# Notation Sentence Examples

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

• This method of notation has various disadvantages.

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

• The 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.

• Denoting 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.

• At 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.

• The 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.

• It 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.

• His 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.

• The 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.

• He 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.

• His notation is rather unwieldy.

• Martius 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.

• Mat 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.

• Owing 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.

• As 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.

• The 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.

• While 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.

• No 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).

• The 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.

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

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

• If 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.

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

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

• The 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.

• The 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 ?

• The 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 + .

• His chief advance on Bombelli was in his notation.

• Along 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.

• In 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.

• Besides 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.

• The 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.

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

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

• The 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.

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

• The 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.

• The 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.

• Over 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.

• In 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.

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

• In 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.

• The 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.

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

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

• The 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.

• The 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.

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

• On 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.

• In 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.

• Under 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).

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

• Addition 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.

• The 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).

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

• This 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.

• They 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.

• A 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.

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

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

• Under 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.

• There 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.

• Even 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.

• It 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.

• In 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).

• If 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.

• For 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.

• The 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.

• These 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.

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

• In 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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

• The filename prefix for each ion follows spectroscopic notation.

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

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

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

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

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

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

• The 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.

• This 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.

• He 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.

• Berthelot'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.

• The 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.

• Notation 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.

• With 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.

• Vieta, 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.

• In 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.

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

• In 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).

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

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

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

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

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

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

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

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

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

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

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

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

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

• When 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.

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

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

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

• Luckily, 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.

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

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

• The 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.

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

• Tablature 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.

• Depending 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.

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

• This 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.

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

• However, 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.

• Tablature, 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.

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

• Consisting (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.

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

• Traditionally, 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.

• Remember 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.

• Take 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.

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

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

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

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

• Since 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.

• One 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.

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

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

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

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

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

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

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

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

• Tablatureis a system of musical notation for those who do not know how to read music.

• This 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.

• This 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.

• Some 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.

• A "made in" notation with the wrong point of origin is a dead giveaway.

• Instead of reading music in standard notation, the position to play notes is displayed by numbers, which represent the location of where you must hold down your string(s).

• However, the video game guitar tabs notation can help with a few techniques to assist you with your music piece, like hammer ons and pull offs, slides, string bends, vibrato and harmonics.

• Video game tabs are a specific form of notation for reading music that does not require you to understand traditional sheet music.

• The tablature system of music notation is a lot easier for beginners to pick up and understand because it directly corresponds to the instrument being played.

• One of the biggest shortcomings of video game tabs, however, is that the notation is not complete, forcing the musician to "play by ear" in terms of how long to hold a particular note or chord.

• When the results come back, you'll see a notation specifying how many Good Sam parks there are that match your search criteria.

• There is a standard notation for dance step illustrations that makes it very easy to read and understand what each step entails.

• There is a notation indicating when the record was created, so you can determine if the information may be out of date.

• If you have a price book, make a notation of what the standard price is for each item.

• Mark the items you have coupons for with a "C" or other notation.

• Close the letter with you signature and name follow by the enclosures notation.

• If you come across something you don't understand, make a notation on a separate piece of paper.

• Not everything in your possession is worthy of notation in your inventory.

• The answer for graphics designers came in the form of hexadecimal notation - which starts with the digits 0-9 just like decimal number systems, but instead of going on to "10" it instead goes into the letters A-F.

• So to write the decimal number "10" in hexadecimal notation, it would be "A".

• By using hexadecimal notation, this can be exact regardless of the screen calibration or even color blindness of the people working on it.

• Each 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.

• 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.

• A word is necessary on Diophantus' notation.

• 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.

• 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.

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

• Such 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.

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

• 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!.

• 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.

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

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

• In 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'.

• But 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.

• Among 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.

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

• The 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).

• Guitar 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.

• 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.

• 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.

• 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.

• 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.

• 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)...

• 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.

• 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.

• 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.

• 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.

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

• 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.

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

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

• 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.

• 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.

• 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.

• 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.