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...

Circle; to inscribe, in given angle, passing through given point,
; to construct, touching given line in given point, also given
smaller circle,

...

; to construct, passing through two given points, and touching
given line,

...

..

; to draw, tangential to two unequal circles,

...

...

...

; to divide, into any number of parts, equal in area and outline,"
area of; to divide, into any number of parts by concentric
circles,
Circles, three; to describe, having given radii, each being tangential
to the other two,
-; to inscribe, in given triangle, each touching two others, and
two sides of triangle,

...

; to inscribe, in given triangle, each touching other two, and one
side of triangle,

172

173

174

175

...

; to inscribe, within given equilateral triangle, touching each

other, and two sides of triangle,

107

; to inscribe, within given circle,

107

; to inscribe, within given equilateral triangle, each touching
other two, and one side of triangle,

Circles, four; to inscribe, in given square, touching each other, and
one side only of square,

108

; to inscribe, in given square, touching each other, and two sides

Circles, five; to inscribe, in given circle,

Circles, six; to inscribe, within equilateral triangle,

; to describe, about and equal to given circle,

Circles, seven; to inscribe, in given circle,

Circles, any number of; to inscribe, in given circle,

; to describe, about a given circle,

Circles, series of; to describe, tangential to two converging lines,

Decagon; to inscribe, within given circle,

-; to construct, on given line,

Dodecagon; to inscribe, within given circle,

Ellipse; to describe, transverse and conjugate diameters given,

; to find centre and axes of,

; to complete curve of, one quarter given,

; to complete curve of, more than half given,

; to describe, about rectangle,

Elliptical figure; to describe, one diameter given,

; to construct, two squares given,

Equilateral triangle; to construct, on given base,

; to construct, height given,

; to inscribe, within given circle,
; to inscribe, in given square,

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Equilateral triangle; to inscribe, in given hexagon,

; to inscribe, in given pentagon,
; to describe, about given square,

; to describe, about given circle,

...

; to construct, equal to given triangle not equilateral,

Foiled figure; to construct, about any polygon,

Four-sided equilateral figure; to inscribe, in a given parallelogram,
Heptagon; to inscribe, within given circle,

89

90

116

...

117

155

123

...

86

179

180

Isosceles triangle; to construct, given base and vertical angle,

; to construct, diameter given,

Hyperbola; to construct, diameter, abscissa, and ordinate given,
Involute of circle, to construct,

Ionic volute, to construct, longest diameter given,

; to construct, given base and altitude,

; to construct, given base and vertical angle of 90°,

; to construct, given base and vertical angle containing a re-
quired number of degrees,

; to construct, given one of equal sides and one of equal angles,
; to construct, given base and perimeter,

...

; to inscribe, within given square, having given base,

...

; to construct, equal in area to, and on one side of, given
square,

; to construct, given altitude and length of its equal sides,
Line; to draw, parallel to given line, at given distance from it,
; to draw, parallel to given line, through given point,

; to divide, into any number of equal parts,

...

90

...

; to divide, proportionally to given divided line,
; to draw, through given point, which, if produced, would pass
through the angular point, towards which the given lines
converge,

Lines; to draw, from any two given points, outside a given line, to
make equal angles with the given line,

; to draw, from any two given points, outside a given line, so
that they may be equal in length,

; to draw, from any two given points, going to the same point
to which lines converge, where the point of convergence is
inaccessible,

—, parallel; to join the extremities of, by a pair of arcs,
Nonagon; to inscribe, within given circle,

; to construct, on given line,

Octagon; to inscribe, within given circle,
; to construct, on given line,
; to inscribe, in given square,

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...

; to construct, about given circle,

Octagon; to construct, within given circle, making one of its angles
coincide with a given point,

Oval; to describe, by arcs of circles,

Parabola; to construct, its ordinate and abscissa being given,
Parallelogram; to construct, on given base equal in area to given
parallelogram,

; to construct, equal to given triangle in area and perimeter,

; to divide, into two parts, proportionate in area to given divided
line,

Pentagon; to inscribe, within given circle,
; to construct, on given line,

; to describe, about a given pentagon, sides parallel, and equal to
given line,
Perpendicular; to draw, to a given straight line, from given point in

the line,

...

