The existence of a rectangle as the equivalent of the fifth postulate [closed]

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How to prove that the existence of a rectangle is equivalent to the fifth postulate?




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closed as unclear what you're asking by David G. Stork, amWhy, Isaac Browne, Arnaud Mortier, hardmath Jul 31 at 23:30


Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.














  • What exactly do you mean by "existence of a rectangle"? Does this entail existence only for one "rectangle" or for a family of rectangles?
    – hardmath
    Jul 31 at 23:30










  • Euclid's construction of a square (Elements, I, 46) is a special case of the construction of a rectangle. And it relies on I, 29: "A straight line falling on parallel straight lines makes...the interior angles on the same side equal to two right angles." And this requires the fifth postulate.
    – Edward Porcella
    Aug 3 at 6:09














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How to prove that the existence of a rectangle is equivalent to the fifth postulate?




geometry




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closed as unclear what you're asking by David G. Stork, amWhy, Isaac Browne, Arnaud Mortier, hardmath Jul 31 at 23:30


Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.














  • What exactly do you mean by "existence of a rectangle"? Does this entail existence only for one "rectangle" or for a family of rectangles?
    – hardmath
    Jul 31 at 23:30










  • Euclid's construction of a square (Elements, I, 46) is a special case of the construction of a rectangle. And it relies on I, 29: "A straight line falling on parallel straight lines makes...the interior angles on the same side equal to two right angles." And this requires the fifth postulate.
    – Edward Porcella
    Aug 3 at 6:09












up vote
-2
down vote

favorite









up vote
-2
down vote

favorite











How to prove that the existence of a rectangle is equivalent to the fifth postulate?




geometry




share|cite|improve this question











How to prove that the existence of a rectangle is equivalent to the fifth postulate?





geometry





share|cite|improve this question










share|cite|improve this question




share|cite|improve this question









asked Jul 31 at 20:47









George

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closed as unclear what you're asking by David G. Stork, amWhy, Isaac Browne, Arnaud Mortier, hardmath Jul 31 at 23:30


Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.






closed as unclear what you're asking by David G. Stork, amWhy, Isaac Browne, Arnaud Mortier, hardmath Jul 31 at 23:30


Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.













  • What exactly do you mean by "existence of a rectangle"? Does this entail existence only for one "rectangle" or for a family of rectangles?
    – hardmath
    Jul 31 at 23:30










  • Euclid's construction of a square (Elements, I, 46) is a special case of the construction of a rectangle. And it relies on I, 29: "A straight line falling on parallel straight lines makes...the interior angles on the same side equal to two right angles." And this requires the fifth postulate.
    – Edward Porcella
    Aug 3 at 6:09
















  • What exactly do you mean by "existence of a rectangle"? Does this entail existence only for one "rectangle" or for a family of rectangles?
    – hardmath
    Jul 31 at 23:30










  • Euclid's construction of a square (Elements, I, 46) is a special case of the construction of a rectangle. And it relies on I, 29: "A straight line falling on parallel straight lines makes...the interior angles on the same side equal to two right angles." And this requires the fifth postulate.
    – Edward Porcella
    Aug 3 at 6:09















What exactly do you mean by "existence of a rectangle"? Does this entail existence only for one "rectangle" or for a family of rectangles?
– hardmath
Jul 31 at 23:30




What exactly do you mean by "existence of a rectangle"? Does this entail existence only for one "rectangle" or for a family of rectangles?
– hardmath
Jul 31 at 23:30












Euclid's construction of a square (Elements, I, 46) is a special case of the construction of a rectangle. And it relies on I, 29: "A straight line falling on parallel straight lines makes...the interior angles on the same side equal to two right angles." And this requires the fifth postulate.
– Edward Porcella
Aug 3 at 6:09




Euclid's construction of a square (Elements, I, 46) is a special case of the construction of a rectangle. And it relies on I, 29: "A straight line falling on parallel straight lines makes...the interior angles on the same side equal to two right angles." And this requires the fifth postulate.
– Edward Porcella
Aug 3 at 6:09















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