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of Russia to entrust him with the education of the Grand Duke;—a proposal accompanied with all the flattering offers that could tempt a man, ambitious of titles, or desirous of making an ample fortune: but the objects of his ambition were tranquillity and study. In the year 1765, he published his “Disserta. tion on the Destruction of the Jesuits.” This piece drew upon him a swarm of adversaries, who only confirmed the merit and credit of his work by their manner of attacking it. Beside the works already mentioned, he published nine volumes of memoirs and treatises, under the title of “Opuscules * in which he has resolved a multitude of problems relating to astronomy, mathematics, and natural philosophy; of which his panegyrist, Condorcet, gives a particular account, more especially of those which exhibit new subjects, or new methods of investigation: He published also “Elements of Music;” and rendered, at length, the system of Rameau intelligible; but he did not think the mathematical theory of the sonorous body sufficient to account for the rules of that art. In the year 1772 he was chosen Secretary to the French Academy of Sciences. He formed, soon after this preferment, the design of writing the lives of all the deceased academicians, from 1700 to 1772; and in the space of three years he executed this design, by composing 70 eulogies. The correspondence which D'Alembert held with eminent literary characters, and his constant intercourse with learned men of all nations, together with his great influence in the academy, concurred to give him a distinguished importance above most of his countrymen. By some, who were jealous of his reputation, he was denominated the Mazarm of literature; but there seems now

no doubt, but that his influence was obtain

ed by his great talents and learning, rather than by artful management and supple address. He was a decided and open enemy to superstition and priestcraft. Without inquiring into the merits of Christianity, he concluded that the religion taught in France, was that which believers in general regarded as the true doctrine, and which he rejected as a fable, unworthy the attention of the philosopher. There is no reason to think that he ever studied the foundations on which natural and revealed religion were built; and it is certain that he adopted a system of deified nature, which bereaves the world of a designing cause, and presiding intelligence. He was zealous even in propagating the opinions which he adopted,

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and might be regarded as an apostse of
atheism. The eccentricity of his opinions
did not destroy the moral virtues of his
heart. A love of truth, and a zeal for the
progress of real science and liberty, formed
the basis of his character: strict probity, a
noble disinterestedness, and an habitual de-
sire of being useful, were its distinguishing
features. To the young who possessed
talents and genius he was a patron and in-
structor: to the poor and oppressed he be-
came a firm and generous friend: to those
who had shewn him kindness he never
ceased to be grateful; a sure evidence of a
great mind. To two ministers who had be-
friended him in their prosperity, he dedicat-
ed works when they were in disgrace with
the court. An instance of a kind, a grate-
ful disposition, was displayed by D'Alembert
in early life. His mother, who had infa-
mously disowned and abandoned him, hear-
ing of the greatness of his talents, and of
the promise which he gave of future cele-
brity, obtained an interview, and laid claim
to the character of a parent. “What do I
hear,” said the indignant youth, “you are
the mother-in-law, the glazier's wife is my
true mother:” for her, indeed, he never
ceased to testify the affection and gratitude
of a child; and under her roof he resided,
as we have seen, many years, till an
alarming illness made it necessary for him
to remove to a more airy lodging. D'Alem-
bert maintained his high rank and reputation
among mathematicians and philosophers till
his death, in October 1783. His loss was
deplored by survivors of every country, but
his particular friends and associates exhibit-
ed, on the occasion, every mark of grief,
which real and unaffected sorrow can alone
supply for undissembled worth.
ALEMBIC, in chemistry, a vessel usually
made of glass or copper, formerly used for
distillation. The bottom, in which the sub-
stance to be distilled is put, is called the
cucurbit; the upper part is called the head,
the beak of which is fitted into the neck of
the receiver. Retorts, and the common
worm-still are now more generally employ-
ed. See CHEMistry, Distill Ation, &c.
ALETRIS, in botany, a genus of the Hex-
andria Monogynia class and order, of the
matural order of Liliae or Liliaceae, of which
there are nine species; A. farinosa, or Ame-
rican aletris, used by the natives in coughs,
and in the pleurisy. Some of the species
are natives of the Cape of Good Hope;
others are found natural in Ceylon and
Guinea. The A. zeylanica, or Ceylon aloe,

