Πολιτικός

Bölümler

257 257–258 258 259 259–260 260 260–261 261 262 262 263 263–264 264 264–265 265 265–266 266 266 266–267 267 267–268 268 268 268–269 269 269–270 270 270 270–271 271 271 272 272 273 274 274–275 275 276 276–277 277 277–278 278 278–279 279 279 280 280–281 281 281–282 282 282–283 283 283–284 284 284 285 285 286 287 287 287–288 288 288–289 289 289–290 290 290–291 291 291–292 292–293 293 293 294 294–295 295 295–296 296 296–297 297 297 298 298–299 299 299–300 300–301 301 301 302 302 302–303 303 303 303–304 304 304–305 305 305–306 306 306–307 307 307–308 308 309 309 309–310 310 311 311

İngilizce Yunanca

266

Stranger

Str. By the diameter, of course, and again by the diameter of the square of the diameter. The word diameter here denotes the diagonal of a square. The early Greek mathematicians worked out their arithmetical problems largely by geometrical methods (cf. Plat. Theaet. 147 D ff). The diagonal of the unit square (√2) was naturally of especial interest. It was called sometimes, as here simply ἡ διάμετρος, sometimes, as just below,ἡ διάμετρος ἡ δυνάμει δίπους, or, more briefly,ἡ διάμετρος δίπους. Given a square the side of which is the unit (i.e. one square foot), the length of the diagonal will be √2 and the square constructed with that diagonal as its side will contain two square feet. The length of the diagonal of this square will be √4=2 feet, and its area will be four square feet. 5

Younger Socrates

Y. Soc. What do you mean by that?

Stranger

Str. Is the nature which our human race possesses related to walking in any other way than as the diameter which is the square root of two feet? There is here a play upon words. Man, being a two-footed (δίπους) animal, is compared to the diagonal of the unit square (√2,διάμετρος δίπους).

Younger Socrates

Y. Soc. No.