Ancient Mathematical Visual Poem

JoAnne Growney has provided us with an ancient mathematical visual poem and its translation. A copy of the original manuscript can be seen above and at this URL here (click here). (Courtesy of ubuweb's early visual poetry page) The poem's explanation was difficult to find--but friend and colleague Sarah Glaz (Mathematics--University of Connecticut) tracked it down in Petrarch and the English Sonnet Sequence, by Thomas Roche, a book appearing in the bibliography of UBU's site of the Lok's poem. Oh ... and check out the square poems on JoAnnes website!

The translation is below:



Here we have a text interpretation of the manuscript photo, on page 166 of Petrarch and the English Sonnet Sequences by Thomas P. Roche, Jr. New York: AMS Press, 1989). In an Appendix on page 549, Roche also provides the text of two Latin mottos that surround the square. I have placed these at the top and at the bottom. Roche’s Appendix G goes on to point out the complexity of the structure within the square. For example, five lines The actual structure of this square poem is quite a bit more complex than the square itself.
For example, the columns down from E and F read:
God makes kings rule for heaue[n]s; your state hold blest
And still stand will their shields; fear yields best rest. [Roche, p. 550]
Embedded in the poem also are other poems, found by tracing the patterns of other squares (for example the sequence 1, 2, 3, 4, 5) and also crosses (using the letters, A, B, C, D, E, and F as reference points—A, B, E, and F, designate columns, as shown below and C, D designate the 5th and 6th rows.