meno-µÚ3ÕÂ
°´¼üÅÌÉÏ·½Ïò¼ü ¡û »ò ¡ú ¿É¿ìËÙÉÏÏ·ҳ£¬°´¼üÅÌÉ쵀 Enter ¼ü¿É»Øµ½±¾ÊéĿ¼ҳ£¬°´¼üÅÌÉÏ·½Ïò¼ü ¡ü ¿É»Øµ½±¾Ò³¶¥²¿£¡
¡ª¡ª¡ª¡ªÎ´ÔĶÁÍꣿ¼ÓÈëÊéÇ©ÒѱãÏ´μÌÐøÔĶÁ£¡
are¡¡said¡¡by¡¡you¡¡to¡¡be¡¡parts¡¡of¡¡virtue¡£
¡¡¡¡Men¡£¡¡What¡¡of¡¡that£¿
¡¡¡¡Soc¡£¡¡What¡¡of¡¡that£¡¡¡Why£»¡¡did¡¡not¡¡I¡¡ask¡¡you¡¡to¡¡tell¡¡me¡¡the¡¡nature¡¡of
virtue¡¡as¡¡a¡¡whole£¿¡¡And¡¡you¡¡are¡¡very¡¡far¡¡from¡¡telling¡¡me¡¡this£»¡¡but
declare¡¡every¡¡action¡¡to¡¡be¡¡virtue¡¡which¡¡is¡¡done¡¡with¡¡a¡¡part¡¡of¡¡virtue£»
as¡¡though¡¡you¡¡had¡¡told¡¡me¡¡and¡¡I¡¡must¡¡already¡¡know¡¡the¡¡whole¡¡of¡¡virtue£»
and¡¡this¡¡too¡¡when¡¡frittered¡¡away¡¡into¡¡little¡¡pieces¡£¡¡And£»¡¡therefore£»
my¡¡dear¡¡I¡¡fear¡¡that¡¡I¡¡must¡¡begin¡¡again¡¡and¡¡repeat¡¡the¡¡same¡¡question£º
What¡¡is¡¡virtue£¿¡¡for¡¡otherwise£»¡¡I¡¡can¡¡only¡¡say£»¡¡that¡¡every¡¡action
done¡¡with¡¡a¡¡part¡¡of¡¡virtue¡¡is¡¡virtue£»¡¡what¡¡else¡¡is¡¡the¡¡meaning¡¡of
saying¡¡that¡¡every¡¡action¡¡done¡¡with¡¡justice¡¡is¡¡virtue£¿¡¡Ought¡¡I¡¡not¡¡to
ask¡¡the¡¡question¡¡over¡¡again£»¡¡for¡¡can¡¡any¡¡one¡¡who¡¡does¡¡not¡¡know
virtue¡¡know¡¡a¡¡part¡¡of¡¡virtue£¿
¡¡¡¡¡¡Men¡£¡¡No£»¡¡I¡¡do¡¡not¡¡say¡¡that¡¡he¡¡can¡£
¡¡¡¡¡¡Soc¡£¡¡Do¡¡you¡¡remember¡¡how£»¡¡in¡¡the¡¡example¡¡of¡¡figure£»¡¡we¡¡rejected¡¡any
answer¡¡given¡¡in¡¡terms¡¡which¡¡were¡¡as¡¡yet¡¡unexplained¡¡or¡¡unadmitted£¿
¡¡¡¡¡¡Men¡£¡¡Yes£»¡¡Socrates£»¡¡and¡¡we¡¡were¡¡quite¡¡right¡¡in¡¡doing¡¡so¡£
¡¡¡¡¡¡Soc¡£¡¡But¡¡then£»¡¡my¡¡friend£»¡¡do¡¡not¡¡suppose¡¡that¡¡we¡¡can¡¡explain¡¡to¡¡any
one¡¡the¡¡nature¡¡of¡¡virtue¡¡as¡¡a¡¡whole¡¡through¡¡some¡¡unexplained¡¡portion
of¡¡virtue£»¡¡or¡¡anything¡¡at¡¡all¡¡in¡¡that¡¡fashion£»¡¡we¡¡should¡¡only¡¡have
to¡¡ask¡¡over¡¡again¡¡the¡¡old¡¡question£»¡¡What¡¡is¡¡virtue£¿¡¡Am¡¡I¡¡not¡¡right£¿
¡¡¡¡¡¡Men¡£¡¡I¡¡believe¡¡that¡¡you¡¡are¡£
¡¡¡¡¡¡Soc¡£¡¡Then¡¡begin¡¡again£»¡¡and¡¡answer¡¡me£»¡¡What£»¡¡according¡¡to¡¡you¡¡and
your¡¡friend¡¡Gorgias£»¡¡is¡¡the¡¡definition¡¡of¡¡virtue£¿
¡¡¡¡¡¡Men¡£¡¡O¡¡Socrates£»¡¡I¡¡used¡¡to¡¡be¡¡told£»¡¡before¡¡I¡¡knew¡¡you£»¡¡that¡¡you
were¡¡always¡¡doubting¡¡yourself¡¡and¡¡making¡¡others¡¡doubt£»¡¡and¡¡now¡¡you¡¡are
casting¡¡your¡¡spells¡¡over¡¡me£»¡¡and¡¡I¡¡am¡¡simply¡¡getting¡¡bewitched¡¡and
enchanted£»¡¡and¡¡am¡¡at¡¡my¡¡wits'¡¡end¡£¡¡And¡¡if¡¡I¡¡may¡¡venture¡¡to¡¡make¡¡a¡¡jest
upon¡¡you£»¡¡you¡¡seem¡¡to¡¡me¡¡both¡¡in¡¡your¡¡appearance¡¡and¡¡in¡¡your¡¡power
over¡¡others¡¡to¡¡be¡¡very¡¡like¡¡the¡¡flat¡¡torpedo¡¡fish£»¡¡who¡¡torpifies¡¡those
who¡¡come¡¡near¡¡him¡¡and¡¡touch¡¡him£»¡¡as¡¡you¡¡have¡¡now¡¡torpified¡¡me£»¡¡I
think¡£¡¡For¡¡my¡¡soul¡¡and¡¡my¡¡tongue¡¡are¡¡really¡¡torpid£»¡¡and¡¡I¡¡do¡¡not
know¡¡how¡¡to¡¡answer¡¡you£»¡¡and¡¡though¡¡I¡¡have¡¡been¡¡delivered¡¡of¡¡an
infinite¡¡variety¡¡of¡¡speeches¡¡about¡¡virtue¡¡before¡¡now£»¡¡and¡¡to¡¡many
persons¡and¡¡very¡¡good¡¡ones¡¡they¡¡were£»¡¡as¡¡I¡¡thought¡at¡¡this¡¡moment¡¡I
cannot¡¡even¡¡say¡¡what¡¡virtue¡¡is¡£¡¡And¡¡I¡¡think¡¡that¡£¡¡you¡¡are¡¡very¡¡wise¡¡in
not¡¡voyaging¡¡and¡¡going¡¡away¡¡from¡¡home£»¡¡for¡¡if¡¡you¡¡did¡¡in¡¡other
places¡¡as¡¡do¡¡in¡¡Athens£»¡¡you¡¡would¡¡be¡¡cast¡¡into¡¡prison¡¡as¡¡a¡¡magician¡£
¡¡¡¡Soc¡£¡¡You¡¡are¡¡a¡¡rogue£»¡¡Meno£»¡¡and¡¡had¡¡all¡¡but¡¡caught¡¡me¡£
¡¡¡¡Men¡£¡¡What¡¡do¡¡you¡¡mean£»¡¡Socrates£¿
¡¡¡¡Soc¡£¡¡I¡¡can¡¡tell¡¡why¡¡you¡¡made¡¡a¡¡simile¡¡about¡¡me¡£
¡¡¡¡Men¡£¡¡Why£¿
¡¡¡¡Soc¡£¡¡In¡¡order¡¡that¡¡I¡¡might¡¡make¡¡another¡¡simile¡¡about¡¡you¡£¡¡For¡¡I¡¡know
that¡¡all¡¡pretty¡¡young¡¡gentlemen¡¡like¡¡to¡¡have¡¡pretty¡¡similes¡¡made¡¡about
them¡as¡¡well¡¡they¡¡may¡but¡¡I¡¡shall¡¡not¡¡return¡¡the¡¡compliment¡£¡¡As¡¡to
my¡¡being¡¡a¡¡torpedo£»¡¡if¡¡the¡¡torpedo¡¡is¡¡torpid¡¡as¡¡well¡¡as¡¡the¡¡cause¡¡of
torpidity¡¡in¡¡others£»¡¡then¡¡indeed¡¡I¡¡am¡¡a¡¡torpedo£»¡¡but¡¡not¡¡otherwise£»
for¡¡I¡¡perplex¡¡others£»¡¡not¡¡because¡¡I¡¡am¡¡clear£»¡¡but¡¡because¡¡I¡¡am¡¡utterly
perplexed¡¡myself¡£¡¡And¡¡now¡¡I¡¡know¡¡not¡¡what¡¡virtue¡¡is£»¡¡and¡¡you¡¡seem¡¡to
be¡¡in¡¡the¡¡same¡¡case£»¡¡although¡¡you¡¡did¡¡once¡¡perhaps¡¡know¡¡before¡¡you
touched¡¡me¡£¡¡However£»¡¡I¡¡have¡¡no¡¡objection¡¡to¡¡join¡¡with¡¡you¡¡in¡¡the
enquiry¡£
¡¡¡¡Men¡£¡¡And¡¡how¡¡will¡¡you¡¡enquire£»¡¡Socrates£»¡¡into¡¡that¡¡which¡¡you¡¡do
not¡¡know£¿¡¡What¡¡will¡¡you¡¡put¡¡forth¡¡as¡¡the¡¡subject¡¡of¡¡enquiry£¿¡¡And¡¡if
you¡¡find¡¡what¡¡you¡¡want£»¡¡how¡¡will¡¡you¡¡ever¡¡know¡¡that¡¡this¡¡is¡¡the
thing¡¡which¡¡you¡¡did¡¡not¡¡know£¿
¡¡¡¡Soc¡£¡¡I¡¡know£»¡¡Meno£»¡¡what¡¡you¡¡mean£»¡¡but¡¡just¡¡see¡¡what¡¡a¡¡tiresome
dispute¡¡you¡¡are¡¡introducing¡£¡¡You¡¡argue¡¡that¡¡man¡¡cannot¡¡enquire
either¡¡about¡¡that¡¡which¡¡he¡¡knows£»¡¡or¡¡about¡¡that¡¡which¡¡he¡¡does¡¡not
know£»¡¡for¡¡if¡¡he¡¡knows£»¡¡he¡¡has¡¡no¡¡need¡¡to¡¡enquire£»¡¡and¡¡if¡¡not£»¡¡he
cannot£»¡¡for¡¡he¡¡does¡¡not¡¡know¡¡the£»¡¡very¡¡subject¡¡about¡¡which¡¡he¡¡is¡¡to
enquire¡£
¡¡¡¡Men¡£¡¡Well£»¡¡Socrates£»¡¡and¡¡is¡¡not¡¡the¡¡argument¡¡sound£¿
¡¡¡¡Soc¡£¡¡I¡¡think¡¡not¡£
¡¡¡¡Men¡£¡¡Why¡¡not£¿
