This website uses cookies to ensure you get the best experience. Learn more

notation

It is therefore better to use some independent notation, such as A Z.

7333There is a complete edition in modern notation by T.

2019Evolution and involution are usually regarded as operations of ordinary algebra; this leads to a notation for powers and roots, and a theory of irrational algebraic quantities analogous to that of irrational numbers.

19192 and lb/in.', in the Hospitaller notation, to be employed in the sequel).

1619(n+--r-1)lr!=n[r]lr!; this may, by analogy with the notation of ï¿½41, be denoted by n [r 7.

1413The symbol e 0 behaves exactly like i in ordinary algebra; Hamilton writes I, i, j, k instead of eo, el, e2, es, and in this notation all the special rules of operation may he summed up by the equalities = - I.

1213In the notation of the integral calculus, this area is equal to f x o udx; but the notation is inconvenient, since it implies a division into infinitesimal elements, which is not essential to the idea of an area.

119Various special algebras (for example, quaternions) may be expressed in the notation of the algebra of matrices.

1112Briggs seems to have used the notation all his life, but in writing it, as appears from manuscripts of his, he added also a small vertical line just high enough to fix distinctly which two figures it was intended to separate: thus he might have written 63 0957379.

109Algebraical division therefore has no definite meaning unless dividend and divisor are rational integral functions of some expression such as x which we regard as the root of the notation (ï¿½ 28 (iv.)), and are arranged in descending or ascending powers of x.

99One drawback of Thomsen's notation is that the nature of the final system is not indicated, although this defect in general causes no ambiguity.

88In this notation the fundamental relation is written (l + a i x +01Y) (I + a 2x+l32Y) (1 + a3x+133y)...

88(v.) It should be mentioned that the notation of the binomial 'coefficients, and of the continued products such as n(n -1).

88Even in ordinary algebra the notation for powers and roots disturbs the symmetry of the rational theory; and when a schoolboy illegitimately extends the distributive law by writing -V (a+b)a+J b, he is unconsciously emphasizing this want of complete harmony.

88It is not, however, necessary that the notation of the calculus should be employed throughout.

88he prints a bar under the decimals; this notation first appears without any explanation in his "Lucubrationes" appended to the Constructio.

66We may here notice the important chemical symbolism or notation introduced by Berzelius, which greatly contributed to the definite and convenient representation of chemical composition and the tracing of chemical reactions.

66Girard is inconsistent in his notation, sometimes following Vieta, sometimes Stevin; he introduced the new symbols ff for greater than and ï¿½ for less than; he follows Vieta in using the plus (+) for addition, he denotes subtraction by Recorde's symbol for equality (=), and he had no sign for equality but wrote the word out.

66Its great merit consists in the complete notation and symbolism, which avoided the cumbersome expressions of the earlier algebraists, and reduced the art to a form closely resembling that of to-day.

66We may here notice the important chemical symbolism or notation introduced by Berzelius, which greatly contributed to the definite and convenient representation of chemical composition and the tracing of chemical reactions.

66These examples show that Napier was in possession of all the conventions and attributes that enable the decimal point to complete so symmetrically our system of notation, viz.

55Accordingly, the typical form for such a complex number is x+yi, and then with this notation the above-mentioned definition of multiplication is invariably adopted.

55Remark.-In this notation (0) = Eai = (i n); (02) _ za l a2 = (2);...

55It is convenient to retain x, to denote x r /r!, so that we have the consistent notation xr =x r /r!, n (r) =n(r)/r!, n[r] =n[r]/r!.

55According to this notation, the three equations of motion are dt2 = b2v2E + (a2 - b2) d.s dt =b2v2rj+(a2 - b2) dy d2 CIF - b2p2+(a2_b2)dz It is to be observed that denotes the dilatation of volume of the element situated at (x, y, z).

55These examples show that Napier was in possession of all the conventions and attributes that enable the decimal point to complete so symmetrically our system of notation, viz.

55He introduced the terms multinomial, trinomial, quadrinomial, &c., and considerably simplified the notation for decimals.

58(19), 1 abA) ' ' we may write 12= (cos 27rv 2 .dv) 2 + (f sin zirv 2 .dv) 2 (20), or, according to our previous notation, 12 = (2 - C 2 +(z - Sv)2= G2 +H2 Now in the integrals represented by G and H every element diminishes as V increases from zero.

59These works possess considerable originality, and contain many new improvements in algebraic notation; the unknown (res) is denoted by a small circle, in which he places an integer corresponding to the power.

511Wertheim (Leipzig, 1890), and an English edition in modern notation (T.

44Observe the notation, which is that introduced by Cayley into the theory of matrices which he himself created.

44Hence, excluding ao, we may, in partition notation, write down the fundamental solutions of the equation, viz.

44Whether this principle may legitimately be extended to the notation adopted in (iii.) (a) of ï¿½ 14 is a moot point.

44In the notation of the calculus the relations become - dH/dp (0 const) = odv /do (p const) (4) dH/dv (0 const) =odp/do (v const) The negative sign is prefixed to dH/dp because absorption of heat +dH corresponds to diminution of pressure - dp. The utility of these relations results from the circumstance that the pressure and expansion co efficients are familiar and easily measured, whereas the latent heat of expansion is difficult to determine.

44Substituting for H its value from (3), and employing the notation of the calculus, we obtain the relation S - s =0 (dp /do) (dv/do),.

44The documents discovered by Dom Germain Morin, the Belgian Benedictine, about 1888, point to the conclusion that Guido was a Frenchman and lived from his youth upwards in the Benedictine monastery of St Maur des Fosses where he invented his novel system of notation and taught the brothers to sing by it.

44Observe the notation, which is that introduced by Cayley into the theory of matrices which he himself created.

44For present purposes the form will be written a0x 1 +(7)a1x1=1 x2+ C 2)o'2x12 x 2 +...+anx2, the notation adopted by German writers; the literal coefficients have a rule placed over them to distinguish them from umbral coefficients which are introduced almost at once.

45Employing the notation in which the molecule is represented vertically with the aldehyde group at the bottom, and calling a carbon atom+or - according as the hydrogen atom is to the left or right, the possible configurations are shown in the diagram.

48At a later date Berzelius denoted an oxide by dots, equal in number to the number of oxygen atoms present, placed over the element; this notation survived longest in mineralogy.

331 Z2' The First Perpetuant Is The Last Seminvariant Written, Viz.: A O (B O B 2 3B O B 3) A L (Bi 2B0B2), Or, In Partition Notation, Ao(21) B (1)A(2)B; And, In This Form, It Is At Once Seen To Satisfy The Partial Differential Equation.

33Expressed Equations.-The simplest forms of arithmetical equation arise out of abbreviated solutions of particular problems. In accordance with ï¿½ 15, it is desirable that our statements should be statements of equality of quantities rather than of numbers; and it is convenient in the early stages to have a distinctive notation, e.g.

33(iii.) Scales of Notation lead, by considering, e.g., how to express in the scale of to a number whose expression in the scale of 8 is 2222222, to (iv.) Geometrical Progressions.

34+n(r)An-rar+ï¿½.ï¿½ +n(n)a n (2), where n(0), introduced for consistency of notation, is defined by n (o) EI (3).

24His notation is based on that of Vieta, but he introduced the sign X for multiplication, - for continued proportion, :: for proportion, ' and denoted ratio by one dot.

25His notation is based primarily on that of Harriot; but he differs from that writer in retaining the first letters of the alphabet for the known quantities and the final letters for the unknowns.

25His notation is based primarily on that of Harriot; but he differs from that writer in retaining the first letters of the alphabet for the known quantities and the final letters for the unknowns.

25,In a fluid, the circulation round an elementary area dxdy is equal to dv du udx + (v+dx) dy- (u+dy) dx-vdy= () dxdy, so that the component spin is dv du (5) 2 dx - dy) in the previous notation of § 24; so also for the other two components and n.

26,In a fluid, the circulation round an elementary area dxdy is equal to dv du udx + (v+dx) dy- (u+dy) dx-vdy= () dxdy, so that the component spin is dv du (5) 2 dx - dy) in the previous notation of § 24; so also for the other two components and n.

262 enclosing a point B, the pressure p at B is the limit of OP/DA; and p =lt(AP/DA) =dP/ dA, (I) in the notation of the differential calculus.

27In the preface to this work, which is dedicated to one Dionysius, Diophantus explains his notation, naming the square, cube and fourth powers, dynamis, cubus, dynamodinimus, and so on, according to the sum in the indices.

13The famous inscriptions with hymns to Apollo accompanied by musical notation were found on stones belonging to this treasury.

