Warning: most of advanced explanations here, although
exerpts of sources quoted in bibliography, are only hypotheses, sometimes
passed on in legend of book in book. If you can contradict me with certainty,
send me a mail { ferreol@mathcurve.com
}
1) Bizarre words
Why "mathematics"?
Word "mathematics" as also that of "philosophy" would be due to Pythagore. It sends back to a Greek term mathema which wants to say "science" in the optics of time, that is all the knowledge ". Mathematika in Greek as mathematica in Latin was used in the plural, that is why one says mathematics. Some try to speak about the mathematic, to show the unity, but it does not set. Let us note that in English one says mathematics with one, but that it is a peculiar word …
Is theorem been similar in theology?
No, it is rather been similar in theater. First syllable does not come of theos "god", but of thea "spectacle". As word "theory", word "theorem" was built from the Greek verb theorein significant "to observe".
Is corollary been similar in corolla?
Yes; these two words come from the Latin " corolla " which meant " small crown "; one gave indeed a small laurel wreath to the actors as bonus. A corollary is so a present given in more by the theorem!
Why "rational" numbers?
The rational numbers are not called(mentioned) so because they would be more rational than the others, as I for a long time believed him(it). Latin etymology "ratio" should not here to set(be taken) in the sense(direction) of reason but in that of the report, quotient (cf. French word "ratio"): the rational numbers are the numbers quotients of complete two.
Expression " complete rational ", for complete relative can then seem bizarre, but it should to set(be taken) in the sense(direction): " complete element of the ring of the rational ". Also, " rational fraction ", which can appear pléonasmique, appeared later " rational function "(office), ratio of two polynômes.
Is there a report between the function sine and sine of the front ?
Yes and not; word "sine" is a significant Latin word " curve, fold, cavity ". It(he) gave in French words "breast" (moreover, in Italian, mathematical sine says himself seno, who means also "breast") and "sinuous". But if sine of the forehead(front) form many cavities, the interpretation according to which mathematical sine would be called so because a sinusoïde is sinuous is a nonsense, because the notion of representation of a function(office) is more recent than that of sine!
Here is the likely history of the word "sine", which comes from a mistranslation.
First time: the Indian mathematician Âryabhata (VIE Century) use word jîva which means rope.
Second time: the Arabic mathematician Al-Fazzârî (VIIIE Century) arabise this word in jîba, word having no meaning in Arabic.
Third time: Gérard of Espagnolette (XIIIèmeCentury) confuses(merges) jîba with jaîb, all the more easily as in Arabic, vowels are sometimes omitted; now jaîb mean " pocket, cavity " and it(he) translates him(it) naturally into Latin by sine...
As for the cosine, it is simply the sine of the additional (of the angle); " co " come from the Latin cum, which means "with".
The tangente, she(it), comes from what it measures a portion of a tangente in the circle trigonométrique; and the cotangent is also the tangente of the additional.
Why "logarithms"?
Term was created in 1614 by the Scottish mathematician John Napier (gallicized in Néper), from Greek words logos being able to mean "calculation" and arithmos "number". Logarithms would be so numbers serving for calculating …
Where from comes word "algorithm"?
In spite of its small Greek air(sight), this word, as a lot(many) beginning by al (as alcohol), come from Arabic. Al-khwarizmi is the nickname of the mathematician Abu Ja farMohammed Ben Musa (c. 780 - c. 850), native of the region of Khwarazm (at present Khiva in Uzbekistan), where from the nickname. One of the pounds of arithmetic was translated into Latin under the name of liber algorismi (Al-khwarizmi's pound). As a result, one indicated(appointed) by algorismus the system of decimal numeration, then it became in French "algorithm" with a more general sense(direction), by the influence of the word arithmos ("number" in Greek) and of "logarithm" which is an anagram of it.
And word algebra?
