325. Arius acknowledged Christ to be God, in a subordinate sense, and considered his death to be a propitiation for sin. The Arians acknowledge, that the Son was the word, though they deny its being eternal, contending only that it had been created prior to all other beings. They maintain that Christ is not the eternal God; but, in opposition to the Unitarians, they contend for his pre-existence, a doctrine which they found on various passages of scripture, particularly these two, "before Abraham was, I am;" and "glorify me with the glory which I had with thee before the world was." Arians differ among themselves as to the extent of the doctrine. Some of them believe Christ to have been the Creator of the world, and on that account has a claim to religious worship; others admit of his pre-existence simply. Hence the appellations, high and low Atians. Dr. Clarke, Rector of St. James, in his "Scripture Doctrine of the Trinity;" Mr. Henry Taylor, Vicar of Portsmouth, in a work entitled, "Ben Mordicai's Apology;" Mr. Tomkins, in his "Mediator" and Mr. Hopkins in his "Appeal to the Common Sense of all Christian People," have been deemed among the most able advocates of Arianism. Dr. Price has been one of the last writers in behalf of this doctrine in his sermons "On the Christian Doctrine," will be found an able defence of low Arianism. See also a tract published in 1805, by Ba

sanistes.

ARIES, in astronomy, a constellation of fixed stars, drawn on the globe in the figure of a ram. It is the first of the twelve signs of the zodiac, from which a twelfth part of the ecliptic takes its denomination. It is marked thus, and consists of sixty-six

stars.

ARISH, a long measure used in Persia, containing 3197 English feet.

ARISTA, among botanists, a long needlelike beard, which stands out from the husk of a grain of corn, grass, &c.

ARISTARCHUS, in biography, a celebrated Greek philosopher and astronomer, and a native of the city of Samos; but at what period he flourished is not certain. It must have been before the time of Archimedes, as some parts of his writings and opinions are cited by that author. He held the doctrine of Pythagoras as to the system of the world, but whether he lived before or after him is not known. He maintained that the sun and stars were fixed in the heavens, and that the earth moved in a circle

about the sun, at the same time that it revolved about its own axis. He determined that the annual orbit of the earth, compared with the distance of the fixed stars, is but as a point. For these his opinions, which time has proved to be undeniably true, he was censured by his contemporaries, some of whom went about to prove that Greece ought to have punished Aristarchus for his heresy. This philosopher invented a peculiar kind of sun-dial, mentioned by Vitruvius. There is now extant only a treatise upon the magnitude and distance of the sun and moon, which was translated into Latin, and commented upon by Commandine, who published it with Pappus's explanations in

1572.

ARISTEA, in botany, a genus of plants of the Triandria Monogynia class and order. Petals six; style declined; stigma funnelform, gaping; capsule inferior, many-seeded. There is but one species: a Cape plant, low; leaves veined and narrow; flowers in downy heads.

ARISTIDA, in botany, a genus of the Triandria Digynia class of plants, the calyx of which is a bivalve subulated glume, of the length of the corolla; the corolla is a glume of one valve, opening longitudinally, hairy at the base, and terminated by three sub-equal patulous arista; the fruit is a connivent glume, containing a naked filiform single seed, of the length of the corolla. There are ten species.

ARISTOCRACY, a form of government where the supreme power is vested in the principal persons of the state, either on account of their nobility, or their capacity and probity.

Aristocracies, says Archdeacon Paley, are of two kinds; first, where the power of the nobility belongs to them in their collective capacity alone; that is, where, although the government reside in an assembly of the order, yet the members of the assembly, separately and individually, possess no authority or privilege beyond the rest of the community: such is the case in the constitution of Venice. Secondly, where the nobles are severally invested with great personal power and immunities, and where the power of the senate is little more than the aggregate power of the individuals who compose it: such was the case in the constitution of Poland. Of these two forms of government, the first is more tolerable than the last; for although many, or even all the members of a senate, should be so profligate as to abuse the authority of their

stations in the prosecution of private designs, yet, whilst all were not under a temptation to the same injustice, and having the same end to gain, it would still be difficult to obtain the consent of a majority to any specific act of oppression, which the iniquity of an individual might prompt him to propose: or, if the will were the same, the power is more confined; one tyrant, whether the tyranny reside in a single person, or a senate, cannot exercise oppression in so many places at the same time, as may be carried on by the dominion of a numerous nobility over their respective vassals and dependents. Of all species of domina tion, this is the most odious; the freedom and satisfaction of private life are more restrained and harassed by it, than by the most vexatious laws, or even by the lawless will of an arbitrary monarch, from whose knowledge, and from whose injustice, the greatest part of his subjects are removed by their distance, or concealed by their obscurity. An aristocracy of this kind has been productive, in several instances, of disas trous revolutions, and the people have concurred with the reigning prince, in exchanging their condition for the miseries of despotism. This was the case in Denmark about the middle of the seventeenth century, and more lately in Sweden. In England, also, the people beheld the depression of the barons, under the house of Tudor, with satisfaction, although they saw the crown acquiring thereby a power which no limitations, provided at that time by the constitution, were likely to confine.

From such events this lesson may be drawn: "That a mixed government, which admits a patrician order into the constitution, ought to circumscribe the personal privileges of the nobility, especially claims of hereditary jurisdiction and local authority, with a jealousy equal to the solicitude with which it provides for its own preservation." Paley's Princ. of Philos.

ARISTOLOCHIA, in botany, birth wort, a genus of plants of the Gynandria Hexandria class and order. Stigmata six; no calyx ; corol one-petalled, tubular, tongueshaped; capsule inferior, six-celled. There are 27 species, most foreign.

ARISTOTELIA, a genus of the Dodecandria Monogynia class and order: calyx five-leaved; petals five; style three-cleft; berry-three-celled, with two seeds in each. One species, found in Chili, a shrub, leaves ever-green; flowers white in axillary ra

cemes,

ARISTOTELIAN, something relating to Aristotle: thus we read of the Aristotelian philosophy, school, &c. See PERIPATETICS.

ARITHMETIC, the art of numbering; or, that part of mathematics, which considers the powers and properties of numbers, and teaches how to compute or calenlate truly, and with expedition and ease. By

At

some authors it is also defined the science of discrete quantity. It consists chiefly in the four great rules or operations of Addition, Subtraction, Multiplication, and Division. Concerning the origin and invention of arithmetic we have very little informa tion; history fixes neither the author nor the time. Some knowledge, however, of numbers must have existed in the earliest ages of mankind. This knowledge would be suggested to them, whenever they opened their eyes, by their own fingers, and by their flocks and herds, and by the variety of objects that surrounded them. first, indeed, their powers of numeration would be of very limited extent; and be fore the art of writing was invented, it must have depended on memory, or on such artificial helps, as might most easily be obtained. To their ten fingers they would, without doubt, have recourse in the first instance; and hence they would be naturally led to distribute numbers into periods, each of which consisted of ten units. This prac tice was common among all nations, the ancient Chinese, and an obscure people mentioned by Aristotle, excepted. But though some kind of computation must have commenced at a very early period, the introduction of arithmetic as a science, and the improvements it underwent, must, in a great degree, depend upon the introduction and establishment of commerce: and as commerce was gradually extended and improved, and other sciences were discovered and cultivated, arithmetic would be improved likewise. It is therefore probable, that if it was not of Tyrian invention, it must have been much indebted to the Phoenicians or Tyrians. Proclus, indeed, in his commentary on the first book of Euclid, says, that the Phoenicians, by reason of their traffic and commerce, were the first inventors of arithmetic; and Strabo also informs us, that in his time it was attributed to the Phoenicians. Others have traced the ori gin of this art to Egypt; and it has been a general opinion, sanctioned by the authori ties of Socrates and Plato, that Theut or Thot was the inventor of numbers; that

from hence the Greeks adopted the idea of ascribing to their Mercury, corresponding to the Egyptian Theut or Hermes, the superintendance of commerce and arithmetic. With the Egyptians we ought also to associate the Chaldeans, whose astronomical disquisitions and discoveries, in which they took the lead, required a considerable acquaintance with arithmetic. From Asia it passed into Egypt, as Josephus says, by means of Abraham. Here it was greatly cultivated and improved; insomuch that a large part of the Egyptian philosophy and theology seems to have turned altogether upon numbers. Kircher shews, that the Egyptians explained every thing by numbers; Pythagoras himself affirming, that the nature of numbers pervades the whole universe, and that the knowledge of numbers is the knowledge of the deity. From Egypt, arithmetic was transmitted to the Greeks by Pythagoras and his followers; and among them it was the subject of particular attention, as we perceive in the writings of Euclid, Archimedes, and others; with the improvements derived from them, it passed to the Romans, and from them it came to us. The ancient arithmetic was very different from that of the moderns in various respects, and particularly in the method of notation. The Indians are at this time very expert in computing, by means of their fingers, without the use of pen and ink; and the natives of Peru, by the different arrangements of their grains of maize, surpass the European, aided by all his rules, with regard both to accuracy and dispatch, The Hebrews and Greeks, however, at a very early period, and after them also the Romans, had recourse to the letters of their alphabet for the representation of numbers, The Greeks, in particular, had two different methods the first resembled that of the Romans, which is sufficiently known, as it is still used for distinguishing the chapters and sections of books, dates, &c. They afterwards had a better method, in which the first nine letters of the alphabet represented the first numbers from 1 to 9, and the next nine letters represented any number of tens, from 1 to 9, that is, 10, 20, &c. to 90. Any number of hundreds they expressed by other letters, supplying what they wanted by some other marks or characters: and in this order they proceeded, using the same letters again, with different marks to express thousands, tens of thousands, hundreds of thousands, &c.; thus approaching very near to the more perfect decuple scale

of progression used by the Arabians, who acknowledge, as some have said, that they received it from the Indians. Archimedes also in his "Arenarius," used a particular scale and notation of his own. In the second century of the christian era, Ptolemy is supposed to have invented the sexagesimal numeration and notation, and this method is still used by astronomers and others, for the subdivision of the degrees of circles. These several modes of notation above recited, were so operose and inconvenient, that they limited the extent, and restrained the progress of arithmetic, so that it was applicable with great difficulty and embarrassment to the other sciences, which required its assistance. The Greeks, if we except Euclid, who in his elements furnished many plain and useful properties of numbers, and Archimedes in his Arenarius, contributed little to the advancement of this science towards perfection. From Boethius we learn, that some Pythagoreans had invented and employed, in their calculations, nine particular characters, whilst others used the ordinary signs, namely, the letters of the alphabet. These characters he calls apices; and they are said greatly to resemble the ancient Arabic characters, which circumstance suggests a suspicion of their authenticity. Indeed, the MSS. of Boethius, in which these characters, resembling those of the Arabian arithmetic, are found, not being more ancient than three or four centuries, confirm the opinion that they are the works of a copyist. Upon the whole, this treatise of Boethius does not warrant our rejecting the commonly received system with regard to the origