magic (noun): via Latin and Greek, probably from Persian magus “member of a priestly caste.” The Indo-European root is magh- “to be able, to have power,” as seen in native English may, might, and main. A related borrowing from Greek is mechanic. Magic squares appear frequently in recreational mathematics and in number theory; their “magic” resides in the fact that the sum of every row, column, and diagonal is the same. In a similar fashion, there are magic cubes, magic stars, and various other magic figures. [123]

magnitude (noun): from Latin magnus “great,” from the Indo-European root meg- “great,” as found in the English cognate much. Related borrowings from Latin are magistrate and the month of May, named after the “great” Roman goddess Maia; from Sanskrit we have maharaja “great king.” In mathematics the magnitude of a vector tells how great (= long) the vector is. [129]

main (adjective): a native English word, from the Indo-European root magh- “to be able, to have power,” as seen also in native English may and might. A related borrowing from Greek is machine. In mathematics the main diagonal of a square matrix is the one that runs from the upper left corner to the lower right corner. [123].

major (adjective): the Latin adjective magnus meant “great, mighty” (this last being a native English cognate). The comparative degree was maior, literally “greater.” The major axis of an ellipse is the greater of the two axes.