????

??????? ???????????? ???


?????? ??????? ??? ???????? ??????? ??????? ??????? , ??? ????? ?? ?????? ???? ????????? [1]

?????? (quantity), ??? (structure), ???????? (change) ??? ????? (space)-?????? ???????? ???????? ???? ???? ???? ???? ???????? ??? ???? ?'? " ????? (figure) ??? ??????? (number) ??????", ?????? ???? ???? ????? ??? ??? ??????? ????? ?????? ????? ????? ???????????? ??? ????? ??? ??? ?????? ???? ????? ?????? (formal) ????????? ??? ???? ?'? ????????????? (logic) ??? ????? ??????-???????? (notation) ??????? ??? ?????????? -???? ?????????? ??????? ???????? (axiomatically defined abstract structures) ??????, ?????? ???? ?'? ??????? ???? ??????? ?????? ???? ??? ????? ??? ?'? ?? ????? ????????? ??? ??????? ????? ???? ??????? ?????? ???? ???? ?? ???????????? (realistic) ?????????? ??? ???? ?'? ??? ???? ????? ?? ?????? ??????, ???? ????????????? (reasoning) ?????????? ??? ??????? ???????? ???? ?????? ???? ?????? ?????? ??????, ?????? ??? ??????? ?????? ????, ??? ??????????? ??? ?'? ????? ????????? ??? ????? ??????? ??????? ????? ??????? ???? ???????? ???? ?????? ????? ??????? ???; ????? ????? "???????? ????", "?????? ????" ??? "????? ???????? ????" ???? ???? ????


????? ????? (????-????), ????????? ???

????? ?????? [ ???????? ??? ]

?????? "mathematics" ?????? Greek: μ?θημα (math?ma "knowledge, study, learning") ????? ??? ????? ??? ???? "???????, ?????, ?? ??????"; μαθηματικ?? (???????????)-? ???? "???????????"? ???????? "mathematics" ?? ???? ???? ?'?? ??????, ?????, ????? ??? ????????? ????????????? ????? ???? ?????? ??????

?????? ??? ????????? [ ???????? ??? ]

??????? ????? ??????? ?????????? (???-??? ??????????)


??????? ??????? ???? [ ???????? ??? ]

?? ??????? ????? ?'? ???????? ???? ?????? ?????????? ???????? ??? ?????? ????,?????? ??????? ????????? ?? ??????? ??? ??????

??????? ??????? ???? [ ???????? ??? ]


????? ????? ????????? [ ???????? ??? ]

???? [ ???????? ??? ]

?????? (??????: Number): ?,?,?,?,?,?,?,?,?,?

????? ?????? ??????????? [ ???????? ??? ]


?????? [ ???????? ??? ]


??? [ ???????? ??? ]


=== ?

===


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????????? [ ???????? ??? ]

  1. No likeness or description of Euclid's physical appearance made during his lifetime survived antiquity. Therefore, Euclid's depiction in works of art depends on the artist's imagination ( see Euclid ).

????????? [ ???????? ??? ]

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