An elementary treatise on cubic and quartic curves, by A. B. Basset.
CHAPTER XI. MISCELLANEOUS CURVES. 307. IN the present chapter we shall consider a variety of miscellaneous curves, some of which like the cycloid and catenary are transcendental ones, whilst others like the three- and fourcusped hypocycloids are algebraic curves which are particular cases of a general class of transcendental curves. The Cycloid. 308. The cycloid is the curve traced out by a point on the circumference of a circle which rolls on a straight line. To find the equation of the cycloid. Let a be the radius of the rolling circle CPG, which rolls on the line AG; and let P be the point which initially coincided
-
Scan 1
Page #1
-
Scan 2
Page #2
-
Scan 3
Page #3
-
Scan 4
Page #4
-
Scan 5
Page #5 - Title Page
-
Scan 6
Page #6
-
Scan 7
Page #7 - Title Page
-
Scan 8
Page #8
-
Scan 9
Page V
-
Scan 10
Page VI
-
Scan 11
Page VII
-
Scan 12
Page VIII
-
Scan 13
Page IX - Table of Contents
-
Scan 14
Page X - Table of Contents
-
Scan 15
Page XI - Table of Contents
-
Scan 16
Page XII - Table of Contents
-
Scan 17
Page XIII - Table of Contents
-
Scan 18
Page XIV - Table of Contents
-
Scan 19
Page XV - Table of Contents
-
Scan 20
Page XVI - Table of Contents
-
Scan 21
Page 1
-
Scan 22
Page 2
-
Scan 23
Page 3
-
Scan 24
Page 4
-
Scan 25
Page 5
-
Scan 26
Page 6
-
Scan 27
Page 7
-
Scan 28
Page 8
-
Scan 29
Page 9
-
Scan 30
Page 10
-
Scan 31
Page 11
-
Scan 32
Page 12
-
Scan 33
Page 13
-
Scan 34
Page 14
-
Scan 35
Page 15
-
Scan 36
Page 16
-
Scan 37
Page 17
-
Scan 38
Page 18
-
Scan 39
Page 19
-
Scan 40
Page 20
-
Scan 41
Page 21
-
Scan 42
Page 22
-
Scan 43
Page 23
-
Scan 44
Page 24
-
Scan 45
Page 25
-
Scan 46
Page 26
-
Scan 47
Page 27
-
Scan 48
Page 28
-
Scan 49
Page 29
-
Scan 50
Page 30
-
Scan 51
Page 31
-
Scan 52
Page 32
-
Scan 53
Page 33
-
Scan 54
Page 34
-
Scan 55
Page 35
-
Scan 56
Page 36
-
Scan 57
Page 37
-
Scan 58
Page 38
-
Scan 59
Page 39
-
Scan 60
Page 40
-
Scan 61
Page 41
-
Scan 62
Page 42
-
Scan 63
Page 43
-
Scan 64
Page 44
-
Scan 65
Page 45
-
Scan 66
Page 46
-
Scan 67
Page 47
-
Scan 68
Page 48
-
Scan 69
Page 49
-
Scan 70
Page 50
-
Scan 71
Page 51
-
Scan 72
Page 52
-
Scan 73
Page 53
-
Scan 74
Page 54
-
Scan 75
Page 55
-
Scan 76
Page 56
-
Scan 77
Page 57
-
Scan 78
Page 58
-
Scan 79
Page 59
-
Scan 80
Page 60
-
Scan 81
Page 61
-
Scan 82
Page 62
-
Scan 83
Page 63
-
Scan 84
Page 64
-
Scan 85
Page 65
-
Scan 86
Page 66
-
Scan 87
Page 67
-
Scan 88
Page 68
-
Scan 89
Page 69
-
Scan 90
Page 70
-
Scan 91
Page 71
-
Scan 92
Page 72
-
Scan 93
Page 73
-
Scan 94
Page 74
-
Scan 95
Page 75
-
Scan 96
Page 76
-
Scan 97
Page 77
-
Scan 98
Page 78
-
Scan 99
Page 79
-
Scan 100
Page 80
-
Scan 101
Page 81
-
Scan 102
Page 82
-
Scan 103
Page 83
-
Scan 104
Page 84
-
Scan 105
Page 85
-
Scan 106
Page 86
-
Scan 107
Page 87
-
Scan 108
Page 88
-
Scan 109
Page 89
-
Scan 110
Page 90
-
Scan 111
Page 91
-
Scan 112
Page 92
-
Scan 113
Page 93
-
Scan 114
Page 94
-
Scan 115
Page 95
-
Scan 116
Page 96
-
Scan 117
Page 97
-
Scan 118
Page 98
-
Scan 119
Page 99
-
Scan 120
Page 100
-
Scan 121
Page 101
-
Scan 122
Page 102
-
Scan 123
Page 103
-
Scan 124
Page 104
-
Scan 125
Page 105
-
Scan 126
Page 106
-
Scan 127
Page 107
-
Scan 128
Page 108
-
Scan 129
Page 109
-
Scan 130
Page 110
-
Scan 131
Page 111
-
Scan 132
Page 112
-
Scan 133
Page 113
-
Scan 134
Page 114
-
Scan 135
Page 115
-
Scan 136
Page 116
-
Scan 137
Page 117
-
Scan 138
Page 118
-
Scan 139
Page 119
-
Scan 140
Page 120
-
Scan 141
Page 121
-
Scan 142
Page 122
-
Scan 143
Page 123
-
Scan 144
Page 124
-
Scan 145
Page 125
-
Scan 146
Page 126
-
Scan 147
Page 127
-
Scan 148
Page 128
-
Scan 149
Page 129
-
Scan 150
Page 130
-
Scan 151
Page 131
-
Scan 152
Page 132
-
Scan 153
Page 133
-
Scan 154
Page 134
-
Scan 155
Page 135
-
Scan 156
Page 136
-
Scan 157
