Axioms on parts reunited to remake their whole
Many restatements of the rule that a divided quantity, rejoined, is not diminished
Two columns of mirror-writing set out, in a long series of nearly identical restatements, a single mathematical axiom: that a whole divided into parts is made whole again when those parts are rejoined, and that a quantity which loses and then regains its parts is not diminished. These logical formulae underpin Leonardo's proofs of area equivalence, where regions are cut away and restored without loss. Two small square diagrams are sketched at the lower left of the sheet.
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A whole rejoined from its parts is reintegrated
Leonardo repeats that the parts of a whole, once rejoined among themselves, always remake their whole. A whole divided into parts returns to its whole by regaining the value of those parts.
A quantity that regains its removed parts is not diminished
The concluding variants state that a quantity is not diminished when the removed parts are restored to it, or when it regains the value of the removed quantity. The point is that equivalence of value, not identity of the original piece, suffices to reintegrate the whole.
Two small square figures at the lower left
Two small square diagrams, one crossed and one enclosing a circle, are drawn at the lower left of the sheet. They are not covered by the transcription but echo the inscribed-square geometry of the facing folios.