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In geometry , the statement that the angles opposite the equal sides of an isosceles triangle are themselves equal is known as the pons asinorum Latin pronunciation: This statement is Proposition 5 of Book 1 in Euclid 's Elements , and is also known as the isosceles triangle theorem.

Its converse is also true: The name of this statement is also used metaphorically for a problem or challenge which will separate the sure of mind from the simple, the fleet thinker from the slow, the determined from the dallier; to represent a critical test of ability or understanding. Euclid's statement of the pons asinorum includes a second conclusion that if the equal sides of the triangle are extended below the base, then the angles between the extensions and the base are also equal.

Euclid's proof involves drawing auxiliary lines to these extensions. But, as Euclid's commentator Proclus points out, Euclid never uses the second conclusion and his proof can be simplified somewhat by drawing the auxiliary lines to the sides of the triangle instead, the rest of the proof proceeding in more or less the same way.

There has been much speculation and debate as to why, given that it makes the proof more complicated, Euclid added the second conclusion to the theorem. One plausible explanation, given by Proclus, is that the second conclusion can be used in possible objections to the proofs of later propositions where Euclid does not cover every case. Proclus' variation of Euclid's proof proceeds as follows: Proclus gives a much shorter proof attributed to Pappus of Alexandria.

This is not only simpler but it requires no additional construction at all. GotPorn


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pons asinorum

For example, the Moscow Papyrus gives a formula for calculating the volume of a truncated pyramid, later clay tablets demonstrate that Babylonian astronomers implemented trapezoid procedures for computing Jupiters position and motion within time-velocity space.

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In geometry, an isosceles triangle is a triangle that has two sides of equal length. After , Bacons activities were restricted by a statute prohibiting the friars of his order from publishing books or pamphlets without prior approval 6.

He further advanced modular arithmetic, greatly simplifying manipulations in number theory, on 8 April he became the first to prove the quadratic reciprocity law. Euclid's Elements Book 1 proposition 5; the pons asinorum.

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These rules were elaborated close to Alexander of Aphrodisias, xwho speaks of a "diagram" and may reasonably be credited with having invented it3 The diagram itself is acknowledged by John Philoponus. The result was a theory of the syllogism paralleling, and in some respects simpler than, the better-known theory embodied in the Barbara Celarent verse.

It is not much discussed by dominant logicians in the thirteenth and fourteenth centuries, but Bochefiski finds it in Thomas Bdeot'se commentary on the obligation of George of Brussels.

Bayle11 speculates that the name ports asinorum, French pont aux dries, arises from a pun at intervals dne and an, x Alexander of Aphrodisias, In Aristotelis Analyticorum Priorum Librum I Commentarium, ed. Commentaria in Aristotelem Graeca, vol. Clarendon Huddle, , p. Thomas Notre Dame, Ind.: University of Notre Dame Press, Superlative, Hereafter referred to as B. Minerva, [Venice, ].

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Journal of the History of Philosophy

Why on earth would he contact me now? These writers are not the first to whom this letter has proved a pons asinorum. the commonest of corruptions in Greek and Latin MSS., we may fairly conjecture . inscription has lately been discovered dating his tenure of Achaia in A.D. Definition of pons asinorum - the point at which many learners fail, especially a theory or Mid 18th century: Latin, literally 'bridge of asses', term taken from the fifth Stay up to date with our latest news and receive new words updates, blog..

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