# Notation Sentence Examples

- It is therefore better to use some independent
**notation**, such as A Z. - (n+--r-1)lr!=n[r]lr!; this may, by analogy with the
**notation**of ï¿½41, be denoted by n [r 7. - Evolution 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. - 2 and lb/in.', in the Hospitaller
**notation**, to be employed in the sequel). - One drawback of Thomsen's
**notation**is that the nature of the final system is not indicated, although this defect in general causes no ambiguity. - In this
**notation**the fundamental relation is written (l + a i x +01Y) (I + a 2x+l32Y) (1 + a3x+133y)... - (v.) It should be mentioned that the
**notation**of the binomial 'coefficients, and of the continued products such as n(n -1). - It 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!. - Algebraical 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. - Various special algebras (for example, quaternions) may be expressed in the
**notation**of the algebra of matrices. - There is a complete edition in modern
**notation**by T. - He prints a bar under the decimals; this
**notation**first appears without any explanation in his "Lucubrationes" appended to the Constructio. - We 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. - Hence, excluding ao, we may, in partition
**notation**, write down the fundamental solutions of the equation, viz. - Even 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. - Girard 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. - Its 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. - According 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). - In 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. - Substituting for H its value from (3), and employing the
**notation**of the calculus, we obtain the relation S - s =0 (dp /do) (dv/do),. - The 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. - Briggs 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. - While 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. - Wertheim (Leipzig, 1890), and an English edition in modern
**notation**(T. - At 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. - Remark.-In this
**notation**(0) = Eai = (i n); (02) _ za l a2 = (2);... - Observe the
**notation**, which is that introduced by Cayley into the theory of matrices which he himself created. - 1 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. - According to the
**notation**adopted by Meyer the atomic susceptibility k=KX atomic-weight/ (density X 1000). - Whether this principle may legitimately be extended to the
**notation**adopted in (iii.) (a) of ï¿½ 14 is a moot point. - Expressed 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. - (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. - +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). - In 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. - His
**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. - His
**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. - Employing 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. - In 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. - These 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. - Accordingly, 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. - For 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. - The 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. - His 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. - (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. - ,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. - The 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. - The famous inscriptions with hymns to Apollo accompanied by musical
**notation**were found on stones belonging to this treasury. - It is not, however, necessary that the
**notation**of the calculus should be employed throughout. - He introduced the terms multinomial, trinomial, quadrinomial, &c., and considerably simplified the
**notation**for decimals. - 2 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. - These 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.