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is common in gardens where exotic plants are preserved. A. guianensis, or Guinea aloe, when in flower, seldom continues in beauty more than two or three days, and never produces seeds in England. The Ceylon, Guinea, and sweet-scented species, are too tender to live through the winter in England, unless in a warm stove; and they will not produce flowers if the plants are not plunged into a tan bed. The creeping roots of the Ceylon and Guinea sorts send up many heads, which should be cut off in June, and after having been laid in the stove a fortnight, that the wounded part may heal; they should be planted in small pots of light sandy earth, plunged into a moderate hotbed, and treated like other tender succulent plants, and be never set abroad in summer. ALEURITES, in botany, a genus of Monoecia Monadelphia class and order, of the natural order of Tricoccas. The flowers are male and female; the calyx of the male is a perianthium; the corollas five petals; the nectary has five-cornered scales; the stamens are numerous filaments; the anthers roundish. The female flowers are few, the calyx, corolla, and nectarium, as in the male, but larger. There are two seeds with a double bark. Only one species, a tree in the islands of the South Seas. ALEXANDRIAN copy of the New Testament, preserved in the British Museum, is referred to as an object of curiosity, as well as of considerable importance, to persons who study the scriptures critically. It consists of four large quarto, or rather folio volumes, containing the whole bible in Greek, including the Old and New Testament, with the Apocrypha, and some smaller pieces, but not quite complete. It was placed in the British Museum in 1758; and had been a present to Charles I. from Cyrillus Lucaris, a native of Crete, and patriarch of Constantinople, by Sir Thomas Rowe, ambassador from England to the Grand Seignior in the year 1628. Cyrillus brought it with him from Alexandria, where it was probably written. It is said to have been written by Thecla, a noble Egyptian lady, about thirteen hundred years ago. In the New Testament there is wanting the beginning as far as Matt. xxv. 6; likewise from John vi. 50, to viii. 52; and from 2 Cor. iv. 19, to xii. 7. It has neither accents nor marks of aspiration; it is written with capital, or, as they are called, uncial letters, and there are no intervals between the words, but the sense of a passage is sometimes terminated by a point, and sometimes

by a vacant space. Dr. Woride published this valuable work in 1786, with types cast for the purpose, line for line, precisely like the original MS: the copy has been examined with the greatest care, and it is found to be so perfect a resemblance of the original, that it may supply its place. The authenticity, antiquity, &c. of this MS. is briefly, but ably discussed in Rees's New Cyclopedia. Vol. I. p. ii. ALGAE, in botany, an order or division of the Cryptogamia class of plants. It is one of the seven families or natural tribes, into which the vegetable kingdom is distributed, in the Philosophia Botanica of Linnaeus; the 57th order of his fragments of a natural method. The plants belonging to this order are described as having their root, leaf, and stem entire, or all one. The whole of the sea-weeds, and various other aquatic plants, are comprehended under this division. From their admitting of little distinction of root, leaf, or stem; and the parts of their flowers being equally incapable of description; the genera are distinguished by the situation of what is supposed to be the flowers or seeds, or by the resemblance which the whole plant bears to some other substance. The parts of fructification are either found in saucers or tubercules, as in lichens; in hollow bladders, as in the fuci; or dispersed through the whole substance of the plants, as in the ulvae. The substance of the plants has much variety; it is flesh-like or leatherlike, membranaceous or fibrous, jelly-like or horn-like, or it has the resemblance of a calcareous earthy matter. Lamarck distributes the algae into three sections: the first comprehends all those plants whose fructification is not apparent or seems doubtful. These commonly live in water, or upon moist bodies, and are membranous, gelatinous, or filamentous. To this section he refers the byssi, conferva, ulva, tremella, and varec. The plants of the second section are distinguished by their apparent fructification, though it be little known, and, they are formed of parts which have no particular and sensible opening or explosion, at any determined period; their substance is ordinarily crustaceous or coriaceous. They include the tassella, ceratosperma, and lichen. The third section comprehends plants which have their fructification very apparent, and distinguished by constituent parts which open at a certain period of maturity, for the escape of the fecundating dust or seeds. These plants

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are more herbaceous, as to both their substance and their colour, than those of the other two sections, asid are more nearly related to the mosses, from which they do not essentially differ. Their flowers are often contained in articulated and very elastic filaments. To this section are referred the riccia, blasia, anthoceros, targiona, hepatica, and junger-manna. In the Linnaean system the algae are divided into two classes, viz. the terrestres and aquatica. The former include the anthoceros, blasia, riccia, lichen, and byssus; and the latter are the ulva, fucus, and conferva. The fructification of the algae, and particularly of those called aquatica, is denominated by a judici. ous botanist, the opprobrium botanicorum. ALGAROTH. See ANT1 Moxy. ALGEBRA, a general method of resolving mathematical problems, by means of equations; or, it is a method of computation by symbols, which have been inverted for expressing the quantities that are the objects of this science, and also thor mutual relation and dependence. These quantities might, probably, in the infancy of the science, be denoted by their names at full length; these, being found inconvenient, were succeeded by abbreviations, or by their mere initials; and, at length, certain letters of the alphabet were adopted as general representations ofall quantities; other symbols or signs were introduced to prevent circumlocution, and to facilitate the comparison of various quantities with one another; and, in consequence of the use of letters or species, and other general symbols, orindeterminate quantities, algebra obtained the appellation of specious, literal, and universalarithmetic. The origin of algebra, like that of other sciences of ancient date and gradual progress, is not easily ascertained. The most ancient treatise on that part of analytics, which is properly called algebra, now extant, is that of Diophantus, a Greek author of Alexandria, who flourished about the year of our Lord 330, and who wrote 13 books, though only six of them are preserved, which were printed together with a single imperfect book on multangular numbers, in a Latin translation by Xylander, in 1575, and afterwards in Greek and Latin, with a Comment, in 1621 and 1670, by Gaspar Bachet, and M. Fermat, Tolosae, fol. These books do not contain a treatise on the elementary parts of algebra, but merely collections of some difficult questions relating to square and cube numbers, and other curious properties of numbers, with their