14While still an undergraduate he formed a league with John Herschel and Charles Babbage, to conduct the famous struggle of "d-ism versus dot-age," which ended in the introduction into Cambridge of the continental notation in the infinitesimal calculus to the exclusion of the fluxional notation of Sir Isaac Newton.

15According to the notation adopted by Meyer the atomic susceptibility k=KX atomic-weight/ (density X 1000).

15His travels and mercantile experience had led E t u eopre him to conclude that the Hindu methods of computing were in advance of those then in general use, and in 1202 he published his Liber Abaci, which treats of both algebra and arithmetic. In this work, which is of great historical interest, since it was published about two centuries before the art of printing was discovered, he adopts the Arabic notation for numbers, and solves many problems, both arithmetical and algebraical.

15The velocity of the ellipsoid defined by X =o is then U= - 2 __ M ((ro b J o (a2 =ab (i -A0), (20) with the notation A or A a a= a (a2bc+ = - 2abc d -- so that in (4) xA x 'UxA x A' 4)' 1 -Ao' (22) in (I) for an ellipsoid.

15The velocity of the ellipsoid defined by X =o is then U= - 2 __ M ((ro b J o (a2 =ab (i -A0), (20) with the notation A or A a a= a (a2bc+ = - 2abc d -- so that in (4) xA x 'UxA x A' 4)' 1 -Ao' (22) in (I) for an ellipsoid.

15Each problem was something unique; the elements of transition from one to another were wanting; and the next step which mathematics had to make was to find some method of reducing, for instance, all curves to a common notation.

00A word is necessary on Diophantus' notation.

00Although the system of Berzelius has been modified and extended, its principles survive in the modern notation.

00Such an expression as a l b 2 -a 2 b i, which is aa 2 ab 2 aa x 2 2 ax1' is usually written (ab) for brevity; in the same notation the determinant, whose rows are a l, a 2, a3; b2, b 2, b 3; c 1, c 2, c 3 respectively, is written (abc) and so on.

00There is no doubt that Guido's method shows considerable progress in the evolution of modern notation.

00(a) The formula may involve numbers or ratios which cannot be expressed exactly in the ordinary notation.

00+ u m-p + zum), which may be denoted by Cp. With this notation, the area as given by Simpson's rule may be written in the form sC l - 3 C2 or CI+ 1 3 `-(C1C2).

00This, in the notation of §§ 46 and 54, may be written?

00In works on sound it is usual to adopt Helmholtz's notation, in which the octave from bass to middle C is written c d e f g a b c'.

00The French notation is as under: C D E F G A B c Ut 1 Re f M] Fa] Sol i La i Si, Utz.

00But a new system of musical notation which he thought he had discovered was unfavourably received by the Academie des sciences, where it was read in August 1742, and he was unable to obtain pupils.

00The system of notation (by figures) concerning which he read a paper before the Academie des Sciences, August 22, 1742, was ingenious, but practically worse than useless, and failed to attract attention, though the paper was published in 1 743 under the title of Dissertation sur la musique moderne.

00Among the natives of Arezzo the most famous are the Benedictine monk Guido of Arezzo, the inventor of the modern system of musical notation (died c. 1050), the poet Petrarch, Pietro Aretino, the satirist (1492-1556), and Vasari, famous for his lives of Italian painters.

00Denoting the value of T at any velocity v by T (v), then (8) T(v) = sum of all the preceding values of AT plus an arbitrary constant, expressed by the notation (9) T(v) =Z(Av)/gp+ a constant, or fdv/gp+ a constant, in which p is supposed known as a function of v.

00so that Denoting dx/dt, the horizontal component of the velocity, by q, (49) v cos i =q, equation (43) becomes (50) dq/dt= -r cos i, and therefore by !(48) (51) dq _dq dt ry di - dt di-g' It is convenient to express r as a function of v in the previous notation (52) Cr = f(v), dq _vf(v) di - Cg ' an equation connecting q and i.

00Now taking equation (72), and replacing tan B, as a variable final tangent of an angle, by tan i or dyldx, (75) tan 4) - dam= C sec n [I(U) - I(u)], and integrating with respect to x over the arc considered, (76) x tan 4, - y = C sec n (U) - f :I(u)dx] 0 But f (u)dx= f 1(u) du = C cos n f x I (u) u du g f() =C cos n [A(U) - A(u)] in Siacci's notation; so that the altitude-function A must be calculated by summation from the finite difference AA, where (78) AA = I (u) 9 = I (u) or else by an integration when it is legitimate to assume that f(v) =v m lk in an interval of velocity in which m may be supposed constant.

00Now calculate the pseudo-velocity uo from =v 95 cos 4) sec n, and then, from the given values of 0 and 8, calculate u e from either of the formulae of (72) or (73): (82) I (u 9) - I (u0) tan 0 - tan 8 C sec n (83) D(ue) =D (uq5) 4)°-B° cos n' Then with the suffix notation to denote the beginning and end of the arc 0-0, mt e = C[Tum) - T (u0)], 5 ((x x9 1l 0.

00The notation of this mass of MSS.

00Gregory's notation is more generally used, and Scrivener's, though still followed by a few English scholars, is likely to become obsolete.

00This method of notation has various disadvantages.

00At present it has not seriously threatened the hold of Gregory's notation on the critical world, but it will probably have to be adopted, at least to a large extent, when von Soden's text is published.

00known in Gregory's notation as 13, 69, 124, 34 6, 543, 788, 826, 828, or in von Soden's as e 368, S 505, e 1211, e 226, e 257, e 1033, e 218, e 219, all which, except 69, in spite of the dating implied by von Soden's notation were probably written in the 12th century in Calabria.

00known in Gregory's notation as I, 118, 131, 209, and in von Soden's as S 50, e 346, S 467 and S 457.

00The dating implied by the latter notation is wrong, as I certainly belongs to the 12th, not to the 10th century, and 118 is probably later than 209.

00It is customary to quote these by small letters of the Latin alphabet, but there is a regrettable absence of unanimity in the details of the notation.

00His edition is historically very important as it introduced the system of notation which, in the amplified form given to it by Gregory, is still in general use.

00(arithmetic) elementary lessons on the notation of decimal fractions.

00The notation log x is generally employed in English and American works, but on the continent of Europe writers usually denote the function by lx or lg x.

00- Nathaniel Roe's Tabulae logarithmicae (1633) was the first complete seven-figure 1 In describing the contents of the works referred to, the language and notation of the present day have been adopted, so that for example a table to radius 10,000,000 is described as a table to 7 places, and so on.

00He also reduced the solar parallax to 14" (less than a quarter of Kepler's estimate), corrected the sun's semi-diameter to 15' 45", recommended decimal notation, and was the first to make tidal observations.

008 4 In modern trigonometrical notation, I +sec 0: tan 0 :: I : tan Z0.

00II) whose centre is 0, AC its chord, and HK the tangent drawn at the middle point of the arc and bounded by OA, OC produced, then, according to Archimedes, AMC AC. In modern trigonometrical notation the propositions to be compared stand as follows: 2 tan 20 >2 sin 28 (Archimedes); tan 10+2 sin 3B>0> 3 sin B (Snell).

00The Above Expression Must Therefore Be Diminished By The Number Of Units In 4, Or By () W (This Notation Being Used To Denote The Quotient, In A Whole Number, That Arises From Dividing X By 4).

00Thus he distrusted, and probably never fully accepted, Gay-Lussac's conclusions as to the combining volumes of gases; he held peculiar and quite unfounded views about chlorine, even after its elementary character had been settled by Davy; he persisted in using the atomic weights he himself had adopted, even when they had been superseded by the more accurate determinations of other chemists; and he always objected to the chemical notation devised by J.

00His notation is rather unwieldy.

00Martius yellow, C10H5(N02)20Na H20, the sodium salt of 2.4 dinitro-a-naphthol (for notation see Naphthalene), is prepared by the action of nitric acid on a-naphthol -2.4-disulphonic acid.

00Mat hematics.T he Egyptian notation for whole numbers was decimal, each power of 10 up to 100,000 being represented by a different figure, on much the same principle as the Roman numerals.

00Owing to the very imperfect notation of sound in the writing, the highly important subject, of the verbal roots and verbal forms was perhaps the obscurest branch of Egyptian grammar when Sethe first attacked it in 1895.

00As a whole, we gain the Impression that a really distinct and more primitive stage of hieroglyphic writing by a substantially vaguer notation of words lay not far behind the time of the 1st Dynasty.

00The infinite superiority of the Greek alphabet with its full notation of vowels was readily seen, but piety and custom as yet barred the way to its full adoption.

00While admitting, therefore, that there are several facts in favour of the theory of an African origin of the Bovidae, final judgment Notation to E to t from from or even f 8va balsa.

