Ⲁϩⲓⲱⲓϣ ⲛϫⲉ ⲛⲓⲟⲩⲉⲓⲛⲓⲛ ⲧⲏⲣⲟⲩ ϫⲉ ⲛⲓⲥⲃⲱⲟⲩⲓ ⲛⲟⲩⲉⲓⲛⲓⲛ ⲁⲩϭⲓ ⲛⲭⲏⲙⲓ ⲁϥϣⲱⲛⲓ ⲛϫⲉ ⲡⲓϫⲓⲛⲉⲣϩⲱⲧ ⲛⲭⲏⲙⲓ ⲛⲟⲩⲉⲛⲕⲁⲓ ⲉϥⲕⲏⲃ ϧⲉⲛ ⲡⲱⲛϧ ⲛⲛⲓⲣⲉϥⲉⲙⲓ ⲛⲉⲙ ⲛⲓⲣⲉϥⲙⲉⲩⲓ ⲛⲟⲩⲉⲓⲛⲓⲛ ⲛⲧⲟⲩϭⲓⲥⲃⲱ ⲛϫⲉ Ⲛⲓⲣⲉϥⲉⲙⲓ ⲛⲛⲓϩⲓⲙⲛⲟϭⲣ.. ⲱⲣϥⲓⲓⲟⲥ ⲛⲉⲙ ϩⲟⲙⲓⲣⲟⲥ ⲛⲉⲙ ⲥⲟⲗⲟⲛ ⲛⲉⲙ ⲑⲁⲗⲏⲥ ⲁⲩϭⲓⲥⲃⲱ ⲉϯⲙⲉⲧⲣⲉϥⲫⲱⲛⲕ ⲛⲣⲉⲙⲛⲭⲏⲙⲓ ⲟⲩⲟϩ ⲁⲩⲓⲛⲓ ⲙⲡⲥⲟⲡⲧⲧ 3:4:5 ⲛⲓⲗⲗⲏⲧⲉ

Ⲉⲗⲍⲏⲛⲧⲉⲣ ⲃⲉⲧⲉⲟⲩⲓ (ⲛⲟϥⲉⲙⲡⲣ 1913 - ⲙⲏⲓ 1986)

Ⲑⲁⲗⲏⲥ ⲁϥⲓⲣⲓ ⲙⲡⲓⲕⲁⲛⲱⲛ ⲛϭⲱⲛⲧ ⲙⲫⲣⲏϯ ⲉϥⲟⲩⲟⲛϩ

Ⲛⲧⲁϥϫⲓⲙⲓ ⲙⲡϭⲣⲟϩ ⲙⲡⲓⲙⲉⲣ ⲫⲏⲉⲧⲁⲩⲥⲱⲟⲩⲛ ⲛⲓⲁϩ-Ⲙⲓⲥ ⲫⲏⲉⲧⲁϥⲥϧⲁⲓ ⲙⲡⲧⲟⲣϥ ⲣⲟⲛⲧ ⲛⲓⲧⲟⲡ ϧⲉⲛ ⲫⲃⲁⲕⲓ ⲙⲙⲏϯ.

