Rachid Matta replies to Mr.Friedemann Brock's questions
Dear readers
You will find below my answers to the mathematical questions sent to my website by Mr.Friedemann Brock AUB Beirut, Department of Mathematics: fb13@aub.edu.lb
Dear readers, you should know that only one correct proof of the fifth postulate is sufficient to found soundly Euclidean geometry and to reject Non-Euclidean geometries and theories based upon them, and you should know, also, that only mathematical knowledge of grade 9 is required to understand the deductions in the three theorems proposed on this website.
Mr.Friedemann wrote: «You add, since December 2007 one message after another to your forum, without even allowing any other opinion to be heard!!!».
Mr.Friedemann Brock, this website is open to any opinion concerning mathematics, but the opinions not related to geometry and which confirm the well known proverb: "The vessel sweats what it contains", will be deleted.
Question 1
Friedemann Brock wrote: «Instead, we-that is, the mathematical community-would be obliged to detect mistakes in HIS proofs. But his own work is only about planar, elementary geometry, in an exclusively Euclidean context».
Rachid Matta's reply
I – If there is no flaw in one of my proofs, the fifth postulate of EUCLID will be duly proved, and all your questions become meaningless.
II - If one of my proofs is correct, the consequences are enormous. All the works of mathematicians done outside Euclidean context and approved by referees of academies of Sciences, or referees of International Mathematical Journals will be wrong. The Non-Euclidean matters taught to future generations destruct their reason instead to form it.
For these very important reasons the mathematical community is obliged to detect a flaw, one flawless proof collapse Non-Euclidean geometries and theories based upon them.
III - Until now, nobody has shown a flaw in my proofs presented to many universities in the world and especially to the following academies of Sciences:
A – The French Academy of Sciences.
B- The Chinese Academy of Sciences.
C- The Swiss Academy of Sciences.
D – The Austrian Academy of Sciences.
E – The Pontifical Academy of Sciences.
Sometimes an error can be rectified and a proof can be refined.
Any report not scientifically justified by correct mathematical reasoning has no value at all.
IV – Your opinion about my "work" is an argument against you, because
if my "work is only about planar elementary geometry in an exclusive Euclidean context", that means that I am working in the right way and I have profoundly understood the geometry and its principles and especially the question of the fifth postulate of EUCLID. Kindly read carefully what follows:
1 – The fifth postulate was introduced by EUCLID for the first time in his proposition 29 to demonstrate that two parallel straight lines cut by a transversal make the interior angles supplementary, the alternate angles and corresponding angles equal (page 312, Book I of the "Elements of EUCLID" translated by Sir Thomas L. HEATH).
2 – Postulate 5 deals with parallel and intersecting straight lines in a plane surface as you can read under page 155 of Book I of the "Elements of Euclid"
Postulate 5: «That, if a straight line falling on two straight lines, make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles».
3 – In the same book I of Euclid's Elements the definition of parallel concerns only the straight lines in the plane surface and not the curved lines. You can read under pages 153 and 154 what follows:
Definition 4: «A Straight line is a line which lies evenly with the points on itself».
Definition 7: « A plane surface is a surface which lies evenly with the straight lines on itself».
Definition 23: «Parallel straight lines are straight lines which, being in the same plane and being produced indefinitely in both directions, do not meet one another in either direction».
4 – All the attempts to prove the fifth postulate from GEMINUS (130-60) to BOLYAI (1802-1860), LOBACHEVSKY (1892-1856), and GAUSS (1777-1855), founders of hyperbolic geometry, were done in an exclusively Euclidean context. I enumerate four of them:
a – Claudius PTOLEMY (85-165) attempt.
b – Nasir al-Din al-TUSI (1201-1274 ) attempt.
c – John WALLIS (1616-1703) attempt.
d – Adrien-Marie LEGENDRE (1752-1833) attempts.
5 – The great philosopher and mathematician PROCLUS (411-485) has well seen that the fifth postulate is a theorem and it must be proved by using only the principles and theorems of Euclidean geometry. In his book "A Commentary on the First Book of Euclid's Elements", translated by Glenn R.MORROW, he wrote under pages 150 and 151 the following items:
A - « This (postulate 5) ought to be struck from the postulates altogether. For it is a theorem- one that invites many questions, which Ptolemy proposed to resolve in one of his books- and requires for its demonstration a number of definitions and theorems. And the converse of it is proved by Euclid himself as a theorem. But perhaps some persons might mistakenly think this proposition deserves to be ranked among the postulates on the ground that the angles less than two right angles makes us at once believe in the convergence and intersection of the straight lines».