008vo, 1814); Sur l'ecriture hieratique (1821); Sur l'ecriture demotique; Précis du systeme hieroglyphique, eec. (1824); Pantheon egyptien, ou collection des personnages mythologiques de l'ancienne Egypte (incomplete); Monumens de l'Egypte et de la Nubie consideres par rapport a l'histoire, la religion, &c.; Grammaire egyptienne (1836), and Dictionnaire egyptienne (1841), edited by his brother; Analyse methodique du texte demotique de Rosette; Apercu des resultats historiques de la decouverte de l'alphabet hieroglyphique (1827); Memoires sur les signes employes par les Egyptiens dans leurs trois systemes graphiques a la notation des principales divisions du temps; Lettres ecrites d'Egypte et de Nubie (1833); and also several letters on Egyptian subjects, addressed at different periods to the duc de Blacas and others.

00No better testimony to the value of the quaternion method could be desired than the constant use made of its notation by mathematicians like Clifford (in his Kinematic) and by physicists like ClerkMaxwell (in his Electricity and Magnetism).

00The letters of abraxes, in the Greek notation, make up the number 365, and the Basilidians gave the name to the 365 orders of spirits which, as they conceived, emanated in succession from the Supreme Being.

0021 sub where X 2 +ï¿½ 2 =1 notation; and sustained a reverse; but on the 12th he again attacked the enemy, whose fleet was double his own strength, and inflicted on them a complete defeat.

00It is convenient to have a notation which shall put in evidence the reciprocal character.

00This notation was employed by R.

00The two diagrams are portions of reciprocal figures, so that Bows notation is applicable.

00It is accordingly convenient to use Bows notation (~ 5), and to distinguish the several compartments of the frame-diagram by letters.

00For a two-dimensional system we have, in the notation of ~ 3, 4,

00Again, for a three-dimensional system, in the notation of ~ 7, 8, ~(X5x+YIy+ZIz)

00If all the masses lie in a plane (1=0) we have, in the notation of (25), c2 = o, and therefore A = Mb, B = Ma, C = M (a +b), so that the equation of the momental ellipsoid takes the form b2x2+a y2+(a2+b2) z1=s4.

00in the notation of elliptic integrals.

00since ~(rn~)=o, 2(m~)=o, and so on, the notation being as in 11.

00With the same notation for moments and products of inertia as in II (38), we have and therefore by (1),

00we have, in the notation of elliptic functions, 4= am u.

00in the notation of Bessels functions, if zf = 4kx.

00Henrici illustrated the subject by a simple and ingenious notation.

00The application of the method of reciprocal figures was facilitated by a system of notation published in Economics of Construction in relation to framed Structures, by Robert H.

00The Musica Enchiriadis, published with other writings of minor importance in Gerbert's Scriptores de Musica, and containing a complete system of musical science as well as instructions regarding notation, has now been proved to have originated about half a century later than the death of the monk Hucbald, and to have been the work of an unknown writer belonging to the close of the 10th century and possibly also bearing the name of Hucbald.

00This work is celebrated chiefly for an essay on a new form of notation described in the present day as Dasia Notation.

00The notation employed by English writers for the general continued fraction is al b2 b3 b4 a 2 "' Continental writers frequently use the notation a 1 ?

00The notation adopted is p n = K a2, a / and it is evident that we have b3, .:.

00The notation for this type of fraction is b4 + b5+ b3+ al b2 + a4 a3 It is obviously equal to the series b 2 b3 b4 b5 al +a 2 +aza3a4 + a2a3a4a 5 + .

00His chief advance on Bombelli was in his notation.

00Since 0(o) is finite, proportional to K, the integrated term vanishes at both limits, and we have simply f 0(z)dz f: (z)dz, (34) and T= ref: z1,1,(z)dz (35) In Laplace's notation the second member of (34), multiplied by 27r, is represented by H.

00Along with Sir John Herschel and George Peacock he laboured to raise the standard of mathematical instruction in England, and especially endeavoured to supersede the Newtonian by the Leibnitzian notation in the infinitesimal calculus.

00He contributed to the Royal Society some notices on the relation between notation and mechanism; and in 1822, in a letter to Sir H.

00In the first volume Of the Entwickelungen he applied the method of abridged notation to the straight line, circle and conic sections, and he subsequently used it with great effect in many of his researches, notably in his theory of cubic curves.

00Besides his edition of the Rumanian Church service-books with musical notation, he published a series of tales, proverbs and songs either from older texts or from oral information; and he made the first collection' of popular songs, Spitalul amorului, " The Hospital of Love " (1850-53), with tunes either composed by himself or obtained from the gipsy musicians who alone performed them.

00The Principia gives no information on the subject of the notation adopted in the new calculus, and it was not until 1693 that it was com municated to the scientific world in the second volume of Dr Wallis's works.

00Notation of Numbers 2.3 15.

00Scales of Notation 2.5 17.

00Notation of Numerical Quantities 2.6 (i) Vigesimal Scale 2.7 (ii) Roman System 2.8 21.

003.4.1 (A) Properties not depending on the Scale of Notation

00Least Common Multiple 3.4.4 (B) Properties depending on the Scale of Notation 3.4.5 48.

00The representation of numbers by spoken sounds is called numeration; their representation by written signs is called notation.

00The systems adopted for numeration and for notation do not always agree with one another; nor do they always correspond with the idea which the numbers subjectively present.

00The notation is then said to be in the scale of which ten is the base, or in the denary scale.

00The figures used in the Hindu notation might be used to express numbers in any other scale than the denary, provided new symbols were introduced if the base of the scale exceeded ten.

00The use of the denary scale in notation is due to its use in numeration (§ 18); this again being due (as exemplified by the use of the word digit) to the primitive use of the fingers for counting.

00Over a large part of the civilized world the introduction of the metric system (§ 118) has caused the notation of all numerical quantities to be in the denary scale.

00In Great Britain and her colonies, however, and in the United States, other systems of notation still survive, though there is none which is consistently in one scale, other than the denary.

00Within each denomination, however, the denary notation is employed exclusively, e.g.

00In order to apply arithmetical processes to a quantity expressed in two or more denominations, we must first express it in terms of a single denomination by means of a varying scale of notation.

00Discrepancies between Numeration and Notation.

00- Although numeration and notation are both ostensibly on the denary system, they are not always exactly parallel.

00Other Methods of Numeration and Notation.

00The system of counting by twenties instead of by tens has existed in many countries; and, though there is no corresponding notation, it still exhibits itself in the names of numbers.

00The Roman notation has been explained above (§ 15).

00The numeration was in the denary scale, so that it did not agree absolutely with the notation.

00The principle of subtraction from a higher number, which appeared in notation, also appeared in numeration, but not for exactly the same numbers or in exactly the same way; thus XVIII was two-from-twenty, and the next number was onefrom-twenty, but it was written XIX, not IXX.

00- The Egyptian notation was purely denary, the only separate signs being those for 1, io, too, &c. The ordinary notation of the Babylonians was denary, but they also used a sexagesimal scale, i.e.

00The Hebrews had a notation containing separate signs (the letters of the alphabet) for numbers from t to to, then for multiplies of to up to zoo, and then for multiples of too up to 400, and later up to moo.

00The earliest Greek system of notation was similar to the Roman, except that the symbols for 50, 500, &c., were more complicated.

00On the island of Ceylon there still exists, or existed till recently, a system which combines some of the characteristics of the later Greek (or Semitic) and the modern European notation; and it is conjectured that this was the original Hindu system.

00In other words, the denary scale, though adopted in notation and in numeration, does not arise in the corresponding mental concept until we get beyond too.

00Under certain conditions it is less; thus IIII, the old Roman notation for four, is difficult to distinguish from III, and this may have been the main reason for replacing it by IV (§ 15).

00Finger-counting is of course natural to children, and leads to grouping into fives, and ultimately to an understanding of the denary system of notation.

00Addition is the process of expressing (in numeration or notation) a whole, the parts of which have already been expressed; while, if a whole has been expressed and also a part or parts, subtraction is the process of expressing the remainder.

00The application of the above principles, and of similar principles with regard to multiplication and division, to numerical quantities expressed in any of the diverse British denominations, presents no theoretical difficulty if the successive denominations are regarded as constituting a varying scale of notation (§17).

00The difficulty may be minimized by using the notation explained in § 17.

00This relation is of exactly the same kind as the relation of the successive digits in numbers expressed in a scale of notation whose base is n.

00They only apply accurately to divisions by 2, 4, 5, 10, 20, 25 or 50; but they have the convenience of fitting in with the denary scale of notation, and they can be extended to other divisions by using a mixed number as numerator.

00Decimal Notation of Percentage.

00A fraction written in this way is called a decimal fraction; or we might define a decimal fraction as a fraction having a power of To for its denominator, there being a special notation for writing such fractions.

