Parallelograms between parallels and the equality axiom
Three parallelograms formed between two parallels, closed by a Euclidean common notion
Under the heading 'Parallelograms,' two parallel lines are subdivided by verticals into three parallelograms, and diagonals are added to join one upright rectangle to another, yielding an elongated slanting parallelogram. Successive views label the diagonal parallelogram and the upright rectangles a, c and b, a to track corresponding parts. Leonardo underwrites the figures with a Euclidean common notion: if two things are equal to one thing, they are equal to each other.
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Parallelograms formed between two parallels
Two parallel lines are cut by vertical segments into three parallelograms. A further view joins the lower base of one upright rectangle to the upper base of another by diagonals, producing a long slanting (diagonal) parallelogram.
Common notion of equality
The construction is underwritten by an axiom: if two things are equal to one thing, they are equal among themselves. The parts are labeled a, c and b, a across the successive views to keep the corresponding figures aligned.