Another word of Arabic origin, beginning by al ("@" in Arabic). It(he) results from the first part of the title of a book of the mathematician Al-khwarizmi, about which we have just spoken: Al jabr w al muqabalah, meaning " discount(delivery) places it and simplification ". Discount(delivery) in place in question is the passage of the negative elements of an equation on the other side of the equal sign to make them positive: here is the point of departure of the algebra. You will moreover be able to see in a Spanish dictionary which algebrista do not mean " algébriste ", but " rebouteux ": indeed, this one puts back(hands) in place the dislocated members!
Why an abscissa, an orderly?
These two names are adjectives substantivés, abbreviation of " line abscissa (that is " cut ", cf. " Split ") and orderly line ". Historically, the orderly appeared before the abscissa; being given a curve described with a point M and a right-hand side (D), the orderly were segments [MP] where P is the thrown(planned) of M on (D); these segments being "regularly" (= ordinatim in Latin) arranged, were called " ordinatim applicatae " in Latin, then ordered in French.
Given a point O on D, abscissas were segments [ OP], which are well cut " lines ".
Word "ordered" would have seemed in first under Pascal's feather in 1658 and word "abscissa" (under the Latin shape abscissa) in 1692 in Leibniz's text.
Let us note that Descartes has never used any of these two terms!
It would be Euler (on 1707 - 1783) who would have the first discovered a symmetry existing between the notions of abscissa and of ordered.
Where from comes word radian?
Of the Latin radius, which means beam(shelf) (cf.
radial nerve). But why beam(shelf)? Because an angle of a radian intercepts
an arc of a circle length of which is equal to the beam(shelf) of the circle!
Term was used(employed) for the first time by Thomson
in 1873.
Why are conics called ellipse, parabola and hyperbola?
Words " ellipse, hyperbola and parabola " were transcribed by Johannes Kepler ( 1571-1630 ) of Greek words elleipsis, huperbolê and parabolê, names which had been given by Aristée (IV-th century before J.C.) and popularized by Perge's Apollonius (env. 262-190 avenue. J.C.).
Greek word elleipsis was created from the verb elleipein which means "missing" (eclipse has the same origin), whereas huperbolê and parabolê are meaning existing Greek words a "excess" and the other "resemblance" or "the a just equivalence ". The suffix bolê comes from the verb balleinmeaning "trow", (cf the "discobolus" and the "ballistics"). Let us notice that for a perfect symmetry, Aristée would have been able to create " hypobole " for ellipse!
Three words " ellipse, parabola and hyperbola " represent also figures of rhetoric, in good equivalence with their etymology: an ellipse is a shortened formula (as " each the tour(tower) " in the place of " each has to wait for its tour(tower) "), a parabola is an allegorical story, a hyperbola is an exaggerated formula (as " to die to laugh ").
In mathematics, an ellipse lacks also anything, a hyperbola presents an excess, but of what? It is there that answers diverge...
For the historic dictionary of French language, an ellipse lacks perfection with regard to a circle. Although plausible, this interpretation kills a symmetry ellipse - hyperbola, around the parabola.
One can as well think as reason comes from what on an ellipse distance in the home(foyer) is smaller than distance to the manageress (eccentricity e < 1), on a parabola, it is equal (e = 1) and on a hyperbola, she(it) is superior (e> 1), but it is a nonsense because the Greeks did not know definition from homes(foyers) and manageresses.
Surer is the following interpretation, because for the Greeks, conics are sections of cone:
One considers the section of a cone by a perpendicular plan in a generator:
-It is an ellipse if the angle of opening of the cone is pointed (deficit with regard to the right angle).
-It is a hyperbola if the angle of opening of the cone is blunt (excess with regard to the right angle).
-It is a parabola if the angle of opening of the cone is right(straight) ( just equivalence).
A second explanation can result from the fact that, in
modern writing, the reduced general equation of a conic is 
,
the ellipse, the parabola and the hyperbola being obtained for respectively 
(in fact 
).
One reads on this equation that the area of the square built on the orderly is equal to the area of the rectangle defined with the abscissa and the rope passing by the summit, the area to which it is necessary to remove or to add a certain area as one has an ellipse or a hyperbola, equality before place for the parabola; this is in Apollonius's book on conics.