; to draw, to a given straight line, from given point outside it,
; to draw, to curve of ellipse, from given point,
Point; to find, which would be situated in the continuation of arc,

centre of arc being not obtainable,

Polygon, any; to inscribe, in given circle,

; to construct, on given line,

to complete, two sides being given,

; to construct, equal in area to given triangle,

Polygon, irregular; to make, equal to given irregular polygon,
Proportional; to find a mean, between two given lines,

third; to find, to two given lines (less),

; to find, to two given lines (greater),

fourth; to find, to three given lines (less),

; to find, to three given lines (greater),

Rectangle; to construct, two sides given,

; to construct, one side and diagonal given,

; to inscribe, in given triangle, side equal to given line,

...

169

84

85

140

...

...

; to construct, having a given side, equal in area to a given
triangle,

; to construct, equal in area to given circle,
Rectilineal figure; to convert, into triangle of equal area,

; to reduce, to an equivalent figure, having a less number of
sides,

; to construct, area being given in proportion to another recti-
lineal figure of the same kind,

144

160.

...

161

; to change, into another rectilineal figure of equal area, but
having one side more, &c.,

Reduced copy; to make, of any given figure,

Rhomboid; to construct, two adjacent sides and diagonal given,

; to construct, two adjacent sides and angle given,
Rhombus; to construct, side and diagonal given,
-; to construct, side and angle given,
Semicircles, three; to inscribe, within equilateral triangle, having

adjacent diameters equal (The Trefoil),

; to inscribe, within given circle,

...

...

Semicircles, four; to inscribe within given square, each touching
two sides of square (The Quatrefoil),

; to inscribe within given square, each touching one side of the

Semicircles, any number of; to inscribe, in given circle,

Spiral; to construct of one revolution,

...

:

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176
40

41

39

40

100

101

102

103

104

178

177

36

37

91

92

92

93

94

94

95

...

; to describe, about circle,

119

;

...

; to construct, within given square, concentric with it,

to construct, equal in area to given rectangle,

; to construct, having any number of square inches,
; to construct, equal in area to given triangle,

; to draw, between two given circles, placed apart,

...

; to construct, area one-third greater than given square,
; to construct, area one-third less than given square,
; to inscribe, within given square, proportional in area,
; to construct, equal in area to trapezium,

; to construct, equal in area to any number of squares,
; to construct, equal in area to any given polygon,

Straight line; to bisect,

...

...

...

; to divide, into extreme and mean proportion,
; to divide, successively into half, third, &c.,

; to divide, in point, ratio 2:3,

; to divide, in point; whole : part :: 5 : 3,

; to draw, equal to half circumference of circle,

Tangent; to draw, to given circle, point of contact in circumference,

; to draw, to given circle, point outside circumference,

; to draw, on outside of two given circles, placed apart,

; to draw, to point of contact in arc of circle, where the centre
cannot be obtained,

6

128

129

...

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...

Tangent; to draw, to curve of ellipse, at given point of contact,
Tangents, exterior; to draw one or two, common to two given

...

...

...

circles,
Trapezium; to construct, equal to given trapezium,

...

; to construct, adjacent pairs of sides given, and diagonal,
; to construct, diagonal and angles at extremities given,
; to construct, similar to given trapezium,
Triangle; to construct, three sides given,

...

82

...

...

; to construct, altitude and angles at base given,

; to construct, base, altitude, and one side given,

; to construct, given base, angles of 60°, 30°, and 90°,

; to bisect, by line parallel to one of its sides,

; to describe, about given circle, angles being equal to those of
given triangle,

...

; to inscribe, within, and equidistant, and similar to, given
triangle,

; to describe, about, and equidistant, and similar to, given
triangle,

; to inscribe, in circle, similar to given triangle,
; to construct, similar to given triangle, perimeter equal to given
straight line,

; to inscribe, within given triangle, similar to another triangle,
; to construct, equal in area to given trapezium,

...

; to construct, on given base, area equal to given triangle,

28

29

; to construct, similar to given triangle, twice its area,

156

; to bisect, line perpendicular to one of its sides,

157

; to construct, equal in area to two dissimilar triangles,

158

; to divide, into any number of equal parts, by lines drawn from
each angle to a point within the triangle,

; to divide, into any number of equal parts, by lines drawn from
a given point in one of its sides,

159

; to divide, into any number of equal parts, by lines drawn from
a given point within the triangle,

160

; to construct, equal in area to any given polygon,
; to construct, equal in area to any given circle,
Undecagon; to inscribe, within given circle,

; to construct, on given line,