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# An Analysis of the Features of Euclid's Writing Style

In Elements book one Euclid incorporates stylistic devices in the process of proving a series of mathematical theories One stylistic aspect of Euclids writing is his use of common notions such as the whole being greater than the part and postulates such as drawing a line from any point to any point His early use of common notions and postulates do not merely help to prove the particular proposition but is used in later propositions to persuade the reader of his proofs as well as to instill confidence in himself and the reader of the conclusions he arrives at in the propositions Even before the actual propositions begin Euclid lists the common notions and postulates of which he and the reader agree with By doing this Euclid and the reader have confidence in the proofs In another way the words common notions and postulates can be substituted by common sense because it is ten points which everyone believes to be true For example the majority of the conclusions in proposition thirteen were arrived at using common notions The last three steps in finally proving proposition thirteen were based on common notions Since everyone agrees with the common notions Euclid is confident that he is making a logical progression in proving that if a straight line set up on a straight line make angles it will make either two right angles or angles equal to two right angles Because of the general agreement of the postulates and the common notions and by listing them in advance Euclid is confident that he is correct when he makes assumptions based on them In the same sense the reader also holds the conclusions that Euclid arrives at to be true Another possibility to Euclids use of postulates and common notions is that he often uses postulates to set up a problem in terms in which he knows to be correct and then concludes the proposition with a common notion

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