Acute angle defined, 1.
Acute angled triangle defined, 2.
Addition, sign for, 18.

Angie defined, 1; acute, defined, 1;
obtuse, defined, 1; right, defined, 1;
measure of, term described, 3.

Angle, problems on the:-to divide an,
into two parts, 7; to set off an, to con-
tain a given number of degree, 7; to
measure an, contained by two straight
lines, 7.

Angles, measurement of, 8; of polygons,
to find the, 10; vertically opposite are
equal theorem, 16.

Arc of a circle defined, 3.

Arc of a circle, problems :-the chord and
height being given, to find the diameter
and chord of half the arc, 26; formulæ
and examples, 26; to find the length of
any, 28; formulæ and examples, 28.
Arched roof, to find the concave surface

of an, 90; examples, 90; to find the
solid content of, 90; examples, 90.
Area, to find the, of irregular figures, 50;
examples, 50.
Artificers' work, methods of measuring,

80; bricklayers', 80; carpenters', 83;
glaziers', 88; joiners', 83; masons', 82;
painters, 88; paviours', 89; plasterers',
87; plumbers', 89; slaters', 86; tilers',

86.

(6.) To find a third proportional to two
numbers, 75. (7.) To find a fourth
proportional to three numbers, 75.
Carpenters' work, method of measuring,
83; doors, 84; joists, 83; partitions, 83;
roofing, 84; staircases, 84; balustrade,
84; wainscoting, 84; window-shutters,
85; examples, 85.

Chain, Gunter's, described, 92; method
of using, 94; land surveying by the, ex-
plained, 108.

Chain and cross, land surveying with, de-
scribed, 97.

Chimney, method of computing the brick-
work of a, 80.

Chord, term defined, 3.

Circle, definition of, 3; arc of described,
3; diameter of, defined 3; divisions of,
described, 3; radius, term defined, 3.
Circle, problems on the:-to find the cen-
tre of a, 8; to describe the circumfer-
ence of a, through three given points, 8;
to draw a tangent to a, through a given
point, 8; to find the diameter and cir-
cumference of a, the one from the
other formula and examples, 25; in
a given, to inscribe any regular poly-
gon, or to divide the circumference into
any number of parts, 10; in or about a,
to describe a square or an octagon, 12;
in a, to describe a trigon hexagon, or a
dodecagon, 12; in a, to inscribe a pen-
tagon or decadon, 13; example, 13; to
inscribe a, in a given triangle, 11; to
describe a, in or about a given square,
11; example, 12; to circumscribe a,
about a given triangle, 11; example,
11; about a, to circumscribe any regular
polygon, 10; to find the area when the
radius or half diameter is given, 42; ex-
amples, 42; when the circumference is
given, 42.

Circle, arc of a, the chord and height
being given, to find the diameter and
chord of half the arc, 26.

Circle, arc of a, to find the length of any,

28; formulæ and examples, 28.
Circle, segment of a, to find the area of,
45; formulæ and examples, 45.
Circle, sector of a, to find the area of, 43;
formulæ and examples, 43.

Circles, concentric, to find the area in-
cluded between two, 47; formulæ and
examples, 47; tables of areas of seg-
ments, 137.

Compasses described, 95.

Cone defined, 53; to find the solidity of
any, 58; to find the convex surface of
a right, 58; formulæ and examples, 58.
Cone, frustrum of a, to find the solid con-
tent of a, 60; formulæ and examples,
60; to find the convex surface, 61;
rules and examples, 61.
Cross described, 93.

Cube, definition of, 53; problem relating
to the, 55; to find the solidity, of, 55;
formulæ and examples, 55.
Cube root, symbol of, described, 18.
Curvature, correction for, described, 118;
table of corrections for, 138.
Curves, railway, method of laying out de-
scribed, 127; forms of, explained, 127;
to lay out a curve by the common
method, 127; examples, 128; to lay
out a curve by offsets from its tangents,
129; examples, 130:-(1.) When the
length does not exceed one quarter of
its radius, 129. (2.) When it is any
required length, 130; table of offsets
for, 138.

Cuttings, railway, to find the contents of,
130; tables described, 130; to take the
diameter, 131; to find the contents
from the depth, 132; examples, 182; to
find the content from the sectional
areas, 133; examples, 134.
Cylinder described, 53; to find the so-
lidity of any, 57; formulæ and exam-
ples, 57; to find the area of the surface,
57.

Datum, line, use of, explained, 122.

Decagon, to inscribe a, in a given circle,

13.

Degree, term described, 3.

Diameter of a circle defined, 3.
Division, sign for, described, 18.
Dodecagon, to describe a, in a given
circle, 12.

Dodecakedron, described, 54.

Dome, to find the surface and solidity of a,
height and base given, 91; examples, 91.

Ellipse, to draw an, 15; with thread, de-
scribed, 15.

Ellipse, problems relating to the :-to con-
struct a figure resembling an, by circu-
lar arcs from four centres, 14; to de-
scribe a true, 15; given any three of
the four following parts to find the
fourth traverse axis, conjugate axis,
the abscissa, and the ordinate, 31; to
find the area of an, 48; formulæ and
examples, 48; given the axis to find
the circumference, 32; formulæ and
examples, 32; segment of an, to find
the area the chord of which is parallel
to one of the axis, 48; examples, 48.
Engineering, surveying, 115; levelling,
term defined, 115, practice of, described,

120; instruments described, 115; Y-
level, 115; levelling staves, 11s; cor-
rection of curvature, 118; for refrac
tion, 119; contents of railway cuttings,
130; method of laying out railway
curves, 127.

Equality, sign for, 18.

Equilateral triangle defined, 2.

Estates, method of surveying large, by
the chain, described, 113.
Exercises, promiscuous, 52.

Field book described, 96; method of en-
tering notes, 96; example of, 180.
Fields, four-sided, method of surveying
with chain and cross, 100; to find the
content, 100; examples, 100.

Fields contained by more than four sides,
method of surveying with chain and
cross, described, 101; to find the con-
tent, 101; examples, 101.

Fields, included by curved sides, method
of surveying with chain and cross, de-
scribed, 104; examples, 105.

Fields in the form of trapeziums, method
of surveying with chain and cross, 99;
examples, 99.

Fields, triangular, to measure with chain

and cross, described, 93; construction,
98; to find the content, 98; examples,
98.

Fields, four-sided, method of surveying
with chain alone, 111; examples, 111.
Fields with more than four sides, 111;
examples, 112.

Fields, triangular, to survey with chain,
108; examples, 108.

Figures all similar are like to one another,
as the squares of their homologous or
like sides: theorem, 17.

Frustrum, term defined, 54; parabolic, to
find the area of a, 49; formulæ and ex-
amples, 49.

Geometrical theorems, 10.

Geometry, practical problems, 4.
Glaziers' work, method of measuring, 88;
examples, 88.

Globe, to find the content of a, 55; for-
mulæ and examples, 65.

Gravatt's levelling staves described, 118.
Gunter's chain described, 92; method of
using, 94.

Height of a pyramid, term defined, 54;
of a solid, term defined, 54.
Heptagon described, 3.
Hexagon defined, 3; to form a, on a given
line, 9; to describe a, in a given circle,
12.

Hexahedron described, 54.
Hyperbola, to construct a, 16,

Icosahedron described, 54.
Irregular pyramid defined, 54.
Isosceles triangle defined, 2.

Joiners' work, measurement of, see Car-
.penters'.