Tommy Robinson isn't the first to that the UK has jailed after a secret trial. Melanie Shaw tried to expose child abuse in a Nottinghamshire kids home -- it wasn't foreigners doing the molesting, but many members of the UK's parliament. The government kidnapped her child and permanently took it away. Police from 3 forces have treated her like a terrorist and themselves broken the law. Police even constantly come by to rob her phone and money. She was tried in a case so secret the court staff had no knowledge of it. Her lawyer, like Tommy's, wasn't present. She has been held for over 2 years in Peterborough Prison. read, read

# Euclid

**Euclid** was a Greek mathematician of the 3rd century B.C.; we are ignorant not only of the dates of his
birth and death, but also of his parentage, his teachers, and the residence of his early years.
In some of the editions of his works he is called *Megarensis*, as if he had been born in Megara in
Greece, a mistake which arose from confounding him with another Euclid, a disciple of Socrates.
Proclus (A.D. 412-485), the authority for most of our information regarding Euclid, states in his
commentary on the first book of the *Elements* that Euclid lived in the time of Ptolemy I., king
of Egypt, who reigned from 323 to 285 B.C., that he was younger than the associates of Plato,
but older than Eratosthenes (276-196 B.C.) and Archimedes (287-212 B.C.). Euclid is said to have
founded the mathematical school of Alexandria, which was at that time becoming a centre, bot only
of commerce, but of learning and research, and for this service to the cause of exact science
he would have deserved commemoration, even if his writings had not secured him a worthier title to
fame. Proclus preserves a reply made by Euclid to King Ptolemy, who asked whether he could not
learn geometry more easily than by studying the *Elements* - "There is no royal road to geometry".
Pappus of Alexandria, in his *Mathematical Collection*, says that Euclid was a man of mild and
inoffensice temperament, unpretending, and kind to all genuine students of mathematics.
This being all that is known of the life and character of Euclid, it only remains therefore to
speak of his works.
Among those which have come down to us the most remarkable is the *Elements*. They consist of
thirteen books; two more are frequently added, but there is reason to believe that they are the
work of a later mathematician, Hypsicles of Alexandria.
The question has often been mooted, to what extent Euclid, in his *Elements*, is a discoverer
or a compiler. To this question no entirely satisfactory answer can be given, for scarcely any of
the writings of earlier geometrics have come down to our times. We are mainly dependent on
Pappus and Proclus for the scanty notices we have of Euclid's predecessors, and of the problems
which engaged their attention; for the solution of problems, and not the discovery of theorems, would
seem to have been their principal object. From these authors we learn that the property of the
right-angled triangle had been found out, the principles of geometrical analysis laid down,
the restriction of constructions in plane geometry to the straight line and the circle agreed
upon, the doctrine of proportion, for both commensurables and incommensurables, as well as loci,
plane and solid, and some of the properties of the conic sections investigated, the five regular
solids (often called the Platonic bodies) and the relation between the volume of a cone or
pyramid and that of its circumscribed cylinder or prism discovered. Elementary works had been
written, and the famous problem of the duplication of the cube reduced to the determination of
two mean proportionals between two given straight lines. Nothwithstanding this amount of discovery,
and all that it implied, Euclid must have made a great advance beyond his predecessors (we are told
that "he arranged the discoveries of Eudoxus, perfected those of Theaetetus, and reduced to
invincible demonstration many things that had previously been more loosely proved"), for his *Elements*
supplanted all similar treatises, and, as Apollonius received the title of "the great geometer",
so Euclid has come down to later ages as "the elementator".
For the past twenty centuries parts of the *Elements*, notably the first six books, have been used
as an introduction to geometry. Though they are now to some extent superseded in most countries,
their long retention is a proof that they were, at any rate, not unsuitable for such a purpose.
They are, speaking generally, not too difficult for novices in the science; the demonstrations
are rigurous, ingenious and often elegant; the mixture of problems and theorems gives perhaps some
variety, and makes their study less monotonouys; and, if regard be had merely to the metrical
properties of space as distinguished from from the graphical, hardly any cardinal geometrical truths
are omitted. With these excellences are combined a good many defects, some of them inevitable
to a system based on a very few axioms and postulates. Thus the arrangement of the propositions seems
arbitrary; associated theorems and problems are not grouped together; the classification, in short,
is imperfect. Other objections, not to mention minor blemishes, are the prolixity of the style, arising
partly from a defective nomenclature, the treatment of parallels depending on an axiom which is not
axiomatic, and the sparing use of superposition as a method of proof.

