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Schaaf W.L. — Plane and Solid Geometry for Home Study
Schaaf W.L. — Plane and Solid Geometry for Home Study

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Название: Plane and Solid Geometry for Home Study

Автор: Schaaf W.L.

Аннотация:

Cultivated by the ancient Greeks more than two thousand years ago, geometry is one of the oldest intellectual pursuits of man. Its origins can be traced back even farther to the Babylonians and Egyptians. In essence, Egyptian geometry was a simple, empirical art of practical measurement, fostered by the necessity of frequent land-surveying due to inundations by the river Nile, and also by the astronomical curiosity and religious tradition of the Egyptians. Their geometry was, in short, a rule-of-thumb geometry.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1944

Количество страниц: 432

Добавлена в каталог: 12.12.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abbreviations, geometric      31
Alternate-interior angles      85 90
Altitudes, of a triangle      163
Analysis      165
angle      9
Angle of elevation      80 117
Angle sum of a triangle      96
Angle, bisector of      108 109 162 234
Angle, central      177
Angle, exterior      73 159
Angle, inscribed      177 194
Angles of a polygon      158
Angles with parallel sides      93
Angles with perpendicular sides      104
Angles, alternate-interior      85 90
Angles, corresponding      84
Angles, vertical      47
Angular measurement      11
Apothem      278
Arc, of a circle      178
Area      265
Area of circle      282
Area of cone      368
Area of cylinder      362
Area of equilateral triangle      270
Area of lune      391
Area of parallelogram      268
Area of prisms      336 337
Area of pyramid      351
Area of rectangle      266 267
Area of regular polygon      280
Area of similar figures      275
Area of sphere      391
Area of spherical triangle      393
Area of square      268
Area of trapezoid      271
Area of triangle      269 270
Area of zone      390
assumptions      39 41 42
Axis, of a sphere      378
Bearings      117
Belts and pulleys      210
Carpenter’s tri-square      208
Cavalieri’s theorem      343
Central angle      177
Centroid      173
chords      177 183 197 244
Circle graph      209
circles      176 178
Circles, area of      282
Circles, basic assumptions      281
Circles, circumference of      281
Circles, line of centers      191
Circles, sectors of      8
Compass, mariner’s      209
Compasses, proportional      260
Concentric circles      177
Concurrency      161
cones      364—373
Cones, altitude of      364
Cones, area of      368
Cones, element of      364
Cones, frustum of      365 368 369
Cones, nappes of      364
Cones, similar      372
Cones, slant height of      365
Cones, volume of      368
Congruent triangles      28 54 59 66 76 99 105
Constructions, bisecting a segment      220
Constructions, bisecting an angle      220
Constructions, dividing a line      222
Constructions, erecting perpendiculars      221
Constructions, geometric      19 220—228 272
Constructions, parallel lines      222
Constructions, proportional segments      256
Constructions, tangents      224
Constructions, triangles      223
Contrapositive      216
CONVERSE      70 216
Corollary      63
Corresponding angles      84
Cylinder of revolution      359 370
cylinders      358—363 370
Cylinders, area of      362
Cylinders, basic assumptions      361
Cylinders, right      359
Cylinders, right section of      359
Cylinders, similar      370
Cylinders, volume of      362
Danger angle      211
Deductive reasoning      37
definitions      38 45 71
demonstration      37 47
Depression, angle of      80 117
Design      21
Diagonal scale      262
Diameter      180
Dihedral angle      312
Dihedral angle, basic assumptions      313
Dihedral angle, bisector of      317
Dihedral angle, plane angle of      313
Directrix      358 364
Distance, from a point to a line      107
Distance, of chord from the center      183
dodecahedron      329 331
Draftsman’s triangles      116
Elevation, angle of      80 117
Equilateral triangle      63
Equilateral triangle, altitude of      252
Equilateral triangle, area of      270
Equilibrant      174
Equivalent figures      272
Euler’s law      329
Exterior angles, of a polygon      159
Exterior angles, of a triangle      73
External division of a segment      232
Face angles      323 324 325
Forces in equilibrium      174
Formal geometry      41 46 50
Generatrix      358 364
Geodesic      378
Geometric forms      1 4
Geometric patterns      2 22
Geometric symbols      31
Geometric truths      37
Gothic arch      23
Great circle      377
Great-circle sailing      378
Hero’s formula      7
hexahedron      329 330
Horizon, distance of      395
Hypothesis      41
Icosohedron      329 331
Inclined plane      262
Indirect measurement      29 259
Indirect method      84
Inequalities      122
Inscribed angles      177 194
Internal division of a segment      231
Inverse      89 90 216
Isosceles triangle      62 72
Line segments      231
lines      9
Loci      13 213
Loci in space      309 32
Loci, basic      217
Loci, demonstration of      214
Loci, intersecting      218
Logic      35 216
Lune      391
Mariner’s compass      209
Median, of a trapezoid      154
Median, of a triangle      164
Mid-join      153
Nappes      364
Oblique lines, from a point in a perpendicular      135—139
Observation      35
octahedron      329 330
Opposite      89 90 216
Ornament      21
Pantograph      261
Parallel lines      83 92 116 146 152
Parallel-ruler      172
Parallelogram      145
Parallelogram of forces      173
Parallelogram, area of      268
Parallelopiped      337 345
Perimeter, of regular polygon      279
Perpendicular bisector      106 161
Plane angle, of dihedral angle      313
Plane angle, of polyhedral angle      323
Plane figures      3
Planes      287
Planes, assumptions concerning      288
Planes, lines parallel to      298
Planes, lines perpendicular to      290—297
Planes, parallel      304—308
Planes, perpendicular      314—320
Planes, preliminary propositions      288
Platonic solids      328
Polar distance      379
Polar triangles      386
Poles      378
Polygon, angles of      158
Polygons, regular      202
Polyhedral angles      322
Polyhedral angles, symmetric      323
Polyhedrons      328
prisms      334—347
Prisms, area of      336 337
Prisms, basic propositions      335
Prisms, classification of      336
Prisms, regular      336
Prisms, volume of      341
Projections      253
Proportional compasses      260
Proportional segments      232 239 247 308
proportions      24 230
Propositions      40
Protractor      12
Pulleys      210
Pyramids      348—356
Pyramids, area of      351
Pyramids, frustum of      348 355
Pyramids, regular^      348
Pyramids, similar      356
Pyramids, slant height of      348
Pyramids, volume of      353
Pythagorean Theorem      6 274
Quadrant      80 379 380
Quadrilateral      144
Quadrilateral, deformability of      172
Radius of a polygon      278
Railway curve      211
Ratio and proportion      230
rectangle      145
Rectangle, area of      266 267
Reflection, law of      118
Regular polygons      202
Regular polygons, area of      278 280
Repeating designs      22
Resultant of a force      173
Rhomboid      145
Rhombus      145
right triangles      105 250
Rigidity, of triangles      81
Rope-stretchers      6
Ruled surface      358
Secant      177 197 200 245
Sector of a circle      8
Similar figures      24
Similar figures, area o      275
Similar polygons      242 276 277
Similar triangles      235—240
Similar triangles, area of      276
Small circle      378
Solids of revolution      359 370—373
Spheres      376—397
Spheres, area of      390
Spheres, axis of      378
Spheres, circles of      377
Spheres, lune      391
Spheres, polar distance      379
Spheres, poles      378
Spheres, spherical angles      380
Spheres, spherical polygons      383 393
Spheres, spherical triangles      384 393
Spheres, tangents to      385
Spheres, volume of      394
Spheres, zones of      389
Spherical angles      380
Spherical degrees      392
Spherical excess      393
Spherical polygons      383
Spherical triangles      384 393
Square      145
Square, area of      268
Square, diagonal of      252
surface      287 358
Surface measure      265
Symmetry      16 323
Synthesis      165
tangents      177 190 197 245
Tangents to spheres      385
tetrahedron      329 330 349
Transformation of polygons      272
Transversals      84 92 152
trapezoid      144
Trapezoid, area of      271
Trapezoid, median of      154
Triangles      53
Triangles, altitudes of      163
Triangles, angle bisectors of      162 234
Triangles, area of      269 270
Triangles, congruent      28 54 59 66 76 99 105
Triangles, equilateral      63
Triangles, isosceles      62 72
Triangles, medians of      154
Triangles, mid-join of      153
Triangles, perpendicular bisectors of      161
Triangles, polar      386
Triangles, right      105 250
Triangles, rigidity of      81
Triangles, similar      235 276
Triangles, spherical      384 393
Triangles, sum of angles of      96
Triangles, unequal sides and angles      126—132
Undefined terms      38
Vertical angles      47
Visible horizon      395
Volume, of cone      368
Volume, of cylinder      362
Volume, of parallelopiped      345
Volume, of prism      341
Volume, of pyramid      353
Volume, of sphere      394
Zone      389 390
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