096: 60. To inscribe a square in a given rhombus.
- Figure 097: 61. To inscribe a circle in a given rhombus.
- Figure 098: 62. To inscribe an equilateral triangle in a given square ABDC.
- Figure 099: 63. To inscribe an isosceles triangle in a given square ABDC, having a base equal to the given line E.
- Figure 100: 64. To inscribe a square in a given trapezium ACBD which has its adjacent pairs of sides equal.
- Figure 101: 65. To inscribe a circle in a given trapezium ACBD which has its adjacent pairs of sides equal.
- Figure 102: To insert a rhombus in a given rhomboid ABDC.
- Figure 103: 67. To inscribe an octagon in a given square.
- Figure 104: 68. To inscribe a square in a given hexagon ABCDEF.
- Figure 105: 69. To inscribe four equal circles in a given square ABDC ; each circle to touch two others, as well as two sides of the given square.
- Figure 106: 70. To inscribe four equal circles in a given square ABDC ; each circle to touch two others, and one side only of the given square.
- Figure 107: 71. To inscribe three equal circles in a given equilateral triangle ABC ; each circle to touch the other two, as well as two sides of the given triangle.
- Figure 108: *** Fix content. 72. In a given equilateral triangle ABC, to inscribe three equal circles touching each other and one side of the triangle only.
- Figure 110: 75. In a given circle to draw four equal circles touching each other.
- Figure 111: 76. In a given circle to inscribe any number of equal circles touching each other. For example, five.
- Figure 112: 77. About a given circle A, to describe six circles equal to it, touching each other as well as the given circle.
- Figure 116: 78. To construct a foiled figure about any regular polygon, having tangential arcs. For example, a hexagon.
- Figure 117: 79. To construct a foiled figure about any regular polygon, having adjacent diameters. For example, a pentagon.
- Figure 118: 80. In a given equilateral triangle ABC, to inscribe a trefoil.
- Figure 119: 81. Within a given circle, to inscribe three equal semicircles having adjacent diameters.
- Figure 120: 82. In a given square ABDC, to inscribe four semicircles having adjacent diameters.
- Figure 121: 83. Within a given circle to inscribe any number of equal semi- circles having adjacent diameters. For example, seven.
- Figure 122: 84. To draw a tangent to a given circle at a given point A.
- Figure 123: 85. To draw a tangent to a given circle from a given point A outside it.
- Figure 124: 86. To draw a tangent to the arc of a circle at a given point A without using the centre.
- Figure 125: 87. To draw a circle with radius equal to line D to touch two straight lines forming a given angle ABC.
- Figure 126: 88. To draw tangents to a circle from a given point A, the centre of the circle not being known.
- Figure 127: 89. In a given angle CAB, to inscribe a circle wliich shall pass through a given point D.
- Figure 128: 90. To draw a circle which shall pass through the given point A and touch a given line BC in D.
- Figure 129: 91. To draw a circle which shall pass through the two given points A and B and touch the given line CD.
- Figure 130: 92. To draw four equal circles, with radius equal to given line E, to touch two given lines AB and CD, which are not parallel.
- Figure 131: 93. To draw an inscribed and an escribed circle, tangential to three given straight lines, forming a triangle ABC. Note. — An escribed circle is also called an excircle.
- Figure 132: 94. A principle of inscribed and escribed circles.
- Figure 133: 95. To draw two circles tangential to three given straight lines, two of which are parallel.
- Figure 134: 96. To draw two circles tangential to three given straight lines, none of which are parallel ; the third line to be drawn to cut the other two.
- Figure 135: 97. To draw direct common tangents to two given circles of unequal radii.
- Figure 136: 98. To draw TRANSVERSE COMMON TANGENTS to two given circles of unequal radii.
- Figure 137: 99. Showing the principle of tangential circles.
- Figure 138: 100. To draw four equal circles with radius equal to given line D, with their centres on a given line AB ; two to touch externally and two internally a given circle, whose centre is C and radius CG.
- Figure 139: 101. To draw four equal circles, with radius equal to given line D, with their centres on a given arc AB ; two to touch externally and two internally a given circle, whose centre is C and radius CG.
- Figure 140: 102 To describe a circle tangential to and including two given equal circles A and B, and touching one of them in a given point C.
- Figure 141: 103. To describe a circle tangential to and including two unequal given circles A and B, and touching one of them in a given point C.
- Figure 142: 104. To draw the arc of a circle having a radius of 1 and 1/4 inches, which shall be tangential to two given unequal circles A and B and include them.
- Figure 143: 105. To inscribe in a segment of a circle, whose centre is E, two given equal circles with a radius equal to line D.
- Figure 144: 106. In a given sector of a circle ABC, to inscribe a circle tangential to it.
- Figure 146: 108. To draw the arc of a circle tangential to two given unequal circles A and B externally, and touch- ing one of them in a given point C.
- Figure 147: 109. To draw a circle, with a radius equal to given line C, tangential to two given unequal circles A and B, to touch A externally and B internally.
- Figure 148: 110. To draw a circle of f of an inch radius tangential to the given line AB and the given circle CDE.
- Figure 166: 111. To find a fourth proportional to three given lines A, B, and C. THE GREATER FOURTH PROPORTIONAL.
- Figure 167: 112. To find a fourth proportional to tliree given lines A, B, and C. THE LESS FOURTH PROPORTIONAL.
- Figure 168: 113. To find a third proportional between two given lines A and B. THE GREATER THIRD PROPORTIONAL.
- Figure 169: 114, To find a third proportional between two given lines A and B. THE LESS THIRD PROPORTIONAL.
- Figure 170: 115. To find the MEAN PROPORTIONAL between two given lines AB and CD.
- Figure 171: 116. To divide a line in medial section, i.e. into EXTREME and MEAN proportion.
- Figure 172: 117. To divide any straight line AB in the point C, so that AC : CB : : 3 : 4.
- Figure 173: 118. To divide a line proportionally to a given divided line.
- Figure 174: 119. To construct a triangle on a given line AB, so that the three angles may he in the proportion of 2 : 3 : 4.
- Figure 175: 120. This problem illustrates an important principle in proportion.
- Figure 176: 121. To divide a right angle into five equal parts.
- Figure 177: 122. To find the Arithmetic, the Geometric, and the Harmonic means between two given lines AB and BC.
- Figure 178: 123. Taking the given line AB as the unit ; find lines representing the square root of 2 and the square root of 3.
- Figure 179: 124. To construct a scale 4 inches long, showing inches and tenths of an inch.