Search results
Results From The WOW.Com Content Network
The converse of the parallel postulate: If the sum of the two interior angles equals 180°, then the lines are parallel and will never intersect. Euclid did not postulate the converse of his fifth postulate, which is one way to distinguish Euclidean geometry from elliptic geometry.
In logic and mathematics, the converse of a categorical or implicational statement is the result of reversing its two constituent statements. For the implication P → Q, the converse is Q → P. For the categorical proposition All S are P, the converse is All P are S. Either way, the truth of the converse is generally independent from that of ...
Re the distinction between the parallel postulate and its converse, this all depends on the question of whether two distinct lines can have two points in common (Parallel_postulate#Converse_of_Euclid.27s_parallel_postulate), which I think is logically equivalent to the question of whether two distinct lines can have a common segment (since the ...
then AD, BE, CF are concurrent, or all three parallel. The converse is often included as part of the theorem. The theorem is often attributed to Giovanni Ceva, who published it in his 1678 work De lineis rectis. But it was proven much earlier by Yusuf Al-Mu'taman ibn Hűd, an eleventh-century king of Zaragoza. [1]
In Euclid's Elements, the first 28 Propositions and Proposition 31 avoid using the parallel postulate, and therefore are valid in absolute geometry.One can also prove in absolute geometry the exterior angle theorem (an exterior angle of a triangle is larger than either of the remote angles), as well as the Saccheri–Legendre theorem, which states that the sum of the measures of the angles in ...
An American Airlines flight departing New York's LaGuardia Airport on Thursday evening had to divert to nearby John F. Kennedy International shortly after takeoff after a reported bird strike ...
Saccheri quadrilaterals. A Saccheri quadrilateral is a quadrilateral with two equal sides perpendicular to the base.It is named after Giovanni Gerolamo Saccheri, who used it extensively in his 1733 book Euclides ab omni naevo vindicatus (Euclid freed of every flaw), an attempt to prove the parallel postulate using the method reductio ad absurdum.
Markeem Benson is accused of murdering Renise Wolfe in Nevada