B – «These considerations make it clear that we should seek a proof of the theorem that lies before us and that it lacks the special character of a postulate. But how it is to be proved, and with what arguments the objections to this proposition may be met, we can only say when the author of the Elements is at the point of mentioning it and using it as obvious. At that time it will be necessary to show that its obvious character does not appear independently of demonstration but is turned in proof into a matter of knowledge».
6 – D'ALEMBERT (1717-1783) considered postulate 5 as a theorem to be demonstrated, and proposed to define a parallel to a given straight line as any other coplanar straight line, which joins two points which are on the same side of and equally distant from the given straight line.
Question 2
Friedemann Brock wrote: « Your "work" has been examined carefully by a commission of 8 Professors of Mathematics at Lebanese Universities, a couple of years ago, and it was found as a DISASTER. One example below:
A straight line in Poincare disc is a circle. You continue to claim at your website, that it has to be a straight line».
Rachid Matta's reply
The reasonable thinkers conclude from the cited example that, neither you, nor any professor of the commission, is able to judge my great achievement in geometry for the reasons listed below in the paragraph subtitled straight line.
The committee of 8 professors (if what you are writing is true) is invited to send me its report, or to publish it. The professors had never contacted me to rectify any eventual mistakes, or flaw. If, I can't rectify the error, then, they are entitled to write in their report that my work is a disaster. They should know that a proof can be refined. Kindly I invite the 8 professors and all the mathematicians in the world to examine the three proofs proposed on this website. I will be ready to publish their report. Only a scientific discussion enables reasonable people to judge who is right.
Straight line
I – Evidently a straight line must be straight and not an arc of circle which is a curved line. The definition 4 cited below is very eloquent.
"A straight line is a line which lies evenly with the points on itself"
The circle is clearly defined under page 153 of Book I.
Definition 15: « A circle is a figure contained by one line such that all the straight lines falling upon it from one point among those lying within the figure are equal to one other».
II – My definition on the web of straight line traduces geometrically the exactitude and the straightness of the straight line as intended by EUCLID. Without a plain insight into the nature of the straight line it is impossible to do valuable and exact geometry.
The following two definitions are extracted from Volume 1 of HEATH.
III – Another famous definition of straight line is: "That line which, when its ends remain fixed itself remains fixed".
IV – GAUSS' form of the precedent interpretation was "The line in which lie all points that, during the revolution of a body (a part of space) about two fixed points, maintain their position unchanged is called a straight line".
V – LOBACHEVSKY, who contradicted EUCLID by denying the fifth postulate, did not attack the identity of the straight line, because he wrote in his "THEORY OF PARALLELS" what follows:
In order not to fatigue my reader with the multitude of those theorems whose proofs present no difficulties, I prefix here only those of which a knowledge is necessary for what follows:
1 – A straight line fits upon itself in all its positions. By this I mean that during the revolution of the surface containing it the straight line does not change its place if it goes through two unmoving points in the surface:
(i. e., if we turn the surface containing it about two points of the line, the line does not move.)
2 – Two straight lines cannot intersect in two points.
3 – A straight line sufficiently produced both ways must go out beyond all bounds, and in such way cuts a bounded plan into two parts.
4 – Two straight lines perpendicular to a third never intersect, how far soever they be produced.
5 – A straight line always cuts another in going from one side of it over to the other side: (i. e., one straight line must cut another if it has points on both sides of it.)
6 – Vertical angles, where the sides of one are production of the side s of the other, are equal. This holds of plane rectilineal angles among them, as also of plane surface angles.
7 – Two straight lines cannot intersect, if a third cuts them at the same angle.
In the other items LOBACHEVSKY distinguishes between the rectilineal plane triangle of two dimensions and the spherical triangle of three dimensions and of curved sides. To introduce the spherical triangle, he starts by defining the perpendicular straight line to a plane surface and thus generating the third dimension of space to permit the generation of the sphere and the spherical triangle of three dimensions.
