Rational and irrational lengths from a semicircle
Right triangles on a diameter; a table of squares 25,16,9,4 and their complements to 36
A semicircle drawn on a horizontal diameter carries four right triangles standing on that diameter, one arm marked 'rational' and the other 'irrational', with the triangle sides on the rational side read as 25, 16, 9 and 4. Alongside runs a table headed 36 that pairs these numbers with their complements — 25 with 11, 16 with 20, 9 with 27, 4 with 32 — under the columns 'rational' and 'irrational', each pair summing to 36. The scheme sorts lengths whose squares are perfect from those that are not. All the numerals were written in the ordinary, non-mirrored sense.
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Right triangles inscribed on a semicircle's diameter
On the diameter of a semicircle four triangles stand with their apex on the arc; one side of the semicircle is marked 'irrational' and the other 'rational'. The triangle sides on the rational side are read 25, 16, 9 and 4.
Table of numbers and complements to 36
A table headed 36 pairs 25 with 11, 16 with 20, 9 with 27 and 4 with 32 under 'rational' and 'irrational' columns — each pair summing to 36. It sorts the perfect squares from the remainders.