solutions. Algebra, however, seems not to have been wholly unknown to the ancient mathematicians, long before the age of Diophantus. We observe the traces and effects of it in many places, though it seems as if they had intentionally concealed it. Something of it appears in Euclid, or at least in Theon upon Euclid, who observes that Plato had begun to teach it. And there are other instances of it in Pappus, and more in Archimedes and Appollonius. But it should be observed, that the analysis used by these authors is rather geometrical than algebraical ; this appears from the examples that occur in their works; and, therefore, Diophantus is the first and only author among the Greeks who has treated professedly of algebra. Our knowledge of the science was derived, not from Diophantus, but from the Moors or Arabians; but whether the Greeks or Arabians were the inventors of it has been a subject of dispute. It is probable, however, that it is much more ancient than Diophantus, because his treatise seems to refer to works similar and prior to his own. + Algebra is a peculiar kind of arithmetic, which takes the quantity sought, whether it be a number, or a line, or any other quantity, as if it were granted; and by means of one or more quantities given, proceeds by a train of deductions, till the quantity at first only supposed to be known, or at least some power of it, is found to be equal to some quantity or quantities which are known, and consequently itself is known. Algebra is of two kinds, numeraland literal. Algebra, numeral or rulgar, is that which is chiefly concerned in the resolution of arithmetical questions. In this, the quantity sought is represented by some letter or character; but all the given quantities are expressed by numbers. Such is the algebra of the more ancient authors, as Diophantus, Paciolus, Stifelius, &c. This is thought by some to have been an introduction to the art of keeping merchants' accounts, by double entry. ALG EBRA, specious or literal, or the new algebra, is that in which all the quantities, known and unknown, are expressed or represented by their species, or letters of the alphabet. There are instances of this method from Cardan, and others about his time; but it was more generally introduced and used by Vieta. Dr. Wallis apprehends that the name of specious arithmetic, applied to algebra, is given to it with a reference to the sense in which the Civilians use

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A, B, C, &c. which he used to represent indefinitely any number or quantity, so circumstanced as the occasion required. This mode of expression frees the memory and imagination from that stress or effort, which is required to keep several matters, necessary for the discovery of the truth investigated, present to the mind; for which reason this art may be properly denominated metaphysical geometry. Specious algebra is not like the numeral, confined to certain kinds of problems; but serves universaily for the investigation or invention of theorems, as well as the solution and demonstration of all kinds of problems, both arithmetical and geometrical. The letters used in algebra, do each of them, separately, represent either lines or numbers, as the problem is either arithmetical or geometrical; and together, they represent planes, solids, and powers, more or less high, as the letters are in a greater or less number. For instance, if there be two letters, a b, they represent a rectangle, whose two sides are expressed, one by the letter a, and the other by b : so that by their mutual multiplication they produce the plane ab. Where the same ietter is repeated twice, as a a, they denote a square. Three letters a be, represent a solid or a rectangular parallelepiped, whose three dimensions are expressed by the three letters a b c ; the length by a, the breadth by b, and the depth by c : so that by their mutual multiplication, they produce the solid at. c. As the multiplication of dimensions is expressed by the multiplication of letters, and as the number of these may be so great as to become incommodious, the method is only to write down the root, and on the right hand to write the index of the power, that is, the number of letters of which the quantity to be expressed consists; as a , a, a”, sc. the last of which signifies as much as a multiplied four times into itself; and so of the rest. But as it is necessary, before any progress can be made in the science of algebra, to understand the method of notation, we shall here give a general view of it. In algebra, as we have already stated, every quantity whether it be known or given, or unknown or required, is usually represented by some letter of the alphabet;

