Land surveying, 92; ditches, method of measuring, 95; ponds and rivers, method of measuring, 94; boundaries, 94; field book described, 96; instru- ments described, 92, 95; method of measuring lines on the ground, 93; planning survey, described, 96. Land surveying with chain and cross, 87; triangular fields, 98; fields in the form of trapeziums, 99; four-sided fields, 100; fields contained by more than four sides, 101; field, included by curved sides, 104; to measure a line across a river, 107.
Land surveying with chain only, 108; triangular fields, 108; four-sided fields, 111; with more than four sides, 111; parishes and large estates, 113. Level book, examples of, 122, 123, and 125.
Levelling, term defined, 115; instru-
ments described, staves described, 118; use of, described, 120; practice of, de- scribed, 120; to find the differences of levels of several points, 120; to draw a sectional line of several in the earth's surface, the levels of which have been taken, 121.
Levelling, practice of, levels for the for- mation of a section, 124; example of level book, 125.
Line defined, 1; datum described, 122; right definition of, 1; straight, defined,
1. Lines, mensuration of, 19; application of, 19; parallel, described, 1.
Linear measure, table of, 19, 97.
Lune, to find the area of a, 47; exam- ples, 48.
Masons' work, method of measuring, 82; examples, 83.
Mensuration described, 1; of lines, ap- plication of, 19.
Mensuration, problems, 19; of solids, 52; of surfaces, 34. Minute, defined, 3.
Miscellaneous exercises, 52. Multiplication, symbol for, described, 18.
Oblique prism defined, 53; pyramid de- fined, 53.
Obtuse angle defined, 1; angled triangle, definition of, 2.
Octagon described, 3.
Octagon, problems relating to the:-to
make an, on a given line, 9; to de- scribe an, in or about a given circle, 12. Octahedron described, 54.
Offset-staff, described, 54; method of using, 94.
Painters' work, method of measuring, 88; exercises, 88.
Parabola, to describe or construct a, 15; Parabola, problems relating to the:-any two of the following parts being given to find the third: the parameter, the ab-
scissa, and the ordinate, 33; formule and examples, 33; to find the area of a, 49; formulæ and examples, 49; to find the length of an arc of a, its ordinate and abscissa being given, 33; formulæ and examples, 33.
Parabolic frustrum, to find the area of a, 49; formulæ and examples, 49. Paraboloid, to find the solidity of a, 72; examples, 72.
Paraboloid, frustrum of a, to find the soli- dity of, 72; examples, 72. Parallel lines defined, 1.
Parallelogram described, 2.
Parallelogram, problems relating to:-to describe a rectangled, having a given length and breadth, 6; to find the area of a, 34; formulæ and examples, 34. Parallelopipedon described, 53; to find the solidity of a, 55; formulæ and ex- amples, 56.
Parishes, method of surveying, with chain, described, 113.
Paviors' work, method of measuring, 89; examples, 89.
Pentagon described, 3.
Pentagon, problems relating to:-to make a regular, on a given line, 9; to in- scribe a, in a given circle, 13; example,
Pentagonal prism defined, 52.
Plane, term defined, 1; triangle, defined, 2. Planning surveys described, 96. Plasterers' work, method of measuring, 87; examples, 87.
Plotting scales, described, 95.
Plumbers' work, method of measuring, 89; examples, 90. Point, term defined, 1. Polygons described, 3.
Polygons, problems relating to;-to make a, on a given line, 9; to inscribe a, in a given circle, 10; to circumscribe a, about a circle, 10; to find the angles of, 10; to find the centre of a, or the centre of its inscribed or circumscribed circle, 11; irregular, to find the area of, 40; examples, 40; regular, to find the area of, 41; formulæ and examples, 41; regular, being given, to find the radii of its inscribed and circumscribed circle, 24; formulæ, 24; examples, 25; tables of, 10, 24.