When one applies edge y2 to the rectangle 2px, the square is at fault in the case of the ellipse (it is the sense(direction) of the Greek term ellipse), in excess in the case of the hyperbola (it is the sense(direction) of the Greek term hyperbola), term parabola meaning the equality of areas.
Why progress, consequences(suites) and average arithmetic, geometrical and harmonious?
Let us remind that numbers are in arithmetical progress if the difference of two consecutive terms is constant (as 8 , 12 , 16, 20), in geometrical progress if the report of two consecutive terms is constant (as 8 , 12 , 18, 27) and in harmonious progress if the inverse are in arithmetical progress (as 3 , 4 , 6, 12); from then on, a continuation(suite) is arithmetical, geometrical, harmonious if its terms are in arithmetical, geometrical, harmonious progress and c is average arithmetic, geometrical, harmonious of has and b if the numbers has, c, b are in arithmetical, geometrical, harmonious progress.
These " arithmetical, geometrical, harmonious " qualifiers are very former(ancient): they are due to pythagoriciens, to the sixth century before Christ.
Expression "arithmetic" is due probably to the fact which complete natures 1 , 2 , 3, 4, (arithmos in Greek) form the most simple of the arithmetical consequences(suites).
"Geometrical" expression results rather from the geometrical average which obtains by a geometrical construction: from two lengthes has and b, one obtains geometrical average c by the process:
"Harmonious" expression should be connected following the inverse of the natures which is the most simple of the harmonious consequences(suites). This continuation(suite) ( 1/n ) gets naturally in music, what explains its name: if a rope of length l vibrates with a frequency f, a rope (of the same mass linéique and of the same tension) of length l/2, 1/3, l/4 will vibrate with frequencies 2f , 3f , 4f which are the "harmonious" of F.
One can add that if term "reason" (of the Latin ratio, report) justifies well itself in the case of the geometrical consequences(suites), where it indicates(appoints) the constant report of a term to the precedent, it is not case - otherwise by analogy - for an arithmetical continuation(suite), where it indicates(appoints) constant difference between a term and the precedent.
Why "intyegral" calculus?
This term results from the Latin integer " complete, total ", probably because a complete is assembling (integration!) of an infinity of tiny terms in a whole. Term is of the Swiss mathematician Jacques Bernoulli in 1696; Leibniz would have preferred at first term calculation " sommatoire " but was convinced by Jean Bernoulli, brother of Jacques; in exchange, the sign of integration arises from the letter S, and not of the letter I...
Why 
is it an integration " by parts "?
English term is partial integration; one should rather speak about integration "partially" …
Why a function(office) " homographique "?
I do not have to be the only one to have for a long time
thought that functions(offices) homographiques
should called so because they have all similar graphs (a hyperbola of asymptotes
parallel to axes). In fact their name results from what the alterations
of the same type of C in C: 
transform the figures of the plan into similar figures (they transform
circles either right-hand sides into circles or right-hand sides).
Term is of for Michel Chasles ( 1793-1880 ).
Does why normal mean ( sometimes ) orthogonal?
Because this word comes from the Latin normalis meaning set square. It is so the first sense(direction) of this word. Word " normé " comes from "standard" having taken the sense(direction) of " standard(cannon), model ". That is why it is better to speak about base orthonormée that of base orthonormale!
Why a distance - type?
Term is a translation from standard English deviation, introduced by the Englishman Egon Pearson in 1893.
Why cavalier perspectives?
A cavalier perspective is a perspective where parallels(parallel lines) remain parallel (contrary to a conical perspective where parallel right-hand sides become generally convergent); she(it) is obtained in theory for an observer situated in the infinity. A possible origin of the expression "cavalier perspective" is that a careful with money rider down from the horse an object with earth(ground) him(it,her) sees almost in cavalier perspective. Term dating the XVIE Century when it(he) was used in military architecture, another interpretation would result from the fact that a rider is, in fortification, a high hillock of earth(ground). Cavalier sight is then the sight which has on the campaign, an observer situated on the height of the rider; cavalier perspective would be so process used by the draftsman of fortifications to return cavalier sight.
