Fractions by the Rule of Three, with 'alius' Declined
How to find what part of a whole the fraction 5/7 is, worked step by step
The page opens with a short Latin declension of the pronoun alius, alia, aliud ('another, of many') at upper right, then gives over its lower half to a lesson in fractions. Leonardo shows how to find what part of a whole an irreducible fraction represents, working 5/7 through the rule of three: taking 5/7 of a soldo (12 denari), he asks 'if 7 were 12, what would 5 be?', multiplies 5 by 12 to get 60, divides by 7 to get 8 with 4/7 remaining, and concludes the answer is almost one half. A brief companion example checks 'if 8 were 12, what would 4 be?'
On this page
Declension of 'alius' (another, of many)
Under the heading 'the other, of many,' the pronoun is declined: nom. alius alia aliud, gen. alius, dat. alii, acc. alium aliam aliud.
A quick rule-of-three check
As a warm-up Leonardo asks 'if 8 were 12, what would 4 be?', answering that it would make 6, that is half a soldo, 4/8.
Finding what part of a whole 5/7 is
To learn what part of a whole an irreducible fraction is, he takes 5/7 of a soldo, which is 12 denari, and applies the rule of three: 'if 7 were 12, what would 5 be?' Setting it in form, 5 times 12 is 60; dividing by 7 gives 8 with 4/7 of a whole remaining, that is, almost one half.