Of the thirty-three ancient books subservient to geometrical analysis, Pappus enumerates first
the *Data* of Euclid. He says it contained 90 propositions, the scope of which he describes; it now
consists of 95. It is not easy to explain this discrepancy, unless we suppose that some of the
propositions, as they existed in the time of Pappus, have since been split into two,
or that what were once scholia have since been erected into propositions. The object of the *Data*
is to show that when certain things -lines, angles, spaces, ratios, etc.- are given by
hypothesis, certain other things are given, that is, determinable. The book, as we are expressly
told, and we may gather from its contents, was intended for the investigation of problems;
and it has been conjectured that Euclid must have extended the method of the *Data* to the investigation
of theorems. What prompts this conjecture is the similarity between the analysis of a theorem and the
method, common enough in the *Elements*, of reductio ad absurdum -the one setting out from the supposition
that the theorem is true, the other from the supposition
that it is false, thence in both cases deducing a chain of consequences which ends in a conclusion
previously known to be true or false.

The *Introduction to Harmony* and the *Section of the Scale*,
treat of music. There is good reason for believing that one at any rate, and probably both,
of these books are not by Euclid. No mention is made of them by any writer previous to
Ptolemy (A.D. 140), or by Ptolemy himself, and in no ancient codex are they ascribed to Euclid.

The *Phaenomena* contains an exposition of the appearances produced by the motion
attributed to the celestial sphere. Pappus, in a few remarks prefatory to his sixth book,
complains of the faults, both of omission and commission, of writers on astronomy,
and cites as an example of the former the second theorem of Euclid's *Phaenomena*,
whence, and from the interpolation of other proofs, David Gregory infers that this treatise
is corrupt.

The *Optics* and *Catoptrics* are ascribed to Euclid by Proclus,
and by Marinus in his preface to the *Data*, but no mentiin is made of
them by Pappus. This latter circumstance, taken in connexion with the fact
that two of the propositions in the sixth book of the *Mathematical Collection*
prove the same thing as three in the Optics, is one of the reasons given by Gregory
for deeming that work spurious. Several other reasons will be
found in Gregory's preface to his edition of Euclid's works.

In some editions of Euclid's works there is given a book on the *Divisions of Superficies*,
which consists of a few propositions, showing a straight line may be drawn
to divide in a given ratio triangles, quadrilaterals and pentagons.
This was supposed by John Dee of London, who transcribed or translated it,
and entrusted it for publication to his friend Federico Commandino
of Urbino, to be the treatise of Euclid referred to by Proclus
as *το περι διαιρέσεων βιβλίον*. Dee mentions that, in the copy from which
he wrote, the book was ascribed to Machomet of Bagdad, and adduces two or
three reasons for thinking it to be Euclid's. This opinion, however,
he does not seem to hold very strongly, nor does it appear that it was
adopted by Commandino. The book does not exist in Greek.

(to be expanded)

*Part of this article consists of modified text from the Encyclopædia Britannica Eleventh Edition of 1911, which is no longer restricted by copyright.*

*Part of this article consists of modified text from Metapedia (which sadly became a Zionist shill), page http:en.metapedia.org/wiki/Euclid and/or Wikipedia (is liberal-bolshevistic), page http:en.wikipedia.org/wiki/Euclid, and the article is therefore licensed under GFDL.*