On the other hand interpretation saying that expression come from the mathematician Cavalieri is fanciful.
Why does one say a PGCD and not a PGDC ( bigger common divisor), a PPCM and not a PPMC (bigger multiple common)?
We have no answer; for the musicality of the expression?
Why a space "refines"?
Term comes from affinity, introduces by Léonard Euler in 1748, which notices (in French in the text) that two obtained curves one of the other one by changing the scale(ladder) of abscissas are not similar, but that they have all the same a certain "affinity". But we do not know which(who) introduced the use of the adjective refines. Maybe is it because of the bend by English that this word which should be affin in the male became refine?
Why sets(groups), groups, rings, bodies?
" Set(group), group and body " have the sense(direction) of " grouping of individuals ", with an increasing cohesion (for "body", to think in " corporate body, diplomatic corps "). Only ring seems to make exception, but this word is translated by German Boxing ring which means also in this language "circle" (as in " encircle philatélique "). Let us note that if the sets(groups) are called generally E, the groups G, and the rings A, the bodies are indicated(appointed) by K, because body says itself in German " Körper ". In an English text, they will be indicated(appointed) by F, because body says himself field (= field). Word "set("group") is due probably to the German Georg Cantor in 1883 (under the German shape of " Menge " which means also "crowd"), word "group" to the Frenchman Augustine Cauchy in 1815, the words "ring" and "body" (under the shape "Boxing ring" and " Körper ") to the German Richard Dedekind in 1871 in the book(pound): " Lehrbuch of Algebra ".
Seventy, eighty (or eighty) and ninety.
They are our seventy, eighty and ninety for Switzerland(Swisses) and Belgian, stemming from Latin words septuaginta, octoginta, nonaginta.
Grévisse (good custom(usage), p. 926) said that Vaugelas condemned seventy and ninety as archaisms, but in fact it would seem whether it is rather the opposite!
It is likely that seventy, eighty and ninety are exactly archaisms stemming from the Gaul, Celtic language, as the Breton. System vigésimal is indeed net in Breton where 20 says himself ugent, 40 daou-ugent, 60 sorting - ugent, 70 dek ha sorting - ugent (it is to say 10 more 3 times 20) etc. And this would result from languages meadow Indo-European using a system vigésimal (it should be said of base 20). For example, in Basque, 20 say to itself hogei, 30 hogeitabat (20 + 10), 40 berrogei (twice 20), 60 hirurogei (3 times 20) etc. In Europe, one still finds the Danish where 50 says itself halvtreds, what means " half of third about twenty "; 70 say to itself halvfjerds (half of the fourth) and 90 halvfems (half of second year of secondary school); 60 say to itself there tres (of tre = 3) and 80 firs (of fire = 4). One finds also a basic track 20 in the name of the very famous orphanage of " Quinze-Vingts " dating 1254, so named(appointed) to accommodate 300 blind veterans.
And it is hegemony francilienne which imposed recently these archaisms in all France (one called still seventy and ninety fifty years ago in the South and the southeast). Switzerland&(Swisses) and Belgians (whose dialects do not know the base 20) resisted!
Let us note that if most of the peoples count in base 10, it is because of our 10 fingers; those that count in base 20 have so inclusive toes …
Why does one say a computer?
French is the only language where one says "computer", and "not computer". This word, which is in Littré as indicating(appointing) adjective " God who puts of the order in the world " was proposed not by a scientist, but by a philologist Jacques Perret, in 1955 , to IBM France, and was held(retained) against the anglicism computeur (impossible in French because of idiot and pute!).
2) Bizarre symbols
Why is the number p called so?
The use of the Greek letter p for the report of the circumference in the diameter was popularized by Léonard Euler in a work on series published in Latin in 1737; but she(it) is due at first to an English mathematician, William Jones, which(who) used her(it) in a book appeared in 1706. However, in 1647 , the English mathematician William Oughtred had already used p to indicate(appoint) the perimeter of a circle (and the report in the diameter). The letter p is at the same moment the initial of perifereia and of perimetros which(who) in Greek indicate(appoint) the circumference of a disc.
And the number e?
Everybody had found: it is the initial of exponential. But there is hardly to bet that Euler, by using this notation for the first time in 1728 in a book on artillery, was not without resources had noticed that it was also the initial of his(her) name!
Where from comes symbol %?
In the XVE
Century, the Italians wrote Pc
° for per cento. It became
bit by bit Ps °
then P 
; then, P disappeared
and symbol became current %. Two forgery zéros
of this symbol were bit by bit likened to the two zéros
of 100; that is why one added a zero to write %0.
Where from comes the symbol of the radicals 
?
This symbol is due to the German Christoff Rudolff in 1525, in the work dieCoss. It is probably one r small letter deformed, initial of "root" (radix in Latin).
Where from comes the symbol of integration 
?
This symbol is due to Gottfried Wilhelm Leibniz ( 1646-1716 ). It is one S lengthened(stretched out), because a complete is a sum (summa in Latin).
Where from comes the symbol of the infinity ¥? "
This symbol is due to John
WALLIS who introduced him(it) in 1655; it(he) draws as one eight slept
but the origin is not symbol 8.
This symbol would come
-Or of one ligature Latin of the letter m, initial of one thousand.
-Or of the Greek letter oméga " w ", because it is the last one of the Greek alphabet (cf. the word of Jesus Christ: " I am the alpha and the oméga ").
It(he) is as likely as J. Wallis thought as well of the fact as the curve of the same shape ( lemniscate ) crosses(goes through) unlimited.
Why does membership note Î?
This symbol arises from the Greek letter epsilon " e? " Which is the initial of esti ( esti ) meaning "is". It(he) was created by Peano in 1890.
Where from come the symbols of quantificateurs" and $?
" Who is read " for everything "or" whatever or " is one A turned(returned) height - low; In is indeed the initial of " alles " which means " everything " in German; notation would be due to David Hilbert ( 1862-1943 ).
$ who is read " for at least one " or " there is at least one such as " is one E turned(returned) right-left; E is indeed the initial of " existieren " which means "existing" in German (word which comes moreover from French); notation would be due to Gottlob Frege (on 1848 - 1925).
Where from comes the nabla
?
You will know soon this symbol which is simply a delta capital letter knocked down, where from the sometimes given name of " atled ". It(he) looks like a lyre, that is why William Hamilton ( 1805-1865 ) called him(it) nabla, Greek word of origin phénicienne indicating(appointing) exactly a sort of lyre in shape of opposite delta. In Hebrew, harp says himself nebel …
Where from comes symbol?
This character was practically unknown in France some years ago hardly, but was popularized with Internet.
It(he) was on the other hand common(the other hand current) in England and in the United States as a replacement of " at ", as the ampersand " et " as a replacement of "and". Example of use: " total What is the cost of 5 apples 5 d? ".
As and, arises from chancelleries; it is ligature of the
Latin " ad " ("in" it French) where has him(it) and 
cursive(cursory) of the onciale eventually
become confused. It(he) established(constituted) the first line of address
of diplomatic documents.
The French name of this character, is according to the AFNOR " in commercial ", as and is " and commercial ". However, the name which give to him(her) the French Internet users turns around its shape: arabesque, roundness, rolled up. But the most frequently used(employed) name is " aroba ", " arobase " or " arrobas ". A confusion comes probably: one finds indeed in the catalogs of French long-distance skiers a character which has about the same written form as, which is called " arobas ", but which corresponds to something completely different: it is the symbol of an ancient(former) unit of weight and still usual capacity in Spain and in Portugal, arroba, amounting to 12 in 15 kg or 10 in 16 l, of which the true French name is moreover " arrobe " or " arobe ". Word results from dialectal Arabic arba significant "four".