Ϧⲉⲣ ⲛⲟⲩϣⲱⲡⲓ ⲛϫⲉ ⲛⲓϩⲓⲙ-ⲛⲟϭⲣ ⲛϩⲁⲛⲁⲕⲣⲓⲃⲏⲥ ⲛⲧⲟⲩϣ ⲧⲉⲙ ϯⲥⲃⲱ ⲉⲛⲁⲓⲥⲃⲟⲩⲓ ⲛⲕⲉⲛⲙⲑⲱⲛ ⲟⲩⲟϩ ϩⲁⲛϩⲓⲙ-ⲛⲟϭⲣ ⲁⲩϩⲏⲃ ⲛⲛⲓⲣⲉϥⲣⲁⲟⲩⲱ ⲙⲃⲉⲣⲓ ϩⲁ ⲛⲟⲩⲁⲣⲏⲟⲩ ϧⲉⲛ ⲕⲉϩⲟⲩⲧ-ⲛⲟϭⲣ ⲉⲩⲙⲉⲩⲓ ϫⲉ ⲛⲑⲱⲟⲩ ϩⲁⲛⲁⲡⲁⲥ ⲛⲉ. Ⲣ ⲡⲫⲟⲣⲡⲉⲣ 233-304 ⲁϥⲓ ⲉϩⲣⲉⲛ ⲛϫⲉ ⲛⲓⲥⲟ ⲓⲁϩ-Ⲙⲓⲥⲏ ⲛϥⲓⲥⲉⲋⲟⲣⲥ ⲫⲏⲉⲧϣⲁϥⲟⲩⲱⲧⲉⲃ ⲙϩⲟⲩⲧ-ⲛⲟϭⲣ ⲓⲟⲩⲛⲟⲩ ⲙⲟⲛ-ⲛⲟϥⲣ ⲟⲩⲟϩ ⲛⲩⲏⲥⲧ ⲁϥⲉⲣⲟⲩⲱⲓϣ ⲛⲁⲩ ϫⲱⲧ ⲥⲛⲁⲩ ⲛⲣⲟⲙⲡⲓ ϧⲉⲛ ⲛⲁⲓϩⲟⲩⲧ-ⲛⲟϭⲣ ⲛⲁϥϩⲟⲣⲡⲓ ⲛⲧⲁϥⲫⲱⲛⲕ ⲥⲑⲃⲉ: ϣⲁϥϫⲓⲙⲓ ⲛϫⲉ ⲡⲓⲭⲁⲓ ⲙⲙⲏϣϩⲟϫϩⲉϫ ⲙⲙⲉⲧⲣⲉϥⲫⲱⲛⲕ ϧⲁⲧⲉⲛ ⲛⲓⲣⲉⲙⲛⲭⲏⲙⲓ ⲛⲓⲧⲱⲡ ⲁⲩⲙⲟⲛⲕ ⲙⲙⲁⲩ ⲉⲓⲉⲙⲃⲓⲗⲉⲕⲥ

Ⲁⲩⲙⲉⲩⲓ ϫⲉ ⲛⲑⲟϥ ⲡⲉ ⲡⲓϩⲟⲩⲓⲧ ⲉⲧⲁϥⲓⲣⲓ ⲙⲡⲓϩⲓⲥⲃ ⲥⲁⲃⲟⲗ ⲙⲡⲓϩⲓⲥⲃ ⲙⲡⲓϫⲓⲛϫⲟⲩϣⲧ ⲉⲛϩⲱⲃ ⲛⲁⲣⲓⲥⲑⲱ ⲧⲉⲛϣϩⲓⲟⲓ ϫⲉ ⲡⲉϥϩⲱⲃ ⲛⲁϥϣⲱⲡⲓ ⲛⲛⲓⲑⲟⲛⲧⲉⲛ ⲛⲁⲡⲥ ⲉⲫⲙⲁ ⲁⲩⲥϧⲁⲓ ⲛⲛⲓⲁⲡⲥ ⲛϩⲁⲛⲧⲉⲗⲧⲉⲗ ⲉϥⲥⲙⲟⲛⲧ ⲙⲫⲣⲏϯ ⲛⲧⲉⲧⲣⲁⲕⲏⲥ ϥⲥⲙⲟⲧ ⲛⲟⲩⲥⲟⲡⲧⲧ ⲉϥϣⲟⲡ ⲛϥⲧⲟⲩ ⲛⲧⲉⲗⲧⲉⲗ ⲛⲧⲁϥⲉⲩϣⲏϣ ⲙⲏⲧ.

Ⲥϯⲙⲉⲩⲓ ⲛϫⲉ Ⲧⲁⲓϫⲓⲛⲉⲣϩⲱⲃ ⲛϩⲁⲛϩⲟϫϩⲉϫ ⲙⲙⲉⲧⲣⲉϥⲫⲱⲛⲕ ⲟⲩⲟϩ ⲛⲓⲧⲉⲗⲧⲉⲗ ⲉⲧⲥⲉⲉⲣⲥⲙⲟⲧ ⲛⲛⲓⲁⲗ ⲛⲏⲉⲧⲁϥⲓⲣⲓ ⲙⲙⲱⲟⲩ ⲛϫⲉ ϥⲓⲥⲉⲋⲱⲣⲥ ϧⲉⲛ ⲛⲉϥⲫⲟⲣⲡⲉⲣ ⲛⲟⲩⲱⲛϩ ⲛⲁⲩϣⲱⲡⲓ ⲡⲉ ⲛϩⲁⲛⲕⲱϫⲛⲗⲁⲕϩ ⲓⲟⲓⲟⲩ ⲛⲁϥϣⲱⲡⲓ ⲛϫⲉ ⲡⲓⲙⲁ ⲫⲏⲉⲧ ⲁⲩⲭⲱ ⲛⲟⲩⲧⲟⲃϥ ϩⲓⲱⲧⲥ ⲛϯⲕⲟⲓ.