Practical geometry, problems in, 4. Prism, definition of, 52; oblique, defined, 53; pentagonal, defined, 52; right, de- fined, 53; square, defined, 52; triangu- lar, defined, 52; to find the solidity of any, 57; formule and examples, 57; to find the area of the surface of a, 57. Prismoid defined, 64; to find the con- tent, 64; formulæ and examples, 64. Promiscuous exercises, 52. Proportion, symbol for, 18. Pyramid, definition of, 53; axis of, de- fined, 53; frustrum of, defined, 54; height of, described, 54; irregular, de- scribed, 54; oblique, defined, 53; regu lar, defined, 54; right, described, 53
segment of a, described, 54; vertex of a, defined, 53. Pyramid, problems relating to the-to find the solidity of a, 58; examples, 58; to find the slant surface of a right, 58; formulæ and examples, 58; frustrum of a, to find the solidity of a, 60; formulæ and exercises, 61; frustrum of a, having its ends polygons, to find the contents, 60; formulæ, 60; examples, 61; frus- trum of a, to find the slant surface, 61.
Quadrant, term defined, 3. Quadrilateral figure described, 2.
Radius of a circle defined, 3. Railway curves, method of laying out, described, 127; forms of curve de- scribed, 127; to lay out a curve by the common method, 127; examples, 128; to lay out a curve by offsets from its tangents, 129:-(1.) When the length of the curve does exceed of its radius, 129; example, 130. (2.) To lay out a curve when it is any required length, 130; table of offsets to, 138. Railway cuttings, to find the contents of, 130; earthwork tables described, 130; to take the dimensions, 131; to find the content from the depth, 132; to find the content from sectional areas, 133; example, 134.
Rectangle described, 2.
Refraction, correction for, explained, 119; table of corrections for, 138. Regular body defined, 54. Regular pyramid defined, 54. Rhomboid described, 2. Rhombus, definition of, 2. Right angle defined, 1.
Right angled triangle defined, 2; line de- fined, 2; a line, cutting two parallel lines, makes the alternate angle: theo- rem, 17; pyramid, defined, 53; prism, definition of a, 53.
Ring, to find the area of a circular, 47; formulæ and examples, 47; cylindrical, to find the solidity of a, 70: to find the surface of a, 70; formulæ and examples, 70.
River, to measure a line across a, with
chain and cross, described, 107. Roofs, to find the concave surface of arched and vaulted, 90; examples, 90; to find the solid contents of materials, 90; examples, 90.
Scales, plotting, described, 95. Seconds defined, 3.
Sector of a circle, definition of the term, 3; to find the area of, 43; formulæ and examples, 43.
Segment of a circle, term defined, 3. Semicircle, definition of, 3.
Slaters' work, method of measuring, 86; examples, 86.
Sliding rule, see Carpenters'.
Solid, term defined, 52; axis of, defined,
53; faces of, described, 54; measure,
table of, 54; segment of, described, 54; frustrum of, defined, 54.
Solidity, to find the, of any regular body, 72; examples, 73.
Solidities of regular bodies, table of, 72. Solids all similar are like to one another,
as the cubes of their like linear dimen- sions: theorem, 17; general rule for finding the contents of, 135; Gompertz's investigation of the above rule, 135; examples, 136; mensuration of, 52. Specific gravity, term defined, 91; table of, 91; to find the weight of a body from its bulk, 92; examples, 92; to find the magnitude of a body from its weight, 92; examples, 92.
Sphere, definition of, 53; axis of, defined, 53; segment of, described, 54. Sphere, problems relating to the :-to find the solid content of a, 65; examples, 66; to find the convex surface, 67; for- mulæ and examples, 68; frustrum of a defined, 54; sector of, defined, 54; zone defined, 54; segment or zone, to find the convex surface, 67; formulæ and examples, 68.
Spherical frustrum, to find the solid con- tents, 67; formule and examples, 67; segment, to find the solidity of a, 66; examples, 66.
Spheriod, to find the solidity, 70; formulæ and examples, 71; middle zone of a, to find the content, the ends being circu- lar, 71; examples, 71.
Spindle, circular, defined, 54. Spindle, problems relating to the:-to find the solidity of a, 68; formulæ and ex- amples, 68; to find the contents of the middle zone, 69; to find the convex surface, 69; examples, 70.
Spindle, circular, problems on:-to find the convex surface of any segment or zone, 69; examples, 70. Square, definition of a, 2.
