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

????? ?????? ?????? (????? ????? ?????? ?????? ) ?? ????? ?? ???? ????? ?? ??????? ???????? ???? ?? ???? ???? ???????? ??????? ???????? . ??? ???? ??? ??????? ?????? ?? ??? ???????? ???????? ???????. ^[1]

?????? ?????? ???? ??? ?? ??? ???? ??? ???? s ????? V ? ??????? ?? ????? ???? ???? ???? ?? ????? ???? 2V ???????? ???? ??? ??? ?????? ?????? $s\cdot {\sqrt[{3}]{2}}$ . ??????? ?????? ????? ??????? ???? ???????? ??????? ???????? ??? ?? ???????? ????? ??? ???? ${\sqrt[{3}]{2}}$ ???????? ????????.

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

???? ??? ?????? ???? ??? ????? ???????? ???? ??????? ??? ????? .

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

???? ??? ??????? ???? ?????? ????? ? ????? ???????? ????? ???? ?? ????? ??????? ???? ????? ????? . ^[2] ????? ???????? ^[3]? ??? ?????? ????? ?? ?? ???????? ????? ???? ?? ?? ???????? ???????? ???????? ?????? ????? ?????? ??? ????? ???????. ????? ??????? ???? ????? ?????? ??? ???? ?????? ????? ??? ??? ??? ???? ????. ?????? ????????? ????? ????????? ??????? ? ????? ????? ??? ?? ??????? ??? ??? ????? ?? ????? ??????? ????? ??? ?????? ?????? ?????? ??????? ?????????? ?????? ?????? ??????????. ^[4]

????? ???????? ? ??? ??????? ??????? ??? ????????? ???????? ????????? ? ?????? ??????????? ?????? ??????? ???? ???? ???? ????? ??? . ^[5] ???? ???? ??? ?? ????? ?? ?? ??????? ???? ????? ???? ???? ?? ?? ??? ??? 350 ?. ? ?? ???? ????? ( ?. 388). ^[6] ??? ???? ????? ???? ???? ?? ????? (????? ???????? ??????????? ) ???? ?? ??????? ????? ???? ????? ???? ????? ???? ?????. ^[7]

?????? ????? ?? ?????? ??? ??? ?????? ?????? ??????? ?? ??? ?????? ????? ???????? ??????? ??? ???? ??????? ????? ????? ?? ?????. ^[8] ?? ????? ??????? ??????? ???? ??? ?? ?? ????? ?????? ????????? ?????? a ?2 a ? ??? ?????? ?????? ????? ????? ?????? ????????? ?????? r ? s ???? ??:

{\frac {a}{r}}={\frac {r}{s}}={\frac {s}{2a}}.

????? ? ???? ??? ??:

r=a\cdot {\sqrt[{3}]{2}}.

??? ?? ??? 1837 ???? ???? ?????? ?? ????? ???????? ?? 2 ??? ???? ??????? ? ???? ???? ??? ?? ???? ?????? ?????? ?????? .

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

????? [ ??? ]

^ Lucye Guilbeau (1930). "The History of the Solution of the Cubic Equation", Mathematics News Letter 5 (4), p. 8-12.
^ L. Zhmud The origin of the history of science in classical antiquity , p.84 , quoting ??????? and ???? ???????? ???? ?????? 2021-04-28 ??? ???? ??? ??? ???? .
^ ??????? , De E apud Delphos 386.E.4 ???? ?????? 2019-07-02 ??? ???? ??? ??? ???? .
^ ??????? , De genio Socratis 579.B
^ (Plut., Quaestiones convivales VIII.ii , 718ef) ???? ?????? 2019-07-28 ??? ???? ??? ??? ???? .
^ Carl Werner Muller, Die Kurzdialoge der Appendix Platonica , Munich: Wilhelm Fink, 1975, pp. 105?106
^ Knorr? Wilbur Richard (1986)? The Ancient Tradition of Geometric Problems ? Dover Books on Mathematics? Courier Dover Publications? p. 4 ? ISBN : 9780486675329 .
^ T.L. Heath A history of Greek mathematics , Vol. 1]

?? ????? ??? ?????? ??: ?????? ??????

[1] Lucye Guilbeau (1930). "The History of the Solution of the Cubic Equation", Mathematics News Letter 5 (4), p. 8-12.

[Zhmud-2] L. Zhmud The origin of the history of science in classical antiquity , p.84 , quoting ??????? and ???? ???????? ???? ?????? 2021-04-28 ??? ???? ??? ??? ???? .

[3] ??????? , De E apud Delphos 386.E.4 ???? ?????? 2019-07-02 ??? ???? ??? ??? ???? .

[4] ??????? , De genio Socratis 579.B

[5] (Plut., Quaestiones convivales VIII.ii , 718ef) ???? ?????? 2019-07-28 ??? ???? ??? ??? ???? .

[6] Carl Werner Muller, Die Kurzdialoge der Appendix Platonica , Munich: Wilhelm Fink, 1975, pp. 105?106

[7] Knorr? Wilbur Richard (1986)? The Ancient Tradition of Geometric Problems ? Dover Books on Mathematics? Courier Dover Publications? p. 4 ? ISBN : 9780486675329 .

[Heath-8] T.L. Heath A history of Greek mathematics , Vol. 1]

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