Book V of Euclid’s Elements contains the theory of proportions of magnitudes. Next to Book X, it is the least accessible book and much more abstract in character then other parts of the Elements. In this article we present a guide to help the reader through Euclid’s text. We explain the notions of magnitude, proportion, equimultiples and present Book V as a theory developed axiomatically. We provide a set of axioms for the theory of proportion and finally we present schemes of propositions V.8 and V.18.
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