00This notation survives in reference to the minute (') and second (") of angular measurement, and has been extended, by analogy, to the foot (') and inch (").

00Various systems were tried before the present notation came to be generally accepted.

00Under one system, for instance, the continued sum 5 + X 5 + 8 X 7 X 5 would be denoted 7 by 8 I 5; this is somewhat similar in principle to a decimal notation, but with digits taken in the reverse order.

00There was, however, no development in the direction of decimals in the modern sense, and the Arabs, by whom the Hindu notation of integers was brought to Europe, mainly used the sexagesimal division in the ' " "' notation.

00Even where the decimal notation would seem to arise naturally, as in the case of approximate extraction of a square root, the portion which might have been expressed as a decimal was converted into sexagesimal fractions.

001585 that a decimal notation was published by Simon Stevinus of Bruges.

00It is worthy of notice that the invention of this notation appears to have been due to practical needs, being required for the purpose of computation of compound interest.

00The present decimal notation, which is a development of that of Stevinus, was first used in 1617 by H.

00By analogy with the notation of fractional numbers, N will be = N X N; and, generally, NI will mean the product of p numbers, the product of q of which is equal to N.

00In each case the grouping system involves rearrangement, which implies the commutative law, while the counting system requires the expression of a quantity in different denominations to be regarded as a notation in a varying scale (§§ 17, 3 2).

00If we have to divide 935 by 240, taking 12 and 20 as factors, the result will depend on the fact that, in the notation (20) (12) of § 1 7, 935=3 " 1 7 " 1 1.

00For the latter, and for systems of notation, reference may also be made to Peacock's article " Arithmetic " in the Encyclopaedia Metropolitana, which contains a detailed account of the Greek system.

00The Greek geometers were perfectly familiar with the property of an ellipse which in the Cartesian notation is x 2 /a 2 +y 2 /b 2 =1, the equation of the curve; but it was as one of a number of properties, and in no wise selected out of the others for the characteristic property of the curve.

00These papers taken together constitute a great treatise on logic, in which he substituted improved systems of notation, and developed a new logic of relations, and a new onymatic system of logical expression.

00Let us use the following notation: x, y, the co-ordinates of the planet relative to the sun as the origin.

00The formation of the larger islands is volcanic, their surface rugged, their vegetation luxuriant, and their appearance very 1 The notation n!

00In modern notation, if we denote the ordinate by y, the distance of the foot of the ordinate from the vertex (the abscissa) by x, and the latus rectum by p, these relations may be expressed as 31 2 for the hyperbola.

00focal length must be spoken of, according to this notation, as a X 10 lens, and a lens of in.

00Von Soden introduces, besides a new notation of MSS.

00ABC notation will tend to mirror the grouping which would be used in standard notation.

00algebraic notation in unusual ways.

00bass clef notation and should be able to play simple pieces for both hands.

00bass clef notation and should be able to play simple pieces for both hands.

00Regular expression pattern strings may not contain null bytes, but can specify the null byte using the \ number notation.

00clef notation and should be able to play simple pieces for both hands.

00Students can choose between a range of topics, including analysis, notation, historical subjects, ethnomusicology, performance and music cognition.

00The notation used here conforms with that being proposed for specifying polynucleotide conformation.

00This notation may impose timing constraints on the process flow.

00decimal notation numbers are:- 10 0 10.

00Decimal notation decimal notation Decimal numbers consist of one or more of the following:- An optional integer part to the left of any decimal point.

00definitive notation to specify synchronization of events 13.

00The server came by, looked at the now desecrated Fifth Floor restaurant cloths, and made a little notation on her pad.

00enharmonic notation?

00exponential notation is recognized.

00hexadecimal notation.

00A quick word about hornpipes The hornpipe rhythm is useful to illustrate one more way abc allows the notation of notes of differing length.

00infix notation instead of the usual message sending format.

00invention of printing also led to the gradual standardization of mathematical notation.

00ViÃ¨te introduced the first systematic algebraic notation in his book In artem analyticam isagoge published at Tours in 1591.

00machine-readable version of dance notation with a virtual dancer.

00The rightmost 6 bytes represent the mantissa in binary notation, with the leftmost bit representing the digit in the 2 -1 place.

00mantissa in binary notation, with the leftmost bit representing the digit in the 2 -1 place.

00mathematical notation.

00One would expect this random method of notation to be discordant, however the resultant music is surprisingly reminiscent of classical piano minuets.

00Children can also learn basic musical notation & learn to recognize 8 musical notation & learn to recognize 8 musical instruments.

00It contains 15 well known jazz tunes with piano accompaniment written in single stave notation with chord symbols.

00Form The dot notation is used to separate each group of Classes.

00To simplify notation we define,, ,, ,, ,, , and the total hemoglobin in all forms.

00I now want to introduce a notation that goes some way toward making this idea precise.

00TWiki HTML Rendering TWiki converts shorthand notation to XHTML 1.0 for display.

00Skills on how to read and interpret the notation on one part of the course will be useful when learning other components.

00notation with chord symbols.

00If using the subscript notation, solvers often create a larger copy of the puzzle or employ a sharp or mechanical pencil.

00We shall use decimal notation for units in this module.

00Children are known to often invent idiosyncratic notation to describe their mathematical findings, or to use algebraic notation in unusual ways.

00IP addresses are normally written in a format known as " dotted decimal notation " .

00A number expressed in exponential notation consists of the following:- A decimal number.

00notation declaration will be reported before any unparsed entities that use it.

00The spacing of ABC notation will tend to mirror the grouping which would be used in standard notation.

00You can use StandardColors or common color codes: hexadecimal notation.

00We can get this if we go to Reverse Polish or postfix notation.

00Each character, in particular those which cannot be typed directly from the keyboard, can also be typed in three digit octal notation.

00Where possible the health gain notation reflects both the type of evidence and the small size of some of the samples.

00To introduce arbitrary characters into a string using octal or hexadecimal notation.

00octal notation.

00Each character, in particular those which cannot be typed directly from the keyboard, can also be typed in three digit octal notation.

00postfix notation is yet another form of intermediate code.

00The filename prefix for each ion follows spectroscopic notation.

00Results explained with reference to scientific theory using correct scientific notation.

00shorthand notation to XHTML 1.0 for display.

00The unquestionable popularity of Curwen's Tonic sol-fa induced many publishers to issue hymnals employing sol-fa notation.

00stave notation with chord symbols.

00subdivision algorithms uses a matrix notation.

00In the subscript notation the candidate numerals are written in subscript notation the candidate numerals are written in subscript in the cells.

00Finger picking patterns are written using tablature and standard music notation.

00With guitar tablature, standard notation, vocal melody, lyrics, chord names, guitar chord diagrams, guitar notation.

00There is no need to read conventional music notation as all the music is written in easy-to-read mandolin tablature.

00A (possibly slightly tongue-in-cheek) example of abc notation in all its multi-faceted glory.

00The non-specific pitch indication was also used with a specific rhythmic notation to achieve rhythmic unisons within ' improvised ' tonalities and harmonies.

00The superiority of this notation over that of Dalton is not so obvious when we consider such simple cases as the above, but chemists are now acquainted with very complex molecules containing numerous atoms; cane sugar, for example, has the formula C 12 H 22 0, 1.

00There is a complete edition in modern notation by T.

00Each problem was something unique; the elements of transition from one to another were wanting; and the next step which mathematics had to make was to find some method of reducing, for instance, all curves to a common notation.

00But to sing the lower Greek modes in or near the vocal octave it was necessary to transpose (yEraj30Xii) a fourth upwards, which is effected in modern notation by a flat placed upon the b line of the staff; thus modulating from our major key of C to that of F.

00This single instance of the use of the decimal point in the midst of an arithmetical process, if it stood alone, would not suffice to establish a claim for its introduction, as the real introducer of the decimal point is the person who first saw that a point or line as separator was all that was required to distinguish between the integers and fractions, and used it as a permanent notation and not merely in the course of performing an arithmetical operation.

00he prints a bar under the decimals; this notation first appears without any explanation in his "Lucubrationes" appended to the Constructio.

00Briggs seems to have used the notation all his life, but in writing it, as appears from manuscripts of his, he added also a small vertical line just high enough to fix distinctly which two figures it was intended to separate: thus he might have written 63 0957379.

00While still an undergraduate he formed a league with John Herschel and Charles Babbage, to conduct the famous struggle of "d-ism versus dot-age," which ended in the introduction into Cambridge of the continental notation in the infinitesimal calculus to the exclusion of the fluxional notation of Sir Isaac Newton.

00This was an important reform, not so much on account of the mere change of notation (for mathematicians follow J.

00He began by reading, with the most profound admiration and attention, the whole of Faraday's extraordinary self-revelations, and proceeded to translate the ideas of that master into the succinct and expressive notation of the mathematicians.