LOBACHEVSKY defines the circle as the intersection of a sphere with a plane.
VI – D'ALEMBET' stated that « Les définitions et les propriétés de la ligne droite, ainsi que des lignes parallèles sont l'écueil et pour ainsi dire le scandale des éléments de Géométrie» and that with a good definition of the straight line both difficulties ought to be avoided in the demonstration of the fifth postulate of EUCLID. (Page 52, NON-EUCLIDEAN GEOMETRY, by Roberto BONOLA).
VII – J.B. FOURIER (1768-1830) in a discussion he carried on with Monge (1746-1818) considered that the demonstration of postulate 5 can be connected with the definition of the straight line (Page 54, same book of BONOLA).
VIII – All the Greek geometers, the geometers of 17th century and the Euclidean geometers agree with the precedent definitions and they know the essence of the straight line.
IX – If the followers of LOBACHEVSKY could understand like him the straight line, they will easily see the contradictions in hyperbolic geometry, and they cease to deform the straight line and the plane surface. Without plain insight into the straight line and the plane surface, it is not possible to comprehend geometry.
X – The Non-Euclidean geometers follow without critic the wrong hypotheses of acute and obtuse angle taken by Johann Heinrich LAMBERT (1728-1877) in considering the arc of a circle as a straight line, for an arc of circle is a curved line which doesn't lie evenly with the points on itself and it has two dimensions, while a straight line has one dimension and lies evenly with the points on itself.
Question 3
Friedemann Brock wrote: « WHEN he claims to deduce the 5th postulate, he USED it before in one or another way».
Rachid Matta's reply
I – Plato could say that your assertion is an opinion unluckily shared by Non-Euclidean mathematicians and the referees of academies of Sciences and International Journals of mathematics.
II – I have received similar opinion from the President of the mathematical Section of the French Academy of Science in 2004. But the President was wise to draw the consequences of my letter to him and directed my two proofs to specialists who should know that Postulate 5 can be deduced from the three first postulates. My book « LES DÉMONSTRATIONS DU THÉORÈME DE LA PARALLÈLE» holding more than 80 proofs will convince them that postulate 5 is to be ranked among the theorems.
III – Your assertion leads to the following wrong and bizarre opinions of Non-Euclidean geometers:
1 - «Any proof of Euclid's fifth postulate is a proof that Euclidean geometry is logically inconsistent». This is the opinion of Mr. Hurkyl on the website: Physics Forums "About the geometry of general relativity".
2 - «If Euclidean geometry is consistent, then so is hyperbolic geometry». This is the content of theorem I stated by BELTRAMI in 1868 without any proof. Any mathematician should know that Euclidean geometry becomes consistent when postulate 5 will be proved and ranked among the theorems. Otherwise Euclidean geometry is submitted to the experience.
3 – In 1870, the historian of mathematics, Guillaume HOÜEL (1823-1886) wrote «Quant aux euclidiens arriérés, à ceux qui cherchent des démonstrations du Postulatum, je ne puis mieux les comparer qu'à ceux qui chercheraient dans l'équation différentielle elle-même la détermination de la constante d'intégration».
IV –Mr. Friedemann Brock you are kindly invited to show me where I am using the fifth postulate in my proofs.
V – I affirm that I never used the fifth postulate in my proofs. All my deductions are conducted correctly by applying the true principles of geometry. My success in proving postulate 5 is due to the following reasons:
1 – I have seen the simplicity of the proof, this simplicity was been remarked by the great mathematician Roberto BONOLA who wrote under page 177of his book, "NON-EUCLIDEAN GEOMETRY" what follows:
«Indeed our geometrical instinct seems to afford us evidence that a proposition, seemingly so simple, if it is provable, ought to be proved by an argument of equal simplicity».
2 - I put the meaning back into geometry and used the definitions and the axioms in their old meaning, that means the definitions must give the essence of the thing defined and the axiom should be self-evident and true, contrarily to modern axiomatic theories.
3 – I have profoundly understood the straight line and plane surface, and the relation of coincidence.
4 – I learnt from the unsuccessful attempts in the past how to avoid the flaws.
