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LA VÉRITÉ ET RIEN QUE LA VÉRITÉ
Dieu s’attribuant la Vérité, le cortège de la mathématique, coiffé par la Géométrie, s'est présenté, pour lui servir d’Ange Gardien.
Consciente de sa noble mission, la géométrie manifesta la gloire de la Magnificence divine dans l'espace à trois dimensions en donnant le plus beau relief au Pays Mission pour accueillir les Cèdres de Dieu.
Depuis , il est impossible de penser la Géométrie, l'Espace et le LIBAN sans DIEU.Le LIBAN en reconnaissance releva le pilier principal de l'Édifice Euclidien pour assurer à la géométrie une base solide, en démontrant le cinquième postulat d'EUCLIDE par plusieurs méthodes.
La géométrie immortalisée par les "Éléments d'EUCLIDE" retrouve son trône pour produire les vérités absolues et éternelles.
Nous plaçons en tête le théorème du LIBAN suivi par le théorème d'IBN AL HAITHAM pour rendre hommage aux Savants Arabes qui ont servi vaillamment la géométrie durant sept siècles.
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Let A, B, and C be three coplanar and non collinear points forming a scalene triangle ABC. We can always construct a circle passing through the three vertices A, B and C of this triangle. |
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We construct the perpendicular bisector (X) of the side BC.
From any point M on (X) we draw the perpendicular line (Y) to the side AB which cut it in H.
Let (Y) be moved perpendicularly to AB toward its mid point G. When H reaches G, (Y) superimposes on the perpendicular bisector (Z) of AB and cuts (X) at O which is the center of the circumscribed circle to the triangle ABC.
Q. E. D.
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Theorem:
«A straight line cuts all the coplanar straight lines of different directions»
By one given point B, outside of a given straight line (D) in a plane surface, let's draw any straight line (S) that cuts (D) in A. Take the bundle (F) of all straight lines around A of which each forms a determined angle with (D). The straight line (F1) that superimposes on (D) forms an angle equal to 0⁰, and the straight line (Fn), that superimposes on (S), forms an angle α. |
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When A and (Fn) translate on (S), the straight line of (F) keep their respective angles with (S) constant, therefore their directions remain fixed, and consequently their angles with (D) remain constant. In sweeping the plane surface, only the positions occupied by (F1) don’t cut (D), while all the positions of the other straight lines of the bundle (F) cut it.
In particular, when A coincide with B, the straight line (D’), occupying the position of (F1), is the only straight line that does not cut (D).
We conclude:
«In the plane surface, by one given point, passes only one parallel to a given straight line».
It is what it was necessary to demonstrate.
Commentary |
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The theorem of EHMEJ applies only the two first postulates to demonstrate the fifth postulate of EUCLIDE by studying the movement of the straight line (Fn) on another straight line (S) which is a translation communicated to all the other straight lines of the bundle (F), each moving in its own direction. In this movement each straight line remains parallel to its different positions. If the founders of the hyperbolic geometry had noticed it, they would have undoubtedly understood that their definition of the parallel is wrong, and that the angle of parallelism can never be an acute angle, but it is necessarily a right angle. They would have been able, maybe, to demonstrate EUCLID’S fifth postulate.
The mathematicians, believing that there is no movement of a straight line in its own direction in hyperbolic geometry, are invited to study the definition of the straight line in order to understand the nature of the straight line, and the movements that it can do in the space of three dimensions.
I hope that the theorem of EHMEJ, my Birth-place, carries the Mathematical Community to reject the Non-Euclidean geometries and to recognize the theorem of EHMEJ as the only true foundation of the geometry. I am ready to defend it before any jury, and to prove that its deductions are infallible. Anyone not convinced must detect a flaw in the theorem of my Birth-place.
A well founded geometry will repair the damages undergone by the human reason since the discoveries of the Hyperbolic and Elliptic geometries. Our future generations have the full right to be taught by soundly founded mathematics. They hope that the intellectual honesty and scientific probity will prevail.
The theorem of EHMEJ invites the cosmologists to look for the origin of the universe in the big truth that is the unique source of all eternal truths generated by geometry. Their Big Bang must let the place to GOD.
The voice of the conscience carried me to address the appeal of the truth to the Chiefs of states participating in the twelfth Summit of the French speaking countries.
Rachid Matta MATTA
October 21, 2008 |
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Proof of IBN Al-HAITHAM |
Completed in 2005 |
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Consider a quadrilateral ABCD such that:
BAD = ABC =  BCD = 90º
F and E are respectively symmetric of C and D with respect to [AB], then
[EF] = [CD]
 EFD =  CDF
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When [EF] is moved in its own direction (perpendicularly to [EC]), the quadrilateral EFMN has always [KH] as the perpendicular bisector. Then [FM] has the same direction as [EC] for all the positions M of its extremity F.
.All the segments [FM], passing through the same point F and having the same direction as [EC], should lie on one unique straight line [FD].
Then the quadrilateral ECDF is a rectangle.
NB:1
- We have proved that the points at equal distance from a straight line lie on a straight line. IBN Al-HAITHAM assumed that as a postulate.
2 - IBN Al-HAITHAM used the motion in geometry and he did not disfigure the straight line and the plane surface by the hypothesis of acute angle and obtuse angle used later by SACCHERI, LAMBERT, and the Founders of Non-Euclidean geometries.
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L'impossible conception des deux parallèles
de la géométrie hyperbolique
La géométrie hyperbolique (non-euclidienne) ne peut sortir du néant, car ses deux fondatrices, les deux parallèles hyperboliques (CC') et (LL'), ne peuvent être conçues par la rotation autour de B de la perpendiculaire issue de ce point à (DD'). En effet quand la droite (X) passe par M, elle se superpose sur [BK) engendrant le triangle rectangle isocèle BAM. En tournant en sens inverse elle engendre le triangle symétrique BAN. Ces deux triangles forment un triangle isocèle BMN inscrit dans un cercle de centre B et de rayon [BA]. La somme des angles intérieurs du triangle BMN est donc 180º. Ce résultat peut être généralisé à un triangle quelconque.
Conclusion
Le triangle euclidien rectangle isocèle BMN empêche la géométrie hyperbolique d'être conçue dans la matrice de l'espace. Cet espace est décrit uniquement par la géométrie euclidienne.
Rachid Matta MATTA
2007-12-18
Le prochain article sera intitulé « L'heure de la vérité a sonné »
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