00The notation which Julius Thomsen employed to express his thermochemical measurements is still extensively used, and is as follows: - The chemical symbols of the reacting substances are written in juxtaposition and separated by commas; the whole is then enclosed in brackets and connected by the sign of equality to the number expressing the thermal effect of the action.

00One drawback of Thomsen's notation is that the nature of the final system is not indicated, although this defect in general causes no ambiguity.

00Berthelot's notation defines both initial and final systems by giving the chemical equation for the reaction considered, the thermal effect being appended, and the state of the various substances being affixed to their formulae after brackets.

00A word is necessary on Diophantus' notation.

00Wertheim (Leipzig, 1890), and an English edition in modern notation (T.

00At a later date Berzelius denoted an oxide by dots, equal in number to the number of oxygen atoms present, placed over the element; this notation survived longest in mineralogy.

00Although the system of Berzelius has been modified and extended, its principles survive in the modern notation.

00Accordingly, the typical form for such a complex number is x+yi, and then with this notation the above-mentioned definition of multiplication is invariably adopted.

00nota, mark, sign, from noscere, to know), a mark, particularly a sign by which a musical sound (also called a note) is indicated in writing (see Musical Notation).

00Remark.-In this notation (0) = Eai = (i n); (02) _ za l a2 = (2);...

00- It will suffice to consider two systems of quantities as the corresponding theory for three or more systems is obtainable by an obvious enlargement of the nomenclature and notation.

00In this notation the fundamental relation is written (l + a i x +01Y) (I + a 2x+l32Y) (1 + a3x+133y)...

001112 which Cayley denotes by (a, b, c, ...)(xi, x2)n (i),(2)Ã¯¿½Ã¯¿½Ã¯¿½ being a notation for the successive binomial coefficients n, 2n (n-I),....

00For present purposes the form will be written a0x 1 +(7)a1x1=1 x2+ C 2)o'2x12 x 2 +...+anx2, the notation adopted by German writers; the literal coefficients have a rule placed over them to distinguish them from umbral coefficients which are introduced almost at once.

00Such an expression as a l b 2 -a 2 b i, which is aa 2 ab 2 aa x 2 2 ax1' is usually written (ab) for brevity; in the same notation the determinant, whose rows are a l, a 2, a3; b2, b 2, b 3; c 1, c 2, c 3 respectively, is written (abc) and so on.

00Hence, excluding ao, we may, in partition notation, write down the fundamental solutions of the equation, viz.

001 Z2' The First Perpetuant Is The Last Seminvariant Written, Viz.: A O (B O B 2 3B O B 3) A L (Bi 2B0B2), Or, In Partition Notation, Ao(21) B (1)A(2)B; And, In This Form, It Is At Once Seen To Satisfy The Partial Differential Equation.

00According to the notation adopted by Meyer the atomic susceptibility k=KX atomic-weight/ (density X 1000).

00The validity of his fundamental position was impaired by the absence of a well-constituted theory of series; the notation employed was inconvenient, and was abandoned by its inventor in the second edition of his Mecanique; while his scruples as to the admission into analytical investigations of the idea of limits or vanishing ratios have long since been laid aside as idle.

00Whether this principle may legitimately be extended to the notation adopted in (iii.) (a) of Ã¯¿½ 14 is a moot point.

00Expressed Equations.-The simplest forms of arithmetical equation arise out of abbreviated solutions of particular problems. In accordance with Ã¯¿½ 15, it is desirable that our statements should be statements of equality of quantities rather than of numbers; and it is convenient in the early stages to have a distinctive notation, e.g.

00Notation of Multiples.-The above is arithmetic. The only thing which it is necessary to import from algebra is the notation by which we write 2X instead of 2 X X or 2.

00(iii.) Scales of Notation lead, by considering, e.g., how to express in the scale of to a number whose expression in the scale of 8 is 2222222, to (iv.) Geometrical Progressions.

00+n(r)An-rar+Ã¯¿½.Ã¯¿½ +n(n)a n (2), where n(0), introduced for consistency of notation, is defined by n (o) EI (3).

00(n+--r-1)lr!=n[r]lr!; this may, by analogy with the notation of Ã¯¿½41, be denoted by n [r 7.

00(v.) It should be mentioned that the notation of the binomial 'coefficients, and of the continued products such as n(n -1).

00It is convenient to retain x, to denote x r /r!, so that we have the consistent notation xr =x r /r!, n (r) =n(r)/r!, n[r] =n[r]/r!.

00Algebraical division therefore has no definite meaning unless dividend and divisor are rational integral functions of some expression such as x which we regard as the root of the notation (Ã¯¿½ 28 (iv.)), and are arranged in descending or ascending powers of x.

00Evolution and involution are usually regarded as operations of ordinary algebra; this leads to a notation for powers and roots, and a theory of irrational algebraic quantities analogous to that of irrational numbers.

00The symbol e 0 behaves exactly like i in ordinary algebra; Hamilton writes I, i, j, k instead of eo, el, e2, es, and in this notation all the special rules of operation may he summed up by the equalities = - I.

00With this notation the values of x and y may be expressed in the forms x q q /N q ', gg /Nq', which are free from ambiguity, since scalars are commutative with quaternions.

00Various special algebras (for example, quaternions) may be expressed in the notation of the algebra of matrices.

00Even in ordinary algebra the notation for powers and roots disturbs the symmetry of the rational theory; and when a schoolboy illegitimately extends the distributive law by writing -V (a+b)a+J b, he is unconsciously emphasizing this want of complete harmony.

00In the preface to this work, which is dedicated to one Dionysius, Diophantus explains his notation, naming the square, cube and fourth powers, dynamis, cubus, dynamodinimus, and so on, according to the sum in the indices.

00His travels and mercantile experience had led E t u eopre him to conclude that the Hindu methods of computing were in advance of those then in general use, and in 1202 he published his Liber Abaci, which treats of both algebra and arithmetic. In this work, which is of great historical interest, since it was published about two centuries before the art of printing was discovered, he adopts the Arabic notation for numbers, and solves many problems, both arithmetical and algebraical.

00These works possess considerable originality, and contain many new improvements in algebraic notation; the unknown (res) is denoted by a small circle, in which he places an integer corresponding to the power.

00He introduced the terms multinomial, trinomial, quadrinomial, &c., and considerably simplified the notation for decimals.

00Vieta, who does not avail himself of the discoveries of his predecessors - the negative roots of Cardan, the revised notation of Stifel and Stevin, &c. - introduced or popularized many new terms and symbols, some of which are still in use.

00Girard is inconsistent in his notation, sometimes following Vieta, sometimes Stevin; he introduced the new symbols ff for greater than and Ã¯¿½ for less than; he follows Vieta in using the plus (+) for addition, he denotes subtraction by Recorde's symbol for equality (=), and he had no sign for equality but wrote the word out.

00Its great merit consists in the complete notation and symbolism, which avoided the cumbersome expressions of the earlier algebraists, and reduced the art to a form closely resembling that of to-day.

00His notation is based on that of Vieta, but he introduced the sign X for multiplication, - for continued proportion, :: for proportion, ' and denoted ratio by one dot.

00(19), 1 abA) ' ' we may write 12= (cos 27rv 2 .dv) 2 + (f sin zirv 2 .dv) 2 (20), or, according to our previous notation, 12 = (2 - C 2 +(z - Sv)2= G2 +H2 Now in the integrals represented by G and H every element diminishes as V increases from zero.

00According to this notation, the three equations of motion are dt2 = b2v2E + (a2 - b2) d.s dt =b2v2rj+(a2 - b2) dy d2 CIF - b2p2+(a2_b2)dz It is to be observed that denotes the dilatation of volume of the element situated at (x, y, z).

002 and lb/in.', in the Hospitaller notation, to be employed in the sequel).

002 enclosing a point B, the pressure p at B is the limit of OP/DA; and p =lt(AP/DA) =dP/ dA, (I) in the notation of the differential calculus.

00In the Eulerian notation u, v, w denote the components of the velocity q parallel to the coordinate axes at any point (x, y, z) at the time t; u, v, w are functions of x, y, z, t, the independent variables; and d is used here to denote partial differentiation with respect to any one of these four independent variables, all capable of varying one at a time.

00Employing the notation in which the molecule is represented vertically with the aldehyde group at the bottom, and calling a carbon atom+or - according as the hydrogen atom is to the left or right, the possible configurations are shown in the diagram.

00The famous inscriptions with hymns to Apollo accompanied by musical notation were found on stones belonging to this treasury.

