Proposition: Angles and Sides in a Triangle IIIedit[id:899](Proposition 24 from Book 1 of “Euklid’s Elements”)If in two triangles \(\triangle{ABC}\), \(\triangle{DEF}\) we have two pairs of sides in each triangle respectively equal to the other, (without loss of generality assume \(\overline{AB}=\overline{DE}\) and \(\overline{AC}=\overline{DF}\)), where the interior angle in one triangle is greater in measure than the interior angle of the other triangle (\(\angle{BAC} > \angle{EDF}\)), then the remaining sides of the triangles will be unequal in length; specifically, the triangle with the greater interior angle will have a greater side than the triangle with the lesser interior angle (\(\overline{BC} > \overline{EF}\)). References [628] Casey, John: “The First Six Books of the Elements of Euclid”, http://www.gutenberg.org/ebooks/21076, 2007 What follows from what?This is (experimental) work in progress - if you miss an axiom, a definition, a theorem or a proof, if you find any inconsistencies you want to correct, or just know about a cool example or explanation you want to share with others, then join our team and help to improve this catalogue. Learn more about the axiomatic approach on BoP...Subordinated Structure: Contribute to BoP: add a new Proof add add a new Axiom add add a new Definition add add a new Motivation add add a new Example add add a new Application add add a new Explanation add add a new Interpretation add add a new Corollary add add a new Algorithm add add a new Open Problem add add a new Bibliography (Branch) add add a new Comment (Branch) add |
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