Square, problems relating to the:-to de- scribe a, whose side shall be of a given length, 6; to describe a circle in, or a given square, 11; examples, 12; to de- scribe a, in or about a given circle, 12; to make a, equal to two given, 14; to make a, equal to the difference between two given, 14; to make a, equal to the sum of any number of squares taken together, 14.
Square measure, tables of, 34, 97; prism, definition of, 52; root, symbol of, 18. Staff, offset described, 93; method of using, 94.
Straight line, definition of, 1.
Straight line, problems on the :-to divide a given, into two parts, 4; to draw a, at a given distance, parallel to a given line, 4; through a given point to draw a straight line parallel to a given straight line, 4; from a given point in a straight line to erect a perpendicular,
Subtraction, symbol for, 18. Surface, definition of, 1.
Surfaces of regular bodies, table of, 72. Superfices, mensuration of, 72; of regu- lar bodies, to find the, 72; examples, 73. Surveys, planning, described, 96. Surveying, see Land Surveying and Engineering Surveying.
Tables, earthwork described, 130; of areas of segments of circles, 137; of corrections for curvature and refrac- tion, 138; of linear measure, 19, 97; of offsets for railway curves, 138; of poly- gons, 10, 24; of solid measure, 54; of specific gravity, 91; of square measure, 34, 97; of surfaces of regular bodies, 72; for measuring timber, 139. Tangent, to draw a, through a given point to a circle, 8. Tetrahedron defined, 54. Theorems, geometrical, 16.
Tilers' work, method of measuring, 86; examples, 86.
Timber measuring, 75; to find the area or content of a plank, 75; examples, 76; to find the area or content by the sliding rule, 76; examples, 76; to find the solid content of squared timber, 76; examples, 77; by sliding rule, 76; example, 77; to find the solid content of unsquared timber, 78; ex- amples, 78; by sliding rule, 78; exam- ples, 79; table, 139. Trapezoid, definition of, 3. Trapezoid, problems relating to the:-the base and two perpendiculars being given, to construct a, 6; to find the area of a, 37; examples, 37. Trapezium, definition of, 2; diagonal de- scribed, 2; to find the area of a, (1.) For any trapezium, 38. (2.) When two opposite angle are supplements of each other, 38; examples, 38; to mea- sure with chain and cross, field in the form of a, 99; to find the content, 99; examples, 99.
Triangle, acute angled, defined, 3; equi- lateral, defined, 2; isosceles, defined, 2; obtuse angled, define, 2; plane, defi- nition of, 2; right angled, defined, 2. Triangle, problems relating to the-to construct a, with three given right lines, any two of which must be greater than the third, 5; given the base and per-
pendicular, with the place of the latter, to construct the triangle, 5; to con- struct a right angled, having a given base and perpendicular, and to find the hypothenuse, 6; given the base and hypothenuse, to construct the right angled triangle, and find the perpen- dicular, 7; to inscribe a circle in a given, 11; examples, 11; about a, to circumscribe a circle, 11; examples, 11; to make a, similar to a given, 13; examples, 13; to find one side of a right angled, two being given, 19; for- mulæ and examples, 20; two sides and base being given, to find the perpen- dicular, 23; formulæ and examples, 23; to find the area of a, 36; formulæ and examples, 36; to find the area of a, by the chain, 109; the greatest side of every, is opposite the greatest angle: theorem, 17; any two angles being given, the, becomes known: theorem, 17; similar, are to one another in the duplicate ratio of their homologous sides: theorem, 17.
Triangular prism, definition of, 52. Triangular fields, method of surveying with chain and cross, 98; construction, 98; to find the content, 98; examples,
Triangular field, method of surveying with chain, 108; examples, 108. Trigon, to describe a, in a given circle, 12.
Vaulted roofs, to find the concave surface of, 90; examples, 90; to find the con- tent of the materials, 90; examples,
Wedge, to find the solidity of a, 63; for- mulæ and examples, 63.
Y-level, construction described, 115; ad- justments described for parallax and collimation, 116; of buble tube, 117; of the axis, perpendicular to the vertical axis, 117.
Zone, circular, to find the diameter of a, its parallel chords and its breadth being given, 30; formulæ and examples, 30; circular, to find the area of a, 46; ex- amples, 46.
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