00In the notation of the calculus the relations become - dH/dp (0 const) = odv /do (p const) (4) dH/dv (0 const) =odp/do (v const) The negative sign is prefixed to dH/dp because absorption of heat +dH corresponds to diminution of pressure - dp. The utility of these relations results from the circumstance that the pressure and expansion co efficients are familiar and easily measured, whereas the latent heat of expansion is difficult to determine.

00Substituting for H its value from (3), and employing the notation of the calculus, we obtain the relation S - s =0 (dp /do) (dv/do),.

00The documents discovered by Dom Germain Morin, the Belgian Benedictine, about 1888, point to the conclusion that Guido was a Frenchman and lived from his youth upwards in the Benedictine monastery of St Maur des Fosses where he invented his novel system of notation and taught the brothers to sing by it.

00There is no doubt that Guido's method shows considerable progress in the evolution of modern notation.

00It is not, however, necessary that the notation of the calculus should be employed throughout.

00(a) The formula may involve numbers or ratios which cannot be expressed exactly in the ordinary notation.

00In the notation of the integral calculus, this area is equal to f x o udx; but the notation is inconvenient, since it implies a division into infinitesimal elements, which is not essential to the idea of an area.

00It is therefore better to use some independent notation, such as A Z.

00+ u m-p + zum), which may be denoted by Cp. With this notation, the area as given by Simpson's rule may be written in the form sC l - 3 C2 or CI+ 1 3 `-(C1C2).

00This, in the notation of §§ 46 and 54, may be written?

00In works on sound it is usual to adopt Helmholtz's notation, in which the octave from bass to middle C is written c d e f g a b c'.

00The French notation is as under: C D E F G A B c Ut 1 Re f M] Fa] Sol i La i Si, Utz.

00But a new system of musical notation which he thought he had discovered was unfavourably received by the Academie des sciences, where it was read in August 1742, and he was unable to obtain pupils.

00The system of notation (by figures) concerning which he read a paper before the Academie des Sciences, August 22, 1742, was ingenious, but practically worse than useless, and failed to attract attention, though the paper was published in 1 743 under the title of Dissertation sur la musique moderne.

00Among the natives of Arezzo the most famous are the Benedictine monk Guido of Arezzo, the inventor of the modern system of musical notation (died c. 1050), the poet Petrarch, Pietro Aretino, the satirist (1492-1556), and Vasari, famous for his lives of Italian painters.

00Denoting the value of T at any velocity v by T (v), then (8) T(v) = sum of all the preceding values of AT plus an arbitrary constant, expressed by the notation (9) T(v) =Z(Av)/gp+ a constant, or fdv/gp+ a constant, in which p is supposed known as a function of v.

00so that Denoting dx/dt, the horizontal component of the velocity, by q, (49) v cos i =q, equation (43) becomes (50) dq/dt= -r cos i, and therefore by !(48) (51) dq _dq dt ry di - dt di-g' It is convenient to express r as a function of v in the previous notation (52) Cr = f(v), dq _vf(v) di - Cg ' an equation connecting q and i.

00Now taking equation (72), and replacing tan B, as a variable final tangent of an angle, by tan i or dyldx, (75) tan 4) - dam= C sec n [I(U) - I(u)], and integrating with respect to x over the arc considered, (76) x tan 4, - y = C sec n (U) - f :I(u)dx] 0 But f (u)dx= f 1(u) du = C cos n f x I (u) u du g f() =C cos n [A(U) - A(u)] in Siacci's notation; so that the altitude-function A must be calculated by summation from the finite difference AA, where (78) AA = I (u) 9 = I (u) or else by an integration when it is legitimate to assume that f(v) =v m lk in an interval of velocity in which m may be supposed constant.

00Now calculate the pseudo-velocity uo from =v 95 cos 4) sec n, and then, from the given values of 0 and 8, calculate u e from either of the formulae of (72) or (73): (82) I (u 9) - I (u0) tan 0 - tan 8 C sec n (83) D(ue) =D (uq5) 4)Ã‚°-BÃ‚° cos n' Then with the suffix notation to denote the beginning and end of the arc 0-0, mt e = C[Tum) - T (u0)], 5 ((x x9 1l 0.

00The notation of this mass of MSS.

00Gregory's notation is more generally used, and Scrivener's, though still followed by a few English scholars, is likely to become obsolete.

00This method of notation has various disadvantages.

00At present it has not seriously threatened the hold of Gregory's notation on the critical world, but it will probably have to be adopted, at least to a large extent, when von Soden's text is published.

00known in Gregory's notation as 13, 69, 124, 34 6, 543, 788, 826, 828, or in von Soden's as e 368, S 505, e 1211, e 226, e 257, e 1033, e 218, e 219, all which, except 69, in spite of the dating implied by von Soden's notation were probably written in the 12th century in Calabria.

00known in Gregory's notation as I, 118, 131, 209, and in von Soden's as S 50, e 346, S 467 and S 457.

00The dating implied by the latter notation is wrong, as I certainly belongs to the 12th, not to the 10th century, and 118 is probably later than 209.

00It is customary to quote these by small letters of the Latin alphabet, but there is a regrettable absence of unanimity in the details of the notation.

00His edition is historically very important as it introduced the system of notation which, in the amplified form given to it by Gregory, is still in general use.

00(arithmetic) elementary lessons on the notation of decimal fractions.

00The notation log x is generally employed in English and American works, but on the continent of Europe writers usually denote the function by lx or lg x.

00- Nathaniel Roe's Tabulae logarithmicae (1633) was the first complete seven-figure 1 In describing the contents of the works referred to, the language and notation of the present day have been adopted, so that for example a table to radius 10,000,000 is described as a table to 7 places, and so on.

00He also reduced the solar parallax to 14" (less than a quarter of Kepler's estimate), corrected the sun's semi-diameter to 15' 45", recommended decimal notation, and was the first to make tidal observations.

008 4 In modern trigonometrical notation, I +sec 0: tan 0 :: I : tan Z0.

00II) whose centre is 0, AC its chord, and HK the tangent drawn at the middle point of the arc and bounded by OA, OC produced, then, according to Archimedes, AMC AC. In modern trigonometrical notation the propositions to be compared stand as follows: 2 tan 20 >2 sin 28 (Archimedes); tan 10+2 sin 3B>0> 3 sin B (Snell).

00The Above Expression Must Therefore Be Diminished By The Number Of Units In 4, Or By () W (This Notation Being Used To Denote The Quotient, In A Whole Number, That Arises From Dividing X By 4).

00Recorde's chief contributions to the progress of algebra were in the way of systematizing its notation (see ALGEBRA, History).

00Thus he distrusted, and probably never fully accepted, Gay-Lussac's conclusions as to the combining volumes of gases; he held peculiar and quite unfounded views about chlorine, even after its elementary character had been settled by Davy; he persisted in using the atomic weights he himself had adopted, even when they had been superseded by the more accurate determinations of other chemists; and he always objected to the chemical notation devised by J.

00His notation is rather unwieldy.

00Martius yellow, C10H5(N02)20Na H20, the sodium salt of 2.4 dinitro-a-naphthol (for notation see Naphthalene), is prepared by the action of nitric acid on a-naphthol -2.4-disulphonic acid.

00Mat hematics.T he Egyptian notation for whole numbers was decimal, each power of 10 up to 100,000 being represented by a different figure, on much the same principle as the Roman numerals.

00Owing to the very imperfect notation of sound in the writing, the highly important subject, of the verbal roots and verbal forms was perhaps the obscurest branch of Egyptian grammar when Sethe first attacked it in 1895.

00As a whole, we gain the Impression that a really distinct and more primitive stage of hieroglyphic writing by a substantially vaguer notation of words lay not far behind the time of the 1st Dynasty.

00The infinite superiority of the Greek alphabet with its full notation of vowels was readily seen, but piety and custom as yet barred the way to its full adoption.

00While admitting, therefore, that there are several facts in favour of the theory of an African origin of the Bovidae, final judgment Notation to E to t from from or even f 8va balsa.

008vo, 1814); Sur l'ecriture hieratique (1821); Sur l'ecriture demotique; PrÃ©cis du systeme hieroglyphique, eec. (1824); Pantheon egyptien, ou collection des personnages mythologiques de l'ancienne Egypte (incomplete); Monumens de l'Egypte et de la Nubie consideres par rapport a l'histoire, la religion, &c.; Grammaire egyptienne (1836), and Dictionnaire egyptienne (1841), edited by his brother; Analyse methodique du texte demotique de Rosette; Apercu des resultats historiques de la decouverte de l'alphabet hieroglyphique (1827); Memoires sur les signes employes par les Egyptiens dans leurs trois systemes graphiques a la notation des principales divisions du temps; Lettres ecrites d'Egypte et de Nubie (1833); and also several letters on Egyptian subjects, addressed at different periods to the duc de Blacas and others.