Ⲡⲥⲁϫⲓ ϩⲁⲓⲡⲟ ⲧⲛⲏⲍ ϥⲙⲏⲓⲛⲓ ⲟⲩⲕⲁⲡ ⲣϥⲫⲟϭⲓ ⲟⲩⲃⲉ ⲙ ⲡⲕⲁⲡ ⲛϩⲁⲓⲡⲟ ⲧⲛⲏⲍ ⲁϥϭⲓⲥⲃⲱ ⲉϯⲧⲏⲟⲩ ⲛⲏⲉⲧⲥⲉϣⲱⲡⲓ ⲉϥⲗⲉⲙⲗⲏⲙ.

Ⲛⲓⲕⲉⲣⲉϥⲉⲙⲓ ⲛⲟⲩⲉⲓⲛⲓⲛ ⲉⲧⲁⲩϭⲓⲥⲃⲱ ⲛⲭⲏⲙⲓ ⲥⲉϣⲱⲏⲓ ⲓⲛⲓϥⲉⲧⲏⲍ ⲛⲉⲙ ϯⲙⲟⲕⲣⲉⲧ.

Ⲁϥϣⲟⲡ ⲛϫⲉ ⲡⲓϧⲁⲉ ⲛϩⲁⲛⲧⲓⲟⲩ ⲛⲣⲟⲙⲡⲓ ⲛⲧⲉϥϭⲓⲥⲃⲱ ⲉⲛⲓⲥⲃⲱ ⲛⲧⲉ ϯⲙⲉⲧⲣⲉϥⲫⲱⲛⲕ ⲛⲉⲙ ⲡⲓϩⲓⲥⲃ ⲛⲁϥϫⲟⲥ ⲡⲉ ⲉϥϣⲟⲩϣⲟⲩ ϫⲉ ⲁⲓⲥⲱⲧⲉⲙ ⲉϩⲁⲛⲭⲁⲓ ⲉϥⲥⲁⲃⲏⲟⲩⲧ ⲱⲡⲟⲩ ⲙⲙⲟⲛ ϩⲗⲓ ⲁϥⲥⲱⲕ ϧⲁϫⲱⲓ ϧⲉⲛ ⲡⲓϫⲓⲛⲕⲱⲧ ⲛⲧⲉ ⲛⲓⲥⲙⲟⲧ ⲛⲥⲓⲣⲁ ⲛⲉⲙ ⲛⲓⲉⲥⲕⲓ ⲣⲱ ⲓⲣⲟⲧⲉⲛ ⲙⲡⲓϣⲃⲟ ⲛⲣⲉⲙⲛⲭⲏⲙⲓ ⲙⲓ ⲁⲩϯⲣⲁⲛ ⲛⲁϥ

Ⲁϥϫⲟⲥ ⲛϫⲉ ⲥⲧⲁⲃⲟ ϫⲉ ⲁⲩⲫⲟⲣⲡⲉⲣ ⲉϫⲱⲓ ⲛⲛⲓⲏⲓ ⲉⲧⲁⲩϣⲟⲡ ⲛⲉⲙ ⲓⲧⲟⲝⲓⲥ. Ⲁϥϣⲟⲡ ⲛϫⲉ ⲡⲁⲓϧⲁⲉ ϣⲁ ⲙⲉⲧ ϣⲟⲙⲧ ⲛⲣⲟⲙⲡⲓ ⲛⲉⲙ ⲛⲓϩⲓⲙ-ⲛⲟϭⲣ ϧⲉⲛ ⲓⲟⲩⲛⲟⲩ ⲁϥⲙⲉⲩⲓ ⲉⲃⲟⲗ ⲛⲛⲓⲣⲉⲙⲛⲭⲏⲙⲓ ⲛϩⲁⲛϣⲱⲧ. Aristotle speaks of the origin of mathematics in Egypt. Euclid lived in Alexandria (Third century B.C.) where he founded a school of mathematics. He might have had training at Athens as a Platonist. His method was not Pythagorean but represented numbers by lines.