and the given quantities are commonly denoted by the initial letters, a, b, c, d, &c. and the unknown ones by the final letters, u, w, x, y, z. These quantities are connected together by certain signs or symbols, which serve to slew their mutual relation, and at the same time to simplify the science, and to reduce its operations into a less compass. Accordingly the sign +, plus, or more, signisies that the quantity to which it is prefixed is to be added, and it is called a positive or affirmative quantity. Thus, a + b expresses the sum of the two quantities a and b, so that if a were 5, and b, 3, a + b would be 5 +3, or 8. . If a quantity have no sign, +, plus, is understood, and the quantity is affirmative or positive. The sign —, minus, or less, denotes that the quantity which it precedes is to be subtracted, and it is called a negative quantity. Thus a b expresses the difference of a and b; so that a being 5, and b, 3, a -b or 5–3 would be equal to 2. If more quantities than two were connected by these signs, the sum of those with the sign — must be subtracted from the sum of those with the sign +. Thus, a + b c.—d represents the quantity which would remain, when c and d are taken from a and b. So that if a were 7, b, 6, c, 5, and d, 3, a + b c d, or 7–H 6–5 – 3, or 13 – 8, would be equal to 5. If two quantities are connected by the sign or, as a w, b, this mode of expression represents the difference of a and b, when it is not known which of them is the greatest. The sign x signifies that the quantities between which it stands are to be multiplied together, or it represents their product. Thus, a x b expresses the product of a and b; a × b x c denotes the product of a, b, and c; a + b x c denotes the product of the compound quantity a + b by the simple quantity c.; and 7-F0-Fc x a-D-F. x a-Fi represents the product of the three compound quantities, multiplied continually into one another; so that if a were 5, b, 4, and c, 3, then would a + b + c x a-b-H c x a-H c be 12 x 4 x 8, or 384. The line connecting the simple quantities and forming a compound one, placed over them, is called a vinculum. Quantities that are joined together without any intermediate sign form a product; thus a b is the same with a x h, and a b c the same with a x b x c. When a quantity is multiplied into itself, or raised to any power, the usual mode of expression is to draw a line over the quantity, and to place the number denoting the power at the end of it, which number is called the index or exponent. Thus, a + blo denotes the same as a + b x a-F5 or second power, or square, of a + b considered as one quantity; and a-FD)' denotes the same as a -F5 x a-F5 x a-FE, or the third power, or cube, of a + b. In expressing the powers of quantities represented by single letters, the lime over the top is usually omitted; thus, a is the same as a a or a xa, and bo the same as b b b or b x b X b, and a b', the same as aa × b b b or a × a × b X b X b. The full point. and the word into, are sometimes used instead of x as the sign of mul. tiplication. Thus, a + b. a+ c, and a +5. into 7-Ec, signify the same thing as a + b x a-Fé, or the product of To by 7-E. The sign -- is the sign of division, as it denotes that the quantity preceding it is to be divided by the succeeding quantity. Thus, c-b signifies that c is to be divided by b, and TV-7-Fr, that a F5 is to be di. vided by a Fe. The mark) is sometimes used as a note of division; thus a +b) a b, denotes that a b is to be divided by a + b. But the division of algebraic quantities is most commonly expressed by placing the divisor under the dividexd with a line between them, like a vulgar fraction. Thus, ; represents the quantity arising by dividing c by b, or the quotient, and

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which is 2. The sign VTwith a figure over it is used to express the cubic or biquadratic root, &c. of any quantity; thus V 64 represents the cube root of 64, or 4, because 4 x 4 x 4 is 64; and Val-Fed the cube root of a b-H ca. In like manner W15 denotes the biquadratic root of 16, or 2, because 2 x 2 x 2 x 2 is 16, and W/a D-F, a denotes the biquadratic root of a b-H c d, and so of others. Quantities thus expressed are called radical quantities, or surds; of which those, consisting of one term only, as va and Vav, are called simple surds; and those cousisting of several terms or numbers, as Vas–bo and A/T-P-Foc are denominated compound surds. Another commodious method of expressing radical quantities is that which denotes the root, by a vulgar fraction, placed at the end of a line drawn over the quantity given. In this notation, the square root is expressed by }, the cube root by 1, the biquadratic root by

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have no radical sign (V) or index annexed to them, are called rational quanti. ties. The sign =, called the sign of equality, signifies that the quantities between which it occurs are equal. Thus 2 +3=5, shews that 2 plus 3 is equal to 5; and r = a b shews that r is equal to the dif. ference of a and b. 'The mark :: signifies that the quantities between which it stands are proportional. As a : b :: c : d denotes that a is in the same proportion to b as c is to d, or that if a be twice, three, or four times, &c. as great as b, c will be twice, thrice, or four times, &c. as great as d. When any quantity is to be taken more than once, the number, which shews how many times it is to

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