00No better testimony to the value of the quaternion method could be desired than the constant use made of its notation by mathematicians like Clifford (in his Kinematic) and by physicists like ClerkMaxwell (in his Electricity and Magnetism).

00The letters of abraxes, in the Greek notation, make up the number 365, and the Basilidians gave the name to the 365 orders of spirits which, as they conceived, emanated in succession from the Supreme Being.

0021 sub where X 2 +Ã¯¿½ 2 =1 notation; and sustained a reverse; but on the 12th he again attacked the enemy, whose fleet was double his own strength, and inflicted on them a complete defeat.

00It is convenient to have a notation which shall put in evidence the reciprocal character.

00This notation was employed by R.

00The two diagrams are portions of reciprocal figures, so that Bows notation is applicable.

00It is accordingly convenient to use Bows notation (~ 5), and to distinguish the several compartments of the frame-diagram by letters.

00For a two-dimensional system we have, in the notation of ~ 3, 4,

00Again, for a three-dimensional system, in the notation of ~ 7, 8, ~(X5x+YIy+ZIz)

00If all the masses lie in a plane (1=0) we have, in the notation of (25), c2 = o, and therefore A = Mb, B = Ma, C = M (a +b), so that the equation of the momental ellipsoid takes the form b2x2+a y2+(a2+b2) z1=s4.

00in the notation of elliptic integrals.

00since ~(rn~)=o, 2(m~)=o, and so on, the notation being as in 11.

00With the same notation for moments and products of inertia as in II (38), we have and therefore by (1),

00we have, in the notation of elliptic functions, 4= am u.

00in the notation of Bessels functions, if zf = 4kx.

00Henrici illustrated the subject by a simple and ingenious notation.

00The application of the method of reciprocal figures was facilitated by a system of notation published in Economics of Construction in relation to framed Structures, by Robert H.

00The Musica Enchiriadis, published with other writings of minor importance in Gerbert's Scriptores de Musica, and containing a complete system of musical science as well as instructions regarding notation, has now been proved to have originated about half a century later than the death of the monk Hucbald, and to have been the work of an unknown writer belonging to the close of the 10th century and possibly also bearing the name of Hucbald.

00This work is celebrated chiefly for an essay on a new form of notation described in the present day as Dasia Notation.

00The notation employed by English writers for the general continued fraction is al b2 b3 b4 a 2 "' Continental writers frequently use the notation a 1 ?

00The notation adopted is p n = K a2, a / and it is evident that we have b3, .:.

00The notation for this type of fraction is b4 + b5+ b3+ al b2 + a4 a3 It is obviously equal to the series b 2 b3 b4 b5 al +a 2 +aza3a4 + a2a3a4a 5 + .

00His chief advance on Bombelli was in his notation.

00Since 0(o) is finite, proportional to K, the integrated term vanishes at both limits, and we have simply f 0(z)dz f: (z)dz, (34) and T= ref: z1,1,(z)dz (35) In Laplace's notation the second member of (34), multiplied by 27r, is represented by H.

00Along with Sir John Herschel and George Peacock he laboured to raise the standard of mathematical instruction in England, and especially endeavoured to supersede the Newtonian by the Leibnitzian notation in the infinitesimal calculus.

00He contributed to the Royal Society some notices on the relation between notation and mechanism; and in 1822, in a letter to Sir H.

00In the first volume of this treatise Plucker introduced for the first time the method of abridged notation which has become one of the characteristic features of modern analytical geometry (see Geometry, Analytical).

00In the first volume Of the Entwickelungen he applied the method of abridged notation to the straight line, circle and conic sections, and he subsequently used it with great effect in many of his researches, notably in his theory of cubic curves.

00Besides his edition of the Rumanian Church service-books with musical notation, he published a series of tales, proverbs and songs either from older texts or from oral information; and he made the first collection' of popular songs, Spitalul amorului, " The Hospital of Love " (1850-53), with tunes either composed by himself or obtained from the gipsy musicians who alone performed them.

00The Principia gives no information on the subject of the notation adopted in the new calculus, and it was not until 1693 that it was com municated to the scientific world in the second volume of Dr Wallis's works.

00Notation of Numbers 2.3 15.

00Scales of Notation 2.5 17.

00Notation of Numerical Quantities 2.6 (i) Vigesimal Scale 2.7 (ii) Roman System 2.8 21.

003.4.1 (A) Properties not depending on the Scale of Notation

00Least Common Multiple 3.4.4 (B) Properties depending on the Scale of Notation 3.4.5 48.

00The representation of numbers by spoken sounds is called numeration; their representation by written signs is called notation.

00The systems adopted for numeration and for notation do not always agree with one another; nor do they always correspond with the idea which the numbers subjectively present.

00The notation is then said to be in the scale of which ten is the base, or in the denary scale.

00The figures used in the Hindu notation might be used to express numbers in any other scale than the denary, provided new symbols were introduced if the base of the scale exceeded ten.

00The use of the denary scale in notation is due to its use in numeration (§ 18); this again being due (as exemplified by the use of the word digit) to the primitive use of the fingers for counting.

00Over a large part of the civilized world the introduction of the metric system (§ 118) has caused the notation of all numerical quantities to be in the denary scale.

00In Great Britain and her colonies, however, and in the United States, other systems of notation still survive, though there is none which is consistently in one scale, other than the denary.

00Within each denomination, however, the denary notation is employed exclusively, e.g.

00In order to apply arithmetical processes to a quantity expressed in two or more denominations, we must first express it in terms of a single denomination by means of a varying scale of notation.

00Discrepancies between Numeration and Notation.

00- Although numeration and notation are both ostensibly on the denary system, they are not always exactly parallel.

00Other Methods of Numeration and Notation.

00The system of counting by twenties instead of by tens has existed in many countries; and, though there is no corresponding notation, it still exhibits itself in the names of numbers.

00The Roman notation has been explained above (§ 15).

00The numeration was in the denary scale, so that it did not agree absolutely with the notation.

00The principle of subtraction from a higher number, which appeared in notation, also appeared in numeration, but not for exactly the same numbers or in exactly the same way; thus XVIII was two-from-twenty, and the next number was onefrom-twenty, but it was written XIX, not IXX.

00- The Egyptian notation was purely denary, the only separate signs being those for 1, io, too, &c. The ordinary notation of the Babylonians was denary, but they also used a sexagesimal scale, i.e.

00The Hebrews had a notation containing separate signs (the letters of the alphabet) for numbers from t to to, then for multiplies of to up to zoo, and then for multiples of too up to 400, and later up to moo.

00The earliest Greek system of notation was similar to the Roman, except that the symbols for 50, 500, &c., were more complicated.

00On the island of Ceylon there still exists, or existed till recently, a system which combines some of the characteristics of the later Greek (or Semitic) and the modern European notation; and it is conjectured that this was the original Hindu system.

00In other words, the denary scale, though adopted in notation and in numeration, does not arise in the corresponding mental concept until we get beyond too.

00Under certain conditions it is less; thus IIII, the old Roman notation for four, is difficult to distinguish from III, and this may have been the main reason for replacing it by IV (§ 15).

00Finger-counting is of course natural to children, and leads to grouping into fives, and ultimately to an understanding of the denary system of notation.

00Addition is the process of expressing (in numeration or notation) a whole, the parts of which have already been expressed; while, if a whole has been expressed and also a part or parts, subtraction is the process of expressing the remainder.

00The application of the above principles, and of similar principles with regard to multiplication and division, to numerical quantities expressed in any of the diverse British denominations, presents no theoretical difficulty if the successive denominations are regarded as constituting a varying scale of notation (§17).

00The difficulty may be minimized by using the notation explained in § 17.

00This relation is of exactly the same kind as the relation of the successive digits in numbers expressed in a scale of notation whose base is n.

00They only apply accurately to divisions by 2, 4, 5, 10, 20, 25 or 50; but they have the convenience of fitting in with the denary scale of notation, and they can be extended to other divisions by using a mixed number as numerator.

00Decimal Notation of Percentage.

00A fraction written in this way is called a decimal fraction; or we might define a decimal fraction as a fraction having a power of To for its denominator, there being a special notation for writing such fractions.

00This notation survives in reference to the minute (') and second (") of angular measurement, and has been extended, by analogy, to the foot (') and inch (").

00Various systems were tried before the present notation came to be generally accepted.

00Under one system, for instance, the continued sum 5 + X 5 + 8 X 7 X 5 would be denoted 7 by 8 I 5; this is somewhat similar in principle to a decimal notation, but with digits taken in the reverse order.

00There was, however, no development in the direction of decimals in the modern sense, and the Arabs, by whom the Hindu notation of integers was brought to Europe, mainly used the sexagesimal division in the ' " "' notation.

00Even where the decimal notation would seem to arise naturally, as in the case of approximate extraction of a square root, the portion which might have been expressed as a decimal was converted into sexagesimal fractions.

001585 that a decimal notation was published by Simon Stevinus of Bruges.

00It is worthy of notice that the invention of this notation appears to have been due to practical needs, being required for the purpose of computation of compound interest.

00The present decimal notation, which is a development of that of Stevinus, was first used in 1617 by H.

00By analogy with the notation of fractional numbers, N will be = N X N; and, generally, NI will mean the product of p numbers, the product of q of which is equal to N.

00In each case the grouping system involves rearrangement, which implies the commutative law, while the counting system requires the expression of a quantity in different denominations to be regarded as a notation in a varying scale (§§ 17, 3 2).

00If we have to divide 935 by 240, taking 12 and 20 as factors, the result will depend on the fact that, in the notation (20) (12) of § 1 7, 935=3 " 1 7 " 1 1.

00For the latter, and for systems of notation, reference may also be made to Peacock's article " Arithmetic " in the Encyclopaedia Metropolitana, which contains a detailed account of the Greek system.

00The Greek geometers were perfectly familiar with the property of an ellipse which in the Cartesian notation is x 2 /a 2 +y 2 /b 2 =1, the equation of the curve; but it was as one of a number of properties, and in no wise selected out of the others for the characteristic property of the curve.

00These papers taken together constitute a great treatise on logic, in which he substituted improved systems of notation, and developed a new logic of relations, and a new onymatic system of logical expression.

00Let us use the following notation: x, y, the co-ordinates of the planet relative to the sun as the origin.

00The formation of the larger islands is volcanic, their surface rugged, their vegetation luxuriant, and their appearance very 1 The notation n!

00In modern notation, if we denote the ordinate by y, the distance of the foot of the ordinate from the vertex (the abscissa) by x, and the latus rectum by p, these relations may be expressed as 31 2 for the hyperbola.

00focal length must be spoken of, according to this notation, as a X 10 lens, and a lens of in.

00Von Soden introduces, besides a new notation of MSS.

00To my dismay I found that it was in the American notation.

00I received another paper and a table of signs by return mail, and I set to work to learn the notation.

00But, when I took up Algebra, I had a harder time still--I was terribly handicapped by my imperfect knowledge of the notation.

00Results explained with reference to scientific theory using correct scientific notation.

00The unquestionable popularity of Curwen 's Tonic Sol-fa induced many publishers to issue hymnals employing sol-fa notation.

00It contains 15 well known tunes written in single stave notation with chord symbols.

00The standard method for defining subdivision algorithms uses a matrix notation.

00In the subscript notation the candidate numerals are written in subscript in the cells.

00Introduction of suffix notation and the summation convention including and.

00Finger picking patterns are written using tablature and standard music notation.

00With guitar tablature, standard notation, vocal melody, lyrics, chord names, guitar chord diagrams, guitar notation.

00There is no need to read conventional music notation as all the music is written in easy-to-read mandolin tablature.

00A (possibly slightly tongue-in-cheek) example of abc notation in all its multi-faceted glory.

00The non-specific pitch indication was also used with a specific rhythmic notation to achieve rhythmic unisons within ' improvised ' tonalities and harmonies.

00That notation will remain on your credit report for up to seven years.

00You may even be faced with a negative notation on your credit report.

00Ask that the notation be added to your credit report that the account was closed at your request.

00Verify that the account was successfully closed and that the proper notation was made.

00The company will make a notation of the card activity on your credit report.

00This service allows the consumer to place a notation on his or her credit report requesting lenders to be sure the applicant for credit is in fact the consumer it is purported to be.

00The credit bureau will place a notation on your credit file for a limited time.

00An extended alert is an option after the initial report, which allows the notation to remain on file for up to seven years.

00In an initial 90 day fraud alert, the notation encourages credit bureaus to seek additional verification of your identification.

00To obtain a fraud alert on a credit report, contact each of the three credit bureaus and request this notation.

00This is different from a fraud alert since credit monitoring services do not provide any notation to potential lenders about the suspected identity theft risks.

00This service will monitor the activity on your credit report and provide you with a notation whenever a significant change occurs.

00Tablature is a music notation system that allows guitar players to learn their favorite songs without having to know how to read music.

00You get tabs, chords with diagrams, standard musical notation, vocal melody lines and lyrics.

00Playing by guitar tabs, where a musician reads the special notation system called guitar tablature to learn the music.

00When looking to learn musical tunes from guitar sheet music, it helps to be familiar with some of the shorthand notation that comes with the territory.

00P-I-M-A - this is the notation for the fingering on the right hand for picking the strings.

00It is possible to sight-read and therefore sight-play a piece of music written in sheet notation.

00This kind of music notation is probably more helpful for the serious student of classical guitar rather than the hobbyist looking to play modern music.

00Luckily, a great system of notation called tablature, or tabs for short, has been developed that allows novice guitarists with no musical training to conquer this all important step.

00Traditional music notation has time signatures, rests, holds, ties, etc. that inform the player about how the music relates to time.

00In addition, tablature is a very specific type of musical notation where every note is recorded.

00The site also features a Tip of the Day video at the end of the notation to give musicians a chance to learn a little something else after they've mastered Sweet Home Alabama.

00If you're good at reading standard musical notation, you can play using the same chords from the piano version on your guitar.

00Tablature is a form of guitar notation that illustrates where guitar players need to put their fingers in order to play a chord or a note.

00Depending on your skill level as a player, you might need to find multiple forms of notation for a particular song to help you learn how to play it correctly.

00All the songs are transcribed in both standard notation and guitar tabs.

00This article will answer the 21st century question, How do u read guitar tabs? by explaining the ancient system of music notation called tablature to you.

00What this means is that, in a way, the notation has nothing to do with music at all.

00These days, tablature, not sheet music, is the primary form of music notation that is available on the Internet.

00However, sheet music is a much more detailed and accurate form of music notation because it takes into account subtleties in the music like dynamics and rhythm.

00Tablature, on the other hand, being a very simplified version of music notation, is very easy to learn and even very novice players can quickly learn how to create tabs.

00Guitar tabs are helpful for all guitar players because they provide an easy to read notation system that can be understood by people who can't read music.

00Be forewarned; some tablature books highlight the full dynamics of a song in tab notation like hammer-on's and staccato notes.

00Consisting (for guitar) of five staff lines and four spaces between the lines, sheet music provides standard musical notation that directs which notes to play at any given moment.

00Once you've learned a few easy steps, reading musical notation will quickly become much easier!

00Traditionally, it is considered more beneficial for players to learn to read the standard musical notation provided in classical guitar sheet music before moving on to tablature in order to develop good playing technique.

00Remember those spaces - With so many lines going on in musical notation, it can be difficult to remember sometimes that the spaces have a note value.

00Take Lessons - Don't hesitate to take at least a few lessons with a professional guitar player or music teacher who can help you learn the basics of musical notation.

00Since notation systems such as chord charts and tabs are so popular for the guitar, many guitarists might wonder why anyone would need sheet music.

00Classical Guitar Pieces - This great text has 50 famous classical guitar songs in both standard notation and tab.

00Fingerpicking Beatles - 30 Beatles songs are included in this excellent book, and they are arranged in standard notation for a solo guitar.

00If you can read standard musical notation, it is definitely in your best interest to invest in good acoustic guitar sheet music.

00Since most of the music notation on the Internet is provided free of charge, this is usually a case of getting what you pay for, but it is still very frustrating.

00One of the best ways to make a piece of music your own is to consult as many types of music notation you can find and start to blend the ideas into one cohesive version.

00Tablature is a form of musical notation that makes it possible for someone with no knowledge of how to read music to play music.

00This allows you to learn scales and skills without having to learn notation.

00Tablature is a form of musical notation that just about anyone can understand.

00You may come up with a number of different varieties of notation for the song, including tablature and chord progressions.

00Generally, the results will say which type of notation the file is in.

00The notation is designed for the person who wants to spend less time learning theory and more time mastering her guitar.

00Still, if you've never done it before, you may find the notation a little confusing.

00Many of the sites offer chord notation as well as tablature.

00Tablature is a system of musical notation for those who do not know how to read music.

00This is done through a method called "tablature" which shows the reader where to physically place her fingers on the guitar's fret board rather than using traditional musical notation.

00This easy-to-learn method of notation will help you play a number of your favorite bossa nova songs, as well as other types of Brazilian music in no time.

00Some of her most notable campaigns include photos in 2007 where she was featured amid smaller models without notation regarding her size - a rarity in conventional fashion advertising.

00

The word usage examples above have been gathered from various sources to reflect current and historial usage. They do not represent the opinions of YourDictionary.com.