¡¡¡¡Soc¡£¡¡I¡¡will¡¡tell¡¡you¡¡why£º¡¡I¡¡have¡¡heard¡¡from¡¡certain¡¡wise¡¡men¡¡and
women¡¡who¡¡spoke¡¡of¡¡things¡¡divine¡¡that¡
¡¡¡¡Men¡£¡¡What¡¡did¡¡they¡¡say£¿
¡¡¡¡Soc¡£¡¡They¡¡spoke¡¡of¡¡a¡¡glorious¡¡truth£»¡¡as¡¡I¡¡conceive¡£
¡¡¡¡Men¡£¡¡What¡¡was¡¡it£¿¡¡and¡¡who¡¡were¡¡they£¿
¡¡¡¡Soc¡£¡¡Some¡¡of¡¡them¡¡were¡¡priests¡¡and¡¡priestesses£»¡¡who¡¡had¡¡studied
how¡¡they¡¡might¡¡be¡¡able¡¡to¡¡give¡¡a¡¡reason¡¡of¡¡their¡¡profession£º¡¡there£»
have¡¡been¡¡poets¡¡also£»¡¡who¡¡spoke¡¡of¡¡these¡¡things¡¡by¡¡inspiration£»¡¡like
Pindar£»¡¡and¡¡many¡¡others¡¡who¡¡were¡¡inspired¡£¡¡And¡¡they¡¡say¡mark£»¡¡now£»¡¡and
see¡¡whether¡¡their¡¡words¡¡are¡¡true¡they¡¡say¡¡that¡¡the¡¡soul¡¡of¡¡man¡¡is
immortal£»¡¡and¡¡at¡¡one¡¡time¡¡has¡¡an¡¡end£»¡¡which¡¡is¡¡termed¡¡dying£»¡¡and¡¡at
another¡¡time¡¡is¡¡born¡¡again£»¡¡but¡¡is¡¡never¡¡destroyed¡£¡¡And¡¡the¡¡moral
is£»¡¡that¡¡a¡¡man¡¡ought¡¡to¡¡live¡¡always¡¡in¡¡perfect¡¡holiness¡£¡¡¡¨For¡¡in¡¡the
ninth¡¡year¡¡Persephone¡¡sends¡¡the¡¡souls¡¡of¡¡those¡¡from¡¡whom¡¡she¡¡has
received¡¡the¡¡penalty¡¡of¡¡ancient¡¡crime¡¡back¡¡again¡¡from¡¡beneath¡¡into¡¡the
light¡¡of¡¡the¡¡sun¡¡above£»¡¡and¡¡these¡¡are¡¡they¡¡who¡¡become¡¡noble¡¡kings
and¡¡mighty¡¡men¡¡and¡¡great¡¡in¡¡wisdom¡¡and¡¡are¡¡called¡¡saintly¡¡heroes¡¡in
after¡¡ages¡£¡¨¡¡The¡¡soul£»¡¡then£»¡¡as¡¡being¡¡immortal£»¡¡and¡¡having¡¡been¡¡born
again¡¡many¡¡times£»¡¡rand¡¡having¡¡seen¡¡all¡¡things¡¡that¡¡exist£»¡¡whether¡¡in
this¡¡world¡¡or¡¡in¡¡the¡¡world¡¡below£»¡¡has¡¡knowledge¡¡of¡¡them¡¡all£»¡¡and¡¡it¡¡is
no¡¡wonder¡¡that¡¡she¡¡should¡¡be¡¡able¡¡to¡¡call¡¡to¡¡remembrance¡¡all¡¡that
she¡¡ever¡¡knew¡¡about¡¡virtue£»¡¡and¡¡about¡¡everything£»¡¡for¡¡as¡¡all¡¡nature¡¡is
akin£»¡¡and¡¡the¡¡soul¡¡has¡¡learned¡¡all¡¡things£»¡¡there¡¡is¡¡no¡¡difficulty¡¡in
her¡¡eliciting¡¡or¡¡as¡¡men¡¡say¡¡learning£»¡¡out¡¡of¡¡a¡¡single¡¡recollection
¡all¡¡the¡¡rest£»¡¡if¡¡a¡¡man¡¡is¡¡strenuous¡¡and¡¡does¡¡not¡¡faint£»¡¡for¡¡all
enquiry¡¡and¡¡all¡¡learning¡¡is¡¡but¡¡recollection¡£¡¡And¡¡therefore¡¡we¡¡ought
not¡¡to¡¡listen¡¡to¡¡this¡¡sophistical¡¡argument¡¡about¡¡the¡¡impossibility
of¡¡enquiry£º¡¡for¡¡it¡¡will¡¡make¡¡us¡¡idle£»¡¡and¡¡is¡¡sweet¡¡only¡¡to¡¡the
sluggard£»¡¡but¡¡the¡¡other¡¡saying¡¡will¡¡make¡¡us¡¡active¡¡and¡¡inquisitive¡£¡¡In
that¡¡confiding£»¡¡I¡¡will¡¡gladly¡¡enquire¡¡with¡¡you¡¡into¡¡the¡¡nature¡¡of
virtue¡£
¡¡¡¡Men¡£¡¡Yes£»¡¡Socrates£»¡¡but¡¡what¡¡do¡¡you¡¡mean¡¡by¡¡saying¡¡that¡¡we¡¡do¡¡not
learn£»¡¡and¡¡that¡¡what¡¡we¡¡call¡¡learning¡¡is¡¡only¡¡a¡¡process¡¡of
recollection£¿¡¡Can¡¡you¡¡teach¡¡me¡¡how¡¡this¡¡is£¿
¡¡¡¡Soc¡£¡¡I¡¡told¡¡you£»¡¡Meno£»¡¡just¡¡now¡¡that¡¡you¡¡were¡¡a¡¡rogue£»¡¡and¡¡now¡¡you
ask¡¡whether¡¡I¡¡can¡¡teach¡¡you£»¡¡when¡¡I¡¡am¡¡saying¡¡that¡¡there¡¡is¡¡no
teaching£»¡¡but¡¡only¡¡recollection£»¡¡and¡¡thus¡¡you¡¡imagine¡¡that¡¡you¡¡will
involve¡¡me¡¡in¡¡a¡¡contradiction¡£
¡¡¡¡Men¡£¡¡Indeed£»¡¡Socrates£»¡¡I¡¡protest¡¡that¡¡I¡¡had¡¡no¡¡such¡¡intention¡£¡¡I
only¡¡asked¡¡the¡¡question¡¡from¡¡habit£»¡¡but¡¡if¡¡you¡¡can¡¡prove¡¡to¡¡me¡¡that
what¡¡you¡¡say¡¡is¡¡true£»¡¡I¡¡wish¡¡that¡¡you¡¡would¡£
¡¡¡¡Soc¡£¡¡It¡¡will¡¡be¡¡no¡¡easy¡¡matter£»¡¡but¡¡I¡¡will¡¡try¡¡to¡¡please¡¡you¡¡to
the¡¡utmost¡¡of¡¡my¡¡power¡£¡¡Suppose¡¡that¡¡you¡¡call¡¡one¡¡of¡¡your¡¡numerous
attendants£»¡¡that¡¡I¡¡may¡¡demonstrate¡¡on¡¡him¡£