The another interpretation is that arobas is a deformation of " has low circle (of breakage) " : " has circle " for has him(it) in a circle, and "lower case", indicating(appointing) the small letters which were at the bottom of the breakage, board with drawers in which were classified the lead forms of letters.
Why small o and big O?
These symbols are known under the name of notations of Baby carriage ( 1877-1938 ). The " o " is the initial from German " Ordnung " which means "order". It is a question indeed of comparing the orders of height of functions(offices) with the neighborhood of a point.
Why N, Z, Q, R, C?
N indicate(appoint) the set(group) of complete natures, baptized so by the Italian Giuseppe Peano ( 1858-1932 ) (naturale in Italian); to say that N is the initial of number is so a nonsense.
Z is the set(group) of the complete relatives, initial due to the German Richard Dedekind ( 1831-1916 ), because "to count" says himself zahlen in German; this will not prevent the Prof.s of mathematics from saying to the pupils that it is the set(group) of " zentiers " …
Q is the set(group) of the rational numbers, baptized so by Peano (quotiente = quotient in Italian).
R is the set(group) of the real numbers, baptized so by the German Georg Cantor ( 1845-1918 ) (Real = reality in German).
C is the set(group) of the complex numbers, baptized so by Karl Friedrich Gauss (on 1777 - 1855) as a replacement of the "imaginary" term.
Why is the symbol of the empty set the letter Æ alphabets Norwegian and Danish?
Because one needed that a symbol which looks like the 0 without being one of it and which the mathematician of the group Bourbaki André Weil who introduced him(it) in 1937 knew the Norwegian.
Why does a pit note " Ker "?
" Ker " does not come word of the Breton meaning "house", but from German Kern, meaning simply "pit". In English, pit says himself also kernel.
Which are the previous history of the sense(direction) of the needles of the watch and the sense(direction) trigonométrique?
Watches and clocks resumed graduations of the horizontal sundials, or gnomons, and the sense(direction) of needles corresponds to that of the shadow. Attention, in the vertical sundials, the shadow turns in the other sense(direction) (and everything this costs moreover only in the north hemisphere!): the 12 is below and the 1 just man in its right-hand side.
Sense(direction) trigonométrique is bound(connected) to the way of which one represents a mark Oxy, and this representation is due probably to our writing from left to right. One can notice that it is the sense(direction) of rotation of the earth(ground) around the sun, for an observer situated towards(as for) the ground North Pole, as well as in the sense(direction) of rotation of the earth(ground) on herself(itself), for an observer placed in the North Pole.
The moon turns also in the sense(direction) trigonométrique
around the earth(ground) and on herself(itself), for an observer placed
in the ground North Pole. The same plan for the most part of planets and
of their satellites.
Bibliography:
Historic dictionary of French language, Robert, on 1998.
S. MEHL, Small chronology of mathematics, http://perso.wanadoo.fr/szmehl/.
The archives of the list of broadcasting(distribution) historia mathematica,
http://forum.swarthmore.edu/epigone/historia_matematica/all
Earliest Known Uses of Some of the Word ofMathematics
Vocabulario Etimológico in Matemáticas
Column of wanted notices in the bulletin of the association of the professors of mathematics of state education ( APMEP).
F. CAJORI, Is history of mathematical notations, short The open publishing company, The Room, Illinois, 1929 old, republished on 1952.
S. SCHWARTZMAN, The words of mathematics, A year etymological dictionary of mathematical terms used in english, The Mathematical Association of America, on 1994.
G. IFRAH, World history of figures, Robert Laffont, on 1994.
B. HAUCHECORNE, D. SURATTEAU, mathematicians of A in Z, Ellipses, on 1996.
P. CEGIELSKI, historic of the elementary theory of the sets(groups), in " fragments of history of mathematics II ", brochure APMEP n ° 65 , 1987.