And the earliest known Indian mathematical texts, written between 800 and 600 B.C., state that a rope stretched across the diagonal of a square produces a square twice as large as the original one.
" If we bear too much to the right, the worst that can happen is wasting a little time by striking the great River too soon and not cutting off the corner."
If they slant, the Nautilus follows the angle of that slant and, under its propeller's thrust, either sinks on a diagonal as steep as it suits me, or rises on that diagonal.
According to Pythagoras Theorem, the diagonal length would be square root of two; but try as he might, Hippasus could not express this as a ratio of two integers.
My dear sir, have you forgotten that the Nautilus is armed with a fearsome spur? Couldn't it be launched diagonally against those tracts of ice, which would break open from the impact?