Page 137
-
Scan 158
Page 138
-
Scan 159
Page 139
-
Scan 160
Page 140
-
Scan 161
Page 141
-
Scan 162
Page 142
-
Scan 163
Page 143
-
Scan 164
Page 144
-
Scan 165
Page 145
-
Scan 166
Page 146
-
Scan 167
Page 147
-
Scan 168
Page 148
-
Scan 169
Page 149
-
Scan 170
Page 150
-
Scan 171
Page 151
-
Scan 172
Page 152
-
Scan 173
Page 153
-
Scan 174
Page 154
-
Scan 175
Page 155
-
Scan 176
Page 156
-
Scan 177
Page 157
-
Scan 178
Page 158
-
Scan 179
Page 159
-
Scan 180
Page 160
-
Scan 181
Page 161
-
Scan 182
Page 162
-
Scan 183
Page 163
-
Scan 184
Page 164
-
Scan 185
Page 165
-
Scan 186
Page 166
-
Scan 187
Page 167
-
Scan 188
Page 168
-
Scan 189
Page 169
-
Scan 190
Page 170
-
Scan 191
Page 171
-
Scan 192
Page 172
-
Scan 193
Page 173
-
Scan 194
Page 174
-
Scan 195
Page 175
-
Scan 196
Page 176
-
Scan 197
Page 177
-
Scan 198
Page 178
-
Scan 199
Page 179
-
Scan 200
Page 180
-
Scan 201
Page 181
-
Scan 202
Page 182
-
Scan 203
Page 183
-
Scan 204
Page 184
-
Scan 205
Page 185
-
Scan 206
Page 186
-
Scan 207
Page 187
-
Scan 208
Page 188
-
Scan 209
Page 189
-
Scan 210
Page 190
-
Scan 211
Page 191
-
Scan 212
Page 192
-
Scan 213
Page 193
-
Scan 214
Page 194
-
Scan 215
Page 195
-
Scan 216
Page 196
-
Scan 217
Page 197
-
Scan 218
Page 198
-
Scan 219
Page 199
-
Scan 220
Page 200
-
Scan 221
Page 201
-
Scan 222
Page 202
-
Scan 223
Page 203
-
Scan 224
Page 204
-
Scan 225
Page 205
-
Scan 226
Page 206
-
Scan 227
Page 207
-
Scan 228
Page 208
-
Scan 229
Page 209
-
Scan 230
Page 210
-
Scan 231
Page 211
-
Scan 232
Page 212
-
Scan 233
Page 213
-
Scan 234
Page 214
-
Scan 235
Page 215
-
Scan 236
Page 216
-
Scan 237
Page 217
-
Scan 238
Page 218
-
Scan 239
Page 219
-
Scan 240
Page 220
-
Scan 241
Page 221
-
Scan 242
Page 222
-
Scan 243
Page 223
-
Scan 244
Page 224
-
Scan 245
Page 225
-
Scan 246
Page 226
-
Scan 247
Page 227
-
Scan 248
Page 228
-
Scan 249
Page 229
-
Scan 250
Page 230
-
Scan 251
Page 231
-
Scan 252
Page 232
-
Scan 253
Page 233
-
Scan 254
Page 234
-
Scan 255
Page 235
-
Scan 256
Page 236
-
Scan 257
Page 237
-
Scan 258
Page 238
-
Scan 259
Page 239
-
Scan 260
Page 240
-
Scan 261
Page 241
-
Scan 262
Page 242
-
Scan 263
Page 243
-
Scan 264
Page 244
-
Scan 265
Page 245
-
Scan 266
Page 246
-
Scan 267
Page 247
-
Scan 268
Page 248
-
Scan 269
Page 249
-
Scan 270
Page 250
-
Scan 271
Page 251
-
Scan 272
Page 252
-
Scan 273
Page 253
-
Scan 274
Page 254
-
Scan 275
Page 255
-
Scan 276
Page #276
-
Scan 277
Page #277
-
Scan 278
Page #278
About this Item
- Title
- An elementary treatise on cubic and quartic curves, by A. B. Basset.
- Author
- Basset, Alfred Barnard, 1854-1930.
- Canvas
- Page 201
- Publication
- Cambridge,: Deighton, Bell,
- 1901.
- Subject terms
- Curves, Cubic.
- Curves, Quartic.
Technical Details
- Link to this Item
-
https://name.umdl.umich.edu/ath7468.0001.001
- Link to this scan
-
https://quod.lib.umich.edu/u/umhistmath/ath7468.0001.001/225
Rights and Permissions
The University of Michigan Library provides access to these materials for educational and research purposes. These materials are in the public domain in the United States. If you have questions about the collection, please contact Historical Mathematics Digital Collection Help at [email protected]. If you have concerns about the inclusion of an item in this collection, please contact Library Information Technology at [email protected].
DPLA Rights Statement: No Copyright - United States
Related Links
IIIF
- Manifest
-
https://quod.lib.umich.edu/cgi/t/text/api/manifest/umhistmath:ath7468.0001.001
Cite this Item
- Full citation
-
"An elementary treatise on cubic and quartic curves, by A. B. Basset." In the digital collection University of Michigan Historical Math Collection. https://name.umdl.umich.edu/ath7468.0001.001. University of Michigan Library Digital Collections. Accessed May 1, 2025.