¡¡¡¡Men¡£¡¡Certainly¡£¡¡Come¡¡hither£»¡¡boy¡£
¡¡¡¡Soc¡£¡¡He¡¡is¡¡Greek£»¡¡and¡¡speaks¡¡Greek£»¡¡does¡¡he¡¡not£¿
¡¡¡¡Men¡£¡¡Yes£»¡¡indeed£»¡¡he¡¡was¡¡born¡¡in¡¡the¡¡house¡£
¡¡¡¡Soc¡£¡¡Attend¡¡now¡¡to¡¡the¡¡questions¡¡which¡¡I¡¡ask¡¡him£»¡¡and¡¡observe
whether¡¡he¡¡learns¡¡of¡¡me¡¡or¡¡only¡¡remembers¡£
¡¡¡¡Men¡£¡¡I¡¡will¡£
¡¡¡¡Soc¡£¡¡Tell¡¡me£»¡¡boy£»¡¡do¡¡you¡¡know¡¡that¡¡a¡¡figure¡¡like¡¡this¡¡is¡¡a¡¡square£¿
¡¡¡¡Boy¡£¡¡I¡¡do¡£
¡¡¡¡Soc¡£¡¡And¡¡you¡¡know¡¡that¡¡a¡¡square¡¡figure¡¡has¡¡these¡¡four¡¡lines¡¡equal£¿
¡¡¡¡Boy¡£¡¡Certainly¡£
¡¡¡¡Soc¡£¡¡And¡¡these¡¡lines¡¡which¡¡I¡¡have¡¡drawn¡¡through¡¡the¡¡middle¡¡of¡¡the
square¡¡are¡¡also¡¡equal£¿
¡¡¡¡Boy¡£¡¡Yes¡£
¡¡¡¡Soc¡£¡¡A¡¡square¡¡may¡¡be¡¡of¡¡any¡¡size£¿
¡¡¡¡Boy¡£¡¡Certainly¡£
¡¡¡¡Soc¡£¡¡And¡¡if¡¡one¡¡side¡¡of¡¡the¡¡figure¡¡be¡¡of¡¡two¡¡feet£»¡¡and¡¡the¡¡other
side¡¡be¡¡of¡¡two¡¡feet£»¡¡how¡¡much¡¡will¡¡the¡¡whole¡¡be£¿¡¡Let¡¡me¡¡explain£º¡¡if¡¡in
one¡¡direction¡¡the¡¡space¡¡was¡¡of¡¡two¡¡feet£»¡¡and¡¡in¡¡other¡¡direction¡¡of¡¡one
foot£»¡¡the¡¡whole¡¡would¡¡be¡¡of¡¡two¡¡feet¡¡taken¡¡once£¿
¡¡¡¡Boy¡£¡¡Yes¡£
¡¡¡¡Soc¡£¡¡But¡¡since¡¡this¡¡side¡¡is¡¡also¡¡of¡¡two¡¡feet£»¡¡there¡¡are¡¡twice¡¡two
feet£¿
¡¡¡¡Boy¡£¡¡There¡¡are¡£
¡¡¡¡Soc¡£¡¡Then¡¡the¡¡square¡¡is¡¡of¡¡twice¡¡two¡¡feet£¿
¡¡¡¡Boy¡£¡¡Yes¡£
¡¡¡¡Soc¡£¡¡And¡¡how¡¡many¡¡are¡¡twice¡¡two¡¡feet£¿¡¡count¡¡and¡¡tell¡¡me¡£
¡¡¡¡Boy¡£¡¡Four£»¡¡Socrates¡£
¡¡¡¡Soc¡£¡¡And¡¡might¡¡there¡¡not¡¡be¡¡another¡¡square¡¡twice¡¡as¡¡large¡¡as¡¡this£»
and¡¡having¡¡like¡¡this¡¡the¡¡lines¡¡equal£¿
¡¡¡¡Boy¡£¡¡Yes¡£
¡¡¡¡Soc¡£¡¡And¡¡of¡¡how¡¡many¡¡feet¡¡will¡¡that¡¡be£¿
¡¡¡¡Boy¡£¡¡Of¡¡eight¡¡feet¡£