Ϩⲓⲣⲱϯⲧⲓⲧⲝ (II.109) ⲛⲉⲙ ⲥⲁⲃⲟ (XVII.3) ⲥⲉⲃⲱⲗ ⲉⲃⲟⲗ ϫⲉ ϯⲛⲟⲩⲛⲓ ⲛⲧⲉ ϯⲙⲉⲧⲣⲉϥⲫⲱⲛⲕ ⲥⲫⲱⲕⲕ ⲉⲛⲓⲣⲉⲙⲛⲭⲏⲙⲓ ⲉⲧⲁⲩⲓⲣⲓ ⲙⲙⲟⲥ ϧⲉⲛ ϯⲙⲉⲧⲟⲩⲱⲓ

Ⲛⲟⲧⲏ ⲛⲏⲃ ⲧⲙⲉⲧⲙⲏⲓ ⲛⲛⲁⲓⲥⲉⲛⲙⲛⲓ ⲧⲏⲣⲟⲩ ⲉⲧⲁⲩϯⲁⲓⲁⲓ ⲉⲣⲱⲟⲩ ⲛϫⲉ ⲡⲁⲓⲡⲉⲋⲟⲣⲥ ⲛⲉⲙ ⲓⲟⲩⲥⲗⲧ ⲧⲁⲫⲙⲏⲓ ⲁⲩⲥⲉϩⲛⲓ ⲛⲁⲛ ϫⲉ ϯⲙⲉⲧⲣⲉϥⲫⲱⲛⲕ ⲛⲉⲙ ⲡⲓϩⲓⲥⲃ ⲁⲩⲫⲓⲣⲓ ϧⲉⲛ ⲭⲏⲙⲓ. Ⲁϥⲥⲉϩⲛⲓ ⲛϫⲉ ⲡⲁϫⲓⲛⲇⲓⲃⲱ ⲉⲡⲓϫϯⲑⲉⲱϣ ⲛϫⲱⲣϫ ϫⲉ ⲧⲉⲛϣϫⲱⲕ ⲛⲛⲓϧⲧⲏⲟⲩ ⲛϩⲱⲣϫ ⲓⲉ ⲧⲉⲛϣϯⲥⲙⲟⲧ ⲉⲣⲱⲟⲩ ϧⲉⲛ ⲡⲓⲥⲉⲣⲁⲥⲉⲣ ⲛⲧⲁⲗⲟ ⲛⲧⲉ ϥⲓⲡⲛⲱϭⲓ ⲓⲉ ⲙⲡⲓϫⲓⲛⲓⲣⲓ ⲛⲛⲓⲙⲱⲓⲧ ⲙⲙⲉⲧⲣⲉϥⲫⲱⲛⲕ ⲙⲡⲓϫⲓⲛⲓⲣⲓ ⲙⲡⲓⲥⲟⲡⲧⲧ ⲛϧ ⲧⲏⲟⲩ 8:5

Ⲁⲩⲙⲁϯ ⲛϫⲉ ⲛⲓⲟⲩⲉⲓⲛⲓⲛ ⲛⲧⲟⲩϭⲓⲥⲃⲱ ⲉⲛⲁⲓⲙⲱⲓⲧ ⲛϧⲧⲏⲟⲩ ⲛⲛⲓⲣⲉⲙⲛⲭⲏⲙⲓ ⲟⲩⲟϩ ⲛⲧⲟⲩⲓⲣⲓ ⲙⲙⲱⲟⲩ ϧⲉⲛ ⲡⲓϫⲱⲣϫ ⲛⲕⲁⲩⲛϩⲉⲟⲩⲛⲏⲃⲟⲩ ϫⲉ ϯⲙⲉⲧⲟⲛⲓ ⲛⲉⲙ ⲡⲓϫⲓⲛϣⲱϣ ⲥⲉϣⲱⲡⲓ ⲛϩⲁⲛⲉⲛⲭⲁⲓ ϩⲱϯ ⲡⲉ ⲛⲧⲁⲛ ⲉϭⲓⲥⲃⲱ ⲉⲣⲱⲟⲩ.

Ⲡⲥⲁϫⲓ ϧⲉⲛ: ⲡⲓϫⲓⲛϯⲑⲱϣ ⲛϫⲱⲣϫ ⲛⲣⲉⲙⲭⲏⲙⲓ ⲛⲁⲡⲁⲥ ϧⲁ ⲡⲓϫⲓⲛϭⲓⲃⲱ ⲉⲡⲓⲕⲱⲧⲛϧⲧⲏⲟⲩ, ⲉⲗⲝⲏⲛⲧⲉⲣ ⲃⲉⲧⲉⲟⲩⲓ. Ⲡϫⲱⲃⲓ 49