Perpendiculars, parallels and squares built on a given line
Concluding figure of the recto's theorem, with citations of Euclidean propositions
The verso completes a theorem begun on the recto and continues with elementary constructions: crossed segments, a given line carrying perpendiculars at both ends, a transversal cutting two parallels with corresponding angles marked by dots, and squares and parallelograms formed from pairs of parallels. Marginal notes justify each step by citing propositions in the manner of Euclid, from the definition of the perpendicular to 'the second of the 28th' and 'the 33rd'. Scattered numerals key the individual figures to those references.
On this page
Perpendiculars raised at both ends of a line
A given line is drawn with perpendiculars raised at its two ends. The note argues that by the definition of the perpendicular the two angles are right, and the perpendiculars are therefore parallel, 'by the second of the 28th'.
Square proved equal by the third proposition
On the left a square is drawn and its parts declared equal 'by the third' and 'by the common notion'. The numeral 11 keys the figure to the running theorem.
Parallelogram from two pairs of parallels
At the foot, from right to left, a parallelogram is built from two pairs of parallel lines, the construction justified 'by the 33rd'. It closes the sequence of parallel-line figures.
Concluding figure of the recto's theorem
To the right of the leading figure a column of proposition references records the closing of the theorem carried over from the recto, listing 'second of the 2nd', 'third', and the parts 33 and 29.