¡¡¡¡Soc¡£¡¡And¡¡now¡¡try¡¡and¡¡tell¡¡me¡¡the¡¡length¡¡of¡¡the¡¡line¡¡which¡¡forms
the¡¡side¡¡of¡¡that¡¡double¡¡square£º¡¡this¡¡is¡¡two¡¡feet¡what¡¡will¡¡that¡¡be£¿
¡¡¡¡Boy¡£¡¡Clearly£»¡¡Socrates£»¡¡it¡¡will¡¡be¡¡double¡£
¡¡¡¡Soc¡£¡¡Do¡¡you¡¡observe£»¡¡Meno£»¡¡that¡¡I¡¡am¡¡not¡¡teaching¡¡the¡¡boy
anything£»¡¡but¡¡only¡¡asking¡¡him¡¡questions£»¡¡and¡¡now¡¡he¡¡fancies¡¡that¡¡he
knows¡¡how¡¡long¡¡a¡¡line¡¡is¡¡necessary¡¡in¡¡order¡¡to¡¡produce¡¡a¡¡figure¡¡of
eight¡¡square¡¡feet£»¡¡does¡¡he¡¡not£¿
¡¡¡¡Men¡£¡¡Yes¡£
¡¡¡¡Soc¡£¡¡And¡¡does¡¡he¡¡really¡¡know£¿
¡¡¡¡Men¡£¡¡Certainly¡¡not¡£
¡¡¡¡Soc¡£¡¡He¡¡only¡¡guesses¡¡that¡¡because¡¡the¡¡square¡¡is¡¡double£»¡¡the¡¡line
is¡¡double¡£
¡¡¡¡Men¡£¡¡True¡£
¡¡¡¡Soc¡£¡¡Observe¡¡him¡¡while¡¡he¡¡recalls¡¡the¡¡steps¡¡in¡¡regular¡¡order¡£¡¡£¨To
the¡¡Boy¡££©¡¡Tell¡¡me£»¡¡boy£»¡¡do¡¡you¡¡assert¡¡that¡¡a¡¡double¡¡space¡¡comes¡¡from¡¡a
double¡¡line£¿¡¡Remember¡¡that¡¡I¡¡am¡¡not¡¡speaking¡¡of¡¡an¡¡oblong£»¡¡but¡¡of¡¡a
figure¡¡equal¡¡every¡¡way£»¡¡and¡¡twice¡¡the¡¡size¡¡of¡¡this¡that¡¡is¡¡to¡¡say¡¡of
eight¡¡feet£»¡¡and¡¡I¡¡want¡¡to¡¡know¡¡whether¡¡you¡¡still¡¡say¡¡that¡¡a¡¡double
square¡¡comes¡¡from¡¡double¡¡line£¿
¡¡¡¡Boy¡£¡¡Yes¡£
¡¡¡¡Soc¡£¡¡But¡¡does¡¡not¡¡this¡¡line¡¡become¡¡doubled¡¡if¡¡we¡¡add¡¡another¡¡such
line¡¡here£¿
¡¡¡¡Boy¡£¡¡Certainly¡£
¡¡¡¡Soc¡£¡¡And¡¡four¡¡such¡¡lines¡¡will¡¡make¡¡a¡¡space¡¡containing¡¡eight¡¡feet£¿
¡¡¡¡Boy¡£¡¡Yes¡£
¡¡¡¡Soc¡£¡¡Let¡¡us¡¡describe¡¡such¡¡a¡¡figure£º¡¡Would¡¡you¡¡not¡¡say¡¡that¡¡this¡¡is
the¡¡figure¡¡of¡¡eight¡¡feet£¿
¡¡¡¡Boy¡£¡¡Yes¡£
¡¡¡¡Soc¡£¡¡And¡¡are¡¡there¡¡not¡¡these¡¡four¡¡divisions¡¡in¡¡the¡¡figure£»¡¡each¡¡of
