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敬響嶄猟利 卦指云慕朕村 厘議慕尺 厘議慕禰 TXT畠云和墮 序秘慕杏 紗秘慕禰

flatland(献棲蒙声)-及21嫗

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!!!!隆堋響頼��紗秘慕禰厮宴和肝写偬堋響��



the coming year�察�the coming century�察�the coming Millennium。 

     My     four  Sons    and   two   orphan    Grandchildren       had   retired  to  their 

several   apartments�察  �and   my  wife   alone   remained   with   me   to   see the   old 

Millennium out and the new one in。 

     I   was   rapt   in   thought�察  �pondering   in   my   mind   some   words   that   had 

casually     issued    from   the   mouth     of  my    youngest     Grandson�察     �a  most 

promising   young   Hexagon   of   unusual   brilliancy   and   perfect   angularity。 

His uncles and I had been giving him his usual practical lesson in Sight 

Recognition�察�turning ourselves upon our centres�察�now rapidly�察�now  more 

slowly�察�and questioning him as to our positions�察�and his answers had been 

so satisfactory that I had been induced to reward him by giving him a few 

hints on Arithmetic�察�as applied to Geometry。 

     Taking nine Squares�察�each an inch every way�察�I had put them together 

so   as   to   make   one   large   Square�察  �with   a   side   of   three   inches�察  �and   I   had 

hence proved to my little Grandson thatthough it was impossible for us 



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to   SEE  the   inside of   the   Square   yet   we   might   ascertain   the number   of 

square inches in a Square by simply squaring the number of inches in the 

side�此    �and    thus�察─  �said   I�察  �we    know     that   three´to´the´second�察       �or  nine�察�

represents   the   number   of   square   inches   in   a   Square   whose   side   is   three 

inches long。; 

     The little Hexagon meditated on this a while and then said to me�察 �But 

you have been teaching me to raise numbers to the third power�此�I suppose 

three´to´the´third must mean something in Geometry�察�what does it mean�拭─�

;Nothing   at   all�察─  �replied   I�察   �not   at   least   in   Geometry�察  �for   Geometry   has 

only Two Dimensions。; And then I began to shew the boy how a Point by 

moving   through   a   length   of   three   inches   makes   a   Line   of   three   inches�察�

which   may   be   represented   by   three�察  �and   how   a   Line   of   three   inches�察�

moving parallel to itself through a length of three inches�察�makes a Square 

of   three   inches   every   way�察  �which   may   be   represented   by   three´to´the´ 

second。      xxx    Upon     this�察 �my    Grandson�察     �again    returning     to  his   former 

suggestion�察 �took   me   up   rather suddenly  and   exclaimed�察  �Well�察 �then�察 �if   a 

Point by moving three inches�察�makes a Line of three inches represented by 

three�察  �and   if   a   straight   Line   of   three   inches�察  �moving   parallel   to   itself�察�

makes   a   Square   of   three   inches   every   way�察  �represented   by   three´to´the´ 

second�察     �it  must   be   that   a  Square     of  three   inches    every    way�察   �moving 

somehow parallel to itself ��but I don't see how�� must make Something else 

��but    I  don't   see   what��     of  three    inches    every    wayand      this   must    be 

represented by three´to´the´third。; 

     ;Go to bed�察─�said I�察�a little ruffled by this interruption�此 �if you would 

talk less nonsense�察�you would remember more sense。; 

     So my  Grandson had   disappeared in   disgrace�察�and there   I sat   by  my 

Wife's side�察�endeavouring to form a retrospect of the year 1999 and of the 

possibilities of the year 2000�察�but not quite able to shake of the thoughts 

suggested   by   the   prattle   of   my   bright   little   Hexagon。   Only   a   few   sands 

now   remained   in   the   half´hour   glass。   Rousing   myself   from  my  reverie   I 

turned the glass Northward for the last time in the old Millennium�察�and in 

the act�察�I exclaimed aloud�察 �The boy is a fool。; 

     Straightway   I   became   conscious   of   a   Presence   in   the   room�察  �and   a 



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chilling breath thrilled through my very being。 ;He is no such thing�察─�cried 

my Wife�察 �and you are breaking the Commandments in thus dishonouring 

your own Grandson。; But I took no notice of her。 Looking around in every 

direction I could see nothing�察�yet still I FELT a Presence�察�and shivered as 

the cold whisper came again。 I started up。 ;What is the matter�拭─�said my 

Wife�察 �there is no draught�察�what are you looking for�拭�There is nothing。; 

There was nothing�察�and I resumed my seat�察�again exclaiming�察 �The boy is 

a   fool�察  �I   say�察  �three´   to´the´third   can   have   no   meaning   in   Geometry。; At 

once   there   came   a   distinctly   audible   reply�察   �The   boy   is   not   a   fool�察  �and 

three´to´the´third has an obvious Geometrical meaning。; 

     My   Wife   as   well   as   myself   heard   the   words�察  �although   she   did   not 

understand their meaning�察�and both of us sprang forward in the direction 

of the sound。 What was our horror when we saw before us a Figure� �At the 

first   glance   it   appeared   to   be   a   Woman�察  �seen   sideways�察  �but   a   moment's 

observation       shewed     me    that   the  extremities     passed     into   dimness     too 

rapidly to represent one of the Female Sex�察�and I should have thought it a 

Circle�察�only that it seemed to change its size in a manner impossible for a 

Circle or for any regular Figure of which I had had experience。 

     But   my   Wife   had   not   my   experience�察  �nor   the   coolness   necessary   to 

note     these   characteristics。     With    the   usual    hastiness     and   unreasoning 

jealousy of her Sex�察�she flew at once to the conclusion that a Woman had 

entered the house through some small aperture。 ;How comes this person 

here�拭─�she exclaimed�察 �you promised me�察�my dear�察�that there should be no 

ventilators in our new house。; ;Nor are they any�察─�said I�察 �but what makes 

you   think   that   the   stranger   is   a   Woman�拭  �I   see   by   my   power   of   Sight 

Recognition ; 

     ;Oh�察  �I   have   no   patience   with   your   Sight   Recognition�察─  �replied   she�察�

;`Feeling is believing' and `A Straight Line to the touch is worth a Circle 

to    the   sight';two     Proverbs�察    �very   common       with    the   Frailer    Sex   in 

Flatland。 

     ;Well�察─  �said   I�察  �for   I   was   afraid   of   irritating   her�察   �if   it   must   be   so�察�

demand an introduction。; Assuming her most gracious manner�察�my Wife 

advanced towards the Stranger�察 �Permit me�察�Madam to feel and be felt by´ 



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                                              Flatland 



´;   then�察  �suddenly   recoiling�察   �Oh�   �it   is   not   a   Woman�察  �and   there   are   no 

angles either�察�not a trace of one。 Can it be that I have so misbehaved to a 

perfect Circle�拭─�

     ;I   am   indeed�察  �in   a   certain   sense   a   Circle
卦指朕村 貧匯匈 和匯匈 指欺競何 壘��0�� 家��0��
隆堋響頼��紗秘慕禰厮宴和肝写偬堋響��
梁椣戻幣�� 梁心弌傍議揖扮窟燕得胎��傍竃徭失議心隈才凪万弌誌育断蛍�輌臆惨軼僑〃�燕慕得珊辛參資誼持蛍才将刮襲潜��範寔亟圻幹慕得 瓜寡追葎娼得辛參資誼寄楚署衛、持蛍才将刮襲潜填��