5 – I used the motion which is the life of geometry. The first postulate introduces the motion of translation in the real space and particularly in the plane surface. The second postulate translates the equality permitting to add the segments of straight lines. The third postulate introduces the motion of rotation in the plane surface. The two fundamental motions in the plane surface are translation and rotation. A segment of straight lines translates when it moves without rotating; in this case it makes a constant angle with any line cutting it in the plane surface. We say it moves in its own direction.
VI – Kindly read the mathematical works of the great mathematician before the 18th century. These mathematicians had the critical spirit and the mind not influenced by Non-Euclidean geometries. You will see that I have done like them.
I give below a list of many great mathematicians who used the same motion that I have used in LEBANON'S THEOREM.
1 – The great mathematician John WALLIS (1616-1703) has used the motion of a straight line in its own direction in his attempt to prove postulate 5. Kindly, read the attempt of John WALLIS under page 210 of Book I of the "Elements of EUCLID". You find what follows:
« He first proved (1) that, if a straight line is placed on an infinite straight line, and is then moved in its own direction as far as we please, it will always lie on the same infinite straight line, (2) that, if an angle be moved so that one leg always slides along an infinite straight line, the angle will remain the same, or equal ».
2 – In "NON-EUCLIDEAN GEOMETRY" Roberto BONOLA wrote under page 16 what follows:
« Let a, b be two straight lines intersected at A, B by the transversal c. Let α, β be the interior angles on the same side of c…Let the line b be now moved continuously along the segment AB, so that the angle which it makes with c remains always equal to β ».
3 – IBN AL-HAITHAM (965-1039) used the motion of a segment of straight line perpendicularly to another straight line. His attempt can be found in the internet resources.
4 – William KINGDON CLIFFORD (1845-1879) used the motion of a straight line in its own direction when he wrote under page 65 of his book "The common sense of the exact science" what follows:
« If we make a point P travel along BA towards A, and, as it moves, draw through it always a line making the same angle with BA that BD makes with BA, then the moving line can never meet AC until it wholly coincides with it ».
5 – The historian of mathematics, Harold E.WOLFE related in his book "Introduction to Non-Euclidean geometry" under page 42 the attempt of Louis BERTRAND to prove the fifth postulate. The motion of a straight line in its own direction is used in the attempt.
6 – Mathematicians believe that a straight line can't move in its own direction in the hyperbolic geometry. The following items show that they are wrong.
a – In hyperbolic geometry, all the straight lines move in their own directions. The only exception is the two hyperbolic parallels because they are fiction and can never be conceived in the real space.
b – If the founders of hyperbolic geometry, GAUSS, BOLYAI and LOBATSCHEVSKY, could read the theorems on my website: www.mathtruth-rachidmatta.com, themselves they will deny their geometry. POINCARÉ is suffering to have presented his beautiful disc to Non-Euclidean geometry.
c – In hyperbolic geometry, when the point B moves along the straight line (X), the perpendicular (GG') to (X) will move in its own direction by remaining perpendicular to the straight line (X).
d – In fact, all the straight lines between A and B and making with (X) an angle inferior to the angle of parallelism α, move in their own directions. All the straight lines between B and infinity, and making an angle with (X) whose value is between α and 90º, move in their own directions.
The only straight lines, not moving in their own directions, are the two hyperbolic parallels (CC') and (LL').
Between A and M, all the straight lines cutting (DD') and making an angle lesser than δ, move in their own directions.
Between M and B, all the straight lines called hyperparallel move in their own directions.
At M, the only straight lines, not moving in their own directions, are the two hyperbolic parallels (RR') and (KK').
The two hyperbolic parallels are constantly flogged by the straight lines moving in their own directions, to become real by cutting the straight line (DD'). Otherwise they do not merit the existence in the real space. This fact is proved by the third theorem on the website.
7 – LOBACHEVSKY, founder of hyperbolic geometry, followed the same path by drawing the perpendicular lines to another straight line.
Under page 20 of his essay entitled "GEOMETRICAL RESEARCHES ON THE THEORY OF PARALLELS by NICHOLAS LOBACHEVSKI
TRANSLATED BY DR. GEORGE BRUCE HALSTED", considered what follows:
The straight lines A'B', A''B'', KB, FG, and CD are perpendicular lines to the semi-straight line AC. The passage from one perpendicular line to another is equivalent to the motion of this straight line in its own direction towards the other straight line. Drawing a perpendicular line from any point of AC is equivalent to the motion of a straight line in its direction which is here perpendicular to the semi-straight line AC.