which¡¡is¡¡equal¡¡to¡¡the¡¡figure¡¡of¡¡four¡¡feet£¿
¡¡¡¡Boy¡£¡¡True¡£
¡¡¡¡Soc¡£¡¡And¡¡is¡¡not¡¡that¡¡four¡¡times¡¡four£¿
¡¡¡¡Boy¡£¡¡Certainly¡£
¡¡¡¡Soc¡£¡¡And¡¡four¡¡times¡¡is¡¡not¡¡double£¿
¡¡¡¡Boy¡£¡¡No£»¡¡indeed¡£
¡¡¡¡Soc¡£¡¡But¡¡how¡¡much£¿
¡¡¡¡Boy¡£¡¡Four¡¡times¡¡as¡¡much¡£
¡¡¡¡Soc¡£¡¡Therefore¡¡the¡¡double¡¡line£»¡¡boy£»¡¡has¡¡given¡¡a¡¡space£»¡¡not¡¡twice£»
but¡¡four¡¡times¡¡as¡¡much¡£
¡¡¡¡Boy¡£¡¡True¡£
¡¡¡¡Soc¡£¡¡Four¡¡times¡¡four¡¡are¡¡sixteen¡are¡¡they¡¡not£¿
¡¡¡¡Boy¡£¡¡Yes¡£
¡¡¡¡Soc¡£¡¡What¡¡line¡¡would¡¡give¡¡you¡¡a¡¡space¡¡of¡¡right¡¡feet£»¡¡as¡¡this¡¡gives
one¡¡of¡¡sixteen¡¡feet£»¡do¡¡you¡¡see£¿
¡¡¡¡Boy¡£¡¡Yes¡£
¡¡¡¡Soc¡£¡¡And¡¡the¡¡space¡¡of¡¡four¡¡feet¡¡is¡¡made¡¡from¡¡this¡¡half¡¡line£¿
¡¡¡¡Boy¡£¡¡Yes¡£
¡¡¡¡Soc¡£¡¡Good£»¡¡and¡¡is¡¡not¡¡a¡¡space¡¡of¡¡eight¡¡feet¡¡twice¡¡the¡¡size¡¡of
this£»¡¡and¡¡half¡¡the¡¡size¡¡of¡¡the¡¡other£¿
¡¡¡¡Boy¡£¡¡Certainly¡£
¡¡¡¡Soc¡£¡¡Such¡¡a¡¡space£»¡¡then£»¡¡will¡¡be¡¡made¡¡out¡¡of¡¡a¡¡line¡¡greater¡¡than
this¡¡one£»¡¡and¡¡less¡¡than¡¡that¡¡one£¿
¡¡¡¡Boy¡£¡¡Yes£»¡¡I¡¡think¡¡so¡£
¡¡¡¡Soc¡£¡¡Very¡¡good£»¡¡I¡¡like¡¡to¡¡hear¡¡you¡¡say¡¡what¡¡you¡¡think¡£¡¡And¡¡now
tell¡¡me£»¡¡is¡¡not¡¡this¡¡a¡¡line¡¡of¡¡two¡¡feet¡¡and¡¡that¡¡of¡¡four£¿
¡¡¡¡Boy¡£¡¡Yes¡£
¡¡¡¡Soc¡£¡¡Then¡¡the¡¡line¡¡which¡¡forms¡¡the¡¡side¡¡of¡¡eight¡¡feet¡¡ought¡¡to¡¡be
more¡¡than¡¡this¡¡line¡¡of¡¡two¡¡feet£»¡¡and¡¡less¡¡than¡¡the¡¡other¡¡of¡¡four¡¡feet£¿
¡¡¡¡Boy¡£¡¡It¡¡ought¡£
¡¡¡¡Soc¡£¡¡Try¡¡and¡¡see¡¡if¡¡you¡¡can¡¡tell¡¡me¡¡how¡¡much¡¡it¡¡will¡¡be¡£
¡¡¡¡Boy¡£¡¡Three¡¡feet¡£
¡¡¡¡Soc¡£¡¡Then¡¡if¡¡we¡¡add¡¡a¡¡half¡¡to¡¡this¡¡line¡¡of¡¡two£»¡¡that¡¡will¡¡be¡¡the
line¡¡of¡¡three¡£¡¡Here¡¡are¡¡two¡¡