The nine common notions (Euclidean axioms)
Equals added to or taken from equals; the whole greater than its part
The folio is headed 'There are nine conceptions' and sets down nine axioms in the manner of Euclid's common notions. They assert that things equal to the same thing are equal to one another; that adding equals to equals, or taking equals from equals, leaves equals; that taking equals from, or adding equals to, unequals leaves unequals; that two things each equal to a third are equal, and each equal to half of a thing are equal to each other; that figures coinciding exactly when superposed are equal; and that every whole is greater than its part. Leonardo copies these foundations before pursuing his geometrical constructions.
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The nine common notions
Written as a title for the folio, the note declares there are nine 'conceptions'. Among them: things equal to one same thing are equal to one another; a figure superposed on another so that neither exceeds it is equal to it; and every whole is greater than its part.
Equal and unequal quantities combined
If equal things are added to equal things the results remain equal, and if equal things are removed from equal things the remainders remain equal. But if equal things are added to or removed from unequal things, the results remain unequal.