This essay is at the end of the book entitled "NON-EUCLIDEAN GEOMETRY" of Roberto BONOLA.
Question 4
Friedemann Brock wrote: «Mr.Matta has not shown to us ANY INTERIOR contradiction in the well-known models of non-Euclidean geometry. To my explicit question about this issue, he responded to me that he does not need to show those contradictions»
Rachid Matta's reply
1 – When a right proof of postulate 5 is found it is not needed to show contradictions in models of Non-Euclidean geometries because these geometries collapse automatically. For this reason the mathematical community is obliged, as you wrote, to detect a flaw in my proofs for saving Non-Euclidean geometries.
2 – In geometry the contradictions are to be found in the principles and the theorems and not in the models. All the theorems of Non-Euclidean geometries contain contradictions, and some of these contradictions are shown in my book «LES DÉMONSTRATIONS DU THÉORÈME DE LA PARALLÈLE».
3 – What you call well known models of Non-Euclidean geometry is an unforgivable logical error committed by BELTRAMI, KLEIN and POINCARÉ.
4 – These models of Non-Euclidean geometry were proposed by BELTRAMI in 1668 and later by KLEIN and POINCARÉ. These mathematicians used the real geometry to visualize fictive lines that can never be conceived in the real space where we are living.
5 – How to represent a line of non-Euclidean geometry, denying the fifth postulate, by a line of Euclidean geometry admitting the truthfulness of the fifth postulate?
6 – Isn't a senseless way to represent a thing by its opposite? When we say an angel is a spirit can we represent him by a body?
7 – We visualize a thing in the space described by its geometry, and we should know the propriety of this thing. In the present case we have to know what a line is in Non-Euclidean geometry.
8 – In Non-Euclidean geometries, nobody is able to say what is a line or a plane surface. I urge you to read what is written under page 226 of the book of Marvin Jay GREENBERG, entitled "Euclidean and Non-Euclidean Geometry, Development and History". This great mathematician wrote what follows:
"To prove Mathematical Theorem I, we have to ask ourselves, what is a line in hyperbolic geometry- in fact, what is the hyperbolic plane?
THE honest answer is that we don't know, it is just an abstraction".
9 – M.Friedemann Brock, this line has not the honor to be an abstraction, because it can't be conceived in the real space. My third theorem on this website proves rigorously the impossibility for the two hyperbolic parallels to be conceived.
10 – BELTRAMI didn't know that the tractrix, generating a surface of revolution called pseudosphere when it rotates about its asymptote, is an Euclidean curved line containing the truthfulness of the fifth postulate of Euclid, because the truthfulness of the fifth postulate is included in any curve of the Analytic geometry which is based on postulate 5.
11 – The only mathematician, who has seen the logical difficulty in using Euclidean geometry to describe Non-Euclidean geometry, was Antonio CREMONA (1830-1903).
12 – POINCARÉ had to know that a circle is a curved line and not a straight line.
13 – The POINCARÉ models hold the truthfulness of the fifth postulate, and POINCARÉ did not see that the sum of the interior angles of the right triangle ABC is equal to 180º. The proof called "Orthogonal circles" is in my book "LES DÉMONSTRATIONS DU THÉORÈME DE LA PARALLÈLE". This proof, presented in one half-page, is very simple. It suffices to remark that the tangent to circle (C, AB) at A rotates similarly as the radius CA. The equality of angles DBA' and ACA' implies that the sum of the interior angles of the quadrilateral ABA'C is 360º and consequently the sum of interior angles of the right triangle ABC is 180º.
14 – In studying this proof, POINCARÉ can see the exactness of the deductions and, certainly, he regrets the model presented by his disk, because he knows that Euclidean geometry is true and the only one to describe the physical space. He was not able to refute the Non-Euclidean geometries. He contented himself to affirm that Euclidean geometry is more commode than Non-Euclidean geometries.
POINCARÉ will be the first reasonable mathematician to approve my demonstration of the fifth postulate and he will be glad to see the Euclidean geometry, finally, very well founded in a sound base.
15 – I have detected more than thirty contradictions in the hyperbolic geometry. My book entitled "LES DÉMONSTRATIONS DU THÉORÈME DE LA PARALLÈLE" contains all the proofs showing these contradictions and it will be published during the first half of 2008, and it will be translated into English.
16 – If SACCHERI have used the fundamental relation in geometry (the relation of coincidence) he was able to reject both hypotheses of acute angle and obtuse angle.
17 – When, one of my proofs rejects the two hypotheses of acute angle and obtuse angle taken by SACCHERI, it will be not needed to show contradictions in a model pretending visualize a line which can never be conceived.
18 – The consistency of hyperbolic geometry stands on an unproved proposition called illegally theorem 1 that you can find under page 225 of the book of GREENBERG cited above. BELTRAMI stated a strange mathematical proposition which he called theorem 1:
"If Euclidean geometry is consistent, then so is hyperbolic geometry".
To give some credibility to hyperbolic geometry BELTRAMI tried to involve the respectable Euclidean geometry by linking it with Non-Euclidean geometry.
Theorem 1 was never proved and it is completely wrong for the following reasons:
I – Any geometry to be consistent must prove all its theorems.
II – A proposition, to be called theorem, must be duly proved. Otherwise it is an opinion.
III – It is impossible to establish a link between two geometries based on opposite postulates.
IV- Hyperbolic geometry must prove its consistency by its proper principles and theorems.
V – Euclidean geometry is not consistent without a correct proof of the fifth postulate of EUCLID.
Question 5
Friedemann Brock wrote: « In one of his letters to me he even attacks David Hilbert for his axiomatic view on mathematics…».
Rachid Matta's reply
I will attack any scientific theory if I can prove that it is wrong, or inconsistent whoever is the author.
I extract from my emails to Mr.Friedemann Brock the following items:
1 – The aim of David HILBERT, by introducing his axiomatic theory in mathematics, was to render the mathematics a game
2 – The Greek mathematicians have introduced the true axiomatic theories. The axioms are self evident and true. The definitions contain the truth of the thing defined. The modern axiomatic theories do not follow the pathway of Greek's axiomatic theories.
Concerning David HILBERT, I do not attack the person, but I attack what is wrong in his mathematical work. His book "Les fondements de la géométrie" published in 1899 can't found soundly the geometry because the postulate 5 is considered as a principle. In putting the parallel postulate among the principles David HILBERT has not distinguished between principles and consequences.
3 – Based on the authority of HILBERT and without any critic, the followers were introduced in error.
4 – The modern axiomatic theories can say nothing about what is true or false in the concrete objects which are the real things in the physical space, because they deal with abstraction. Mathematics is not a game. Next year (2009) this question will be the main subject on my website.
Question 6
Friedemann Brock wrote: « Mr.Matta has not published a single article in an International Mathematical Journal».
Rachid Matta's reply
1 – The publication in international Mathematical Journal is not a criterion that the mathematical work is correct. The eloquent examples are the judgments concerning Non-Euclidean geometries.
The demonstration of postulate 5 requires special treatment because all the specialists and referees are convinced of the impossibility of proving it and they are influenced by Non-Euclidean geometries.
The best way is that all mathematicians participate to public discussions to be sure that there are no flaws in the deductions.
I am ready to enter in scientific discussion with academies of Sciences, with International Mathematical Journals, and with mathematicians over the world. But I never accept any judgment if it is not justified and not supported by good mathematical reasoning. For this reason I say that mathematicians must detect a flaw in my proofs.
2 – My proofs are in many academies over the world. I will be grateful to any referee who could find a flaw in them. Every one of us should accept the law of truth.
Question 7
Friedemann Brock wrote:
«That is, he lies on his website when he claims to have found 30 contradictions…». « Therefore it is not surprising that few people are keen to read "80" proofs».
Rachid Matta's reply
1 – When, during 2300 years, not one single proof was found by all the mathematicians, and that one person is able to find more than 80 ways leading to the resolution of postulate 5, I think all the thinkers and reasonable men are keen to read the book holding the significant title: "LES DÉMONSTRATIONS DU THÉORÈME DE LA PARALLÈLE".
The professors and students in mathematics will be interested to learn the right way to conduct their mind.
2 - The proofs, detecting contradictions in Non-Euclidean geometries exceed the number 30. The intellectual property rights for this book were obtained at the end of last year 2007. This confirms that I never lie. You can see some of these contradictions in my first published book entitled: «TROIS SIÈCLES DE SÉDUCTION DANS LA GÉOMÉTRIE»
This book shows that postulate 5 can be deduced from the first three postulates contrarily to the wrong saying of referees.
3 - Nowadays the proofs of the fifth postulate of EUCLID exceed 80 and they will be more and more because the abundant graces of GOD are enabling me to put more ways to discover the eternal truth when my mathematical soul relies on the First Geometer.
Question 8
Friedemann Brock wrote: «Mr.Matta advertises himself in an arrogant way, claims that he was chosen by god to restore the truth».
Rachid Matta's reply
We write GOD with capital letters, even if we are atheist.
I am proud to affirm that GOD gives me the graces to save geometry and mathematics by restoring the truth of Euclidean geometry and by putting back the meaning into mathematics. It is an honor for me to fulfill this mission.
To produce perfect and exact mathematics the human soul must always turn towards its Unique Source: GOD. The affirmation of the existence of the Ultimate Truth is not arrogance, but heroism and honesty.
The Non-Euclidean mathematicians have done their best to kill GOD by expelling the eternal truth from geometry, and their representative, Eric Temple BELL, affirms it expressly in his book "LES GRANDS MATHÉMATICIENS". The following extracts from page 332 and 333 are eloquent:
1 – "À l'époque où il (EUCLIDE) s'est occupé de la théorie de l'espace, c'est-à–dire de «géométries», les hypothèses pures qu'il a incorporées dans ses postulats avaient déjà pris l'aspect de vérités vénérables et immuables, révélées à l'humanité par une intelligence supérieure comme la véritable essence de toutes les choses matérielles. Il a fallu plus de deux mille ans pour expulser de la géométrie ces vérités éternelles et ce fut l'œuvre de Lobatchevsky".
2 – "Le coup qu'il (Lobatchevsky) a porté avec sa méthode d'attaque des axiomes n'a probablement pas encore été ressenti dans toute sa plénitude mais il n'est pas exagéré d'appeler Lobatchevsky le Copernic de la géométrie, car la géométrie n'est qu'une portion du vaste domaine qu'il a rénové; il serait même juste de l'appeler le Copernic de toute la pensée".
3 – "Ce qui importe, c'est que Lobatchevsky a aboli le dogme de la «vérité » absolue de la géométrie euclidienne, et sa géométrie n'a été que la première de plusieurs autres construites par ses successeurs".
4 – " À un certain point de vue, on a cru pendant 2200 ans qu"Euclide avait découvert, avec son système de géométrie, une vérité absolue ou un mode nécessaire de la perception humaine; la création de Lobatchevsky a été la démonstration pragmatique de l'erreur de cette croyance".
Rachid Matta infirms BELL
Le mathématicien Libanais Rachid Matta MATTA, par sa démonstration du cinquième postulat d'EUCLIDE, infirme les dires de BELL en relevant plus de 30 contradictions dans la géométrie hyperbolique de LOBACHEVSKY, BOLYAI et GAUSS. Cette performance anéantit les rêves des matérialistes en rendant les vérités éternelles à la géométrie d'EUCLIDE, reine des sciences. La raison humaine illuminée par DIEU reprend son trône et s'y assoit dignement pour raisonner correctement et rigoureusement afin de produire des œuvres exactes dans le domaine de la mathématique. Les mathématiciens n'ont pu résoudre le cinquième postulat parce qu'ils n'ont pas compris l'exactitude de la ligne droite engendrée par l'âme appuyée à sa Norme Ultime: DIEU
Conclusion
Mr. Friedemann Brock, your reaction and those of mathematicians against the apparition of the geometric truth is understandable because you know very well its unavoidable consequences. But you should accept the eternal truth in Euclidean geometry established by a right proof of postulate 5 and you should be the courageous pioneer of the converted mathematicians acting for recognizing my proofs by the mathematical community.
The reasons of our future generations must be formed by the teaching of exact mathematics which enables them to produce true sciences and not fictions. The Sun of Euclidean geometry will shine very soon in the sky of mathematics.
Rachid Matta MATTA
1-23-2008
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