-
[169]
-
Altitude, of cone,
57,
60.
-
of cylinder, 33,
39.
-
of frustum of cone,
71.
-
of prism, 29.
-
of prismatoid, 76.
-
of pyramid, 46,
51.
-
of spherical segment,
98.
-
of zone, 95.
-
Angle, dihedral,
15.
-
plane angle of dihedral,
15.
-
polyhedral, 15.
-
Angles, 15.
-
Antilogarithm,
151.
-
Areas of plane figures,
2-4.
-
Axial section;
114.
-
Axis, of circle of sphere,
87.
-
of cone, 58.
-
of right circular cylinder,
39.
-
Base, of cone, 57.
-
of pyramid, 46.
-
of spherical sector,
103.
-
Bases, of cylinder,
32.
-
of prism, 28.
-
of prismatoid, 75.
-
of rectangular parallelepiped,
21.
-
of right circular cylinder,
39.
-
of spherical segment,
98.
-
of zone, 95.
-
Cavalieri's theorem,
25.
proof of, 145.
-
Center of gravity,
110.
-
Center of sphere,
87.
-
Circles of sphere,
87.
-
Circular cone, 58.
right, 60.
-
Circular cylinder,
36.
right, 39.
-
Circumscribed prism,
33,
36.
-
Computation suggestions,
1.
-
Cone, altitude of,
57,
60.
-
axis of, 58.
base of, 57.
-
circular, 58.
-
axis of, 58.
-
element of, 57.
vertex of, 57.
-
frustum of, 71.
-
lateral area of,
60.
-
lateral area of frustum of,
72.
-
of revolution, 60.
slant height of, 60 right circular, 60. slant height of, 60.
-
spherical, 103.
-
Cones, 57,
60.
similar, 53.
-
Conical surface,
57.
-
Convex polyhedron, Cross section,
29.
-
Cube, 18.
-
Cylinder, 32.
-
bases of, 32.
-
altitude of, 33.
element of, 33. lateral area of, 33. right section of, 33.
-
circular, 36.
21.
-
right circular,
39.
-
truncated, 81.
-
Cylinders, 32,
36,
39.
-
Cylindrical surface,
32.
-
Determined, plane,
10.
-
Diagonal of polyhedron,
116.
-
Dihedral angle,
15.
edge of, 15. faces of, 15. plane angle of, 15.
-
[170]
-
Dimensions of parallelepiped,
22.
-
Directrix, 32,
57.
-
Dodecahedron, regular,
116.
-
Edge of dihedral angle,
15.
-
Edges, of polyhedral angle,
15.
-
Element, of conical surface,
57.
-
of cylindrical surface,
32.
-
Face angles of polyhedral angle,
15.
-
Faces, of dihedral angle,
15.
of polyhedral angle, 15.
-
Foot of line, 9.
-
Formula, prismoidal,
77,
123.
-
Formulas, summary of,
131,
132.
-
Frustum of cone,
71.
altitude of, 71. lateral area of,
72.
slant height of, 71.
-
Frustum of pyramid,
67.
cone, 71.
slant height of,
67.
-
Generator, 32,
57.
-
Geometry, solid, 9.
-
Great circle, axis of,
87.
of sphere, 87.
-
Hexahedron, regular,
117.
-
Historical references:
-
Apollo, 20.
-
Athenians, 20.
-
Bunker Hill Monument,
84.
-
Cavalien, 146.
-
Cestius, 53.
-
Chinese wall,
133.
-
Cleopatra's Needle,
70.
-
Delians, 20.
Delos, 20.
-
Fingal's Cave,
133.
-
Guldin, 111.
-
Hippasus, 116.
-
Island of Staffa,
133.
-
Kepler, 111.
-
Newton, 76.
-
Ninus, 65.
-
Panama Canal,
134.
-
Pappus, 111.
-
Pickett's Monument,
-
Frontispiece. Plato,
20.
-
Pythagoras, 116.
-
Queen Semiramis,
65.
-
Sterling, James,
76.
-
Washington Monument,
69,
141.
-
Woolworth Building,
136.
-
Icosahedron, regular,
116,
119.
-
Inclination of line,
10.
-
Inscribed prism in cylinder,
33,
36.
-
Inscribed sphere in polyhedron,
116.
-
Lateral area, of cone,
60.
-
of cylinder, 33.
-
of frustum of cone,
72.
-
of prism, 29.
-
of pyramid, 47,
51.
-
Lateral edges, of prism,
28.
-
Lateral faces, of prism,
28.
-
Limits, a theorem on,
144.
-
Line, foot of, 9.
-
inclination of,
10.
-
parallel, 9.
-
projection of, 10.
-
straight, parallel to plane,
9.
-
perpendicular to plane,
10,
13.
-
Logarithms, 1,
150,
153.
-
Mid-section of prismatoid,
76.
-
Normal, 10.
-
Octahedron, regular,
116,
119.
-
Pappus, Theorems of, for surfaces,
110.
-
Parallel planes,
12.
-
Parallelepiped, rectangular,
21.
-
Perpendicular planes,
15.
-
Plane, 9.
-
determined, 10.
-
of reference, passed,
9.
-
straight line oblique to,
10.
-
straight line parallel to,
9.
-
straight line perpendicular to,
10.
-
tangent to sphere,
87.
-
Plane angle of dihedral angle,
15.
-
Plane figures, 1.
-
Planes, parallel,
12.
-
Point, projection of,
10.
-
Poles of circle of sphere,
87.
-
Polyhedral angle,
15.
edges of, 15. face angles of, 15. faces of, 15. vertex of, 15.
-
Polyhedral angles,
15.
-
Polyhedron, 18,
115.
-
convex, 116.
-
diagonal of, 116.
-
edges of, 18,
115.
-
faces of, 18,
116.
-
inscribed sphere in,
116.
-
regular, 116.
-
vertices of, 18,
116.
-
Polyhedrons, 18,
115.
similar, 53.
-
Prism, 28.
-
bases of, 28.
lateral edges of, 28. lateral faces of, 28.
-
altitude of, 29.
lateral area of, 29. right, 29. right section of, 29.
-
circumscribed about cylinder,
33,
36.
-
inscribed in cylinder,
33,
36.
-
truncated, 81.
-
Prismatoid, 75.
-
altitude of, 76.
mid-section of, 76.
-
general, 120.
general section of, 120.
-
theorem, 121.
-
[171]
-
Prismoidal formula,
77,
123.
-
Projection, of a line,
10.
of a point, 10.
-
Proportional parts,
151.
-
Pyramid, 46,
50.
-
altitude of, 46,
51.
-
base of, 46.
-
frustum of, 67.
-
lateral area of,
47,
51.
-
lateral edges of, 50.
-
lateral faces of, 46, 50.
-
regular, 50.
-
slant height of frustum of regular,
67.
-
slant height of regular, 50.
-
triangular, 47.
-
vertex of, 46.
-
Pythagorean theorem,
3.
-
Rectangular parallelepiped,
21.
-
References from plane geometry,
146.
-
Regular polyhedron,
116.
-
Regular dodecahedron, 116,
119.
-
Regular hexahedron, 116, 119.
-
Regular icosahedron, 116, 119.
-
Regular octahedron, 116, 119.
-
Regular tetrahedron, 116, 119.
-
Regular pyramid,
50.
slant height of, 50.
-
Revolution, cone of,
60.
-
cylinder of, 39.
-
solids of, 111.
surfaces of, 111.
-
Right circular cone,
60.
-
Right circular cylinder,
39.
-
Right prism, 29.
-
Right section, of cylinder,
33.
-
Section, 18.
-
axial, 114.
-
cross, 29.
right, 29.
-
Sector, base of spherical,
103.
-
Segment, base of spherical,
98.
spherical, 97.
-
[172]
-
Similar figures, 4,
53.
solids, 53.
-
Similar polyhedrons, 53.
-
Slant height, of cone of revolution,
60.
-
of frustum of cone,
72.
-
of frustum of pyramid,
67.
-
of regular pyramid,
50.
-
Slide rule, 1,
2.
-
Small circle of sphere,
37.
-
Solid, 18.
volume of, 19.
-
Solid geometry, 9.
-
Solids, for which V = Bh,
18.
-
for which V = *Bah,
46.
-
for which V = (mean B)h,
6
-
of revolution,
111.
-
Sphere, 87.
-
axis of circle of, 87. center of, 87. great circle of, 87.
-
inscribed in polyhedron,
116.
-
plane tangent to, 87. small circle of, 87.
-
terrestrial, 94.
-
Spherical cone,
103.
-
Spherical sector, 103. base of, 103.
-
Spherical segment,
97.
altitude of, 98.
bases of, 98. of one base, 98.
-
Straight line, oblique to plane,
10.
parallel to plane,
9.
-
Straight line (continued) perpendicular to plane,
10.
-
Summary of formulas,
131
-
Surface, conical,
57.
-
Surfaces of revolution,
111.
-
Tabular difference,
150.
-
Tetrahedron, regular,
118.
-
Theorem, Cavalieri's,
25.
-
of Pappus, 110.
-
on limits, 144.
-
prismatoid, 123.
-
volume, 27.
-
Theorems of solid geometry,
10.
-
typical proofs of,
13.
7.
-
Triangular pyramid,
116.
-
Truncated cylinder,
81.
-
Truncated prism,
81.
-
Unit of volume,
19.
-
Vertex, of polyhedral angle,
15.
-
Vertices of polyhedron,
18,
116.
-
Volume, of solid,
19.
-
Zone, 95.
altitude of, 95. area of, 95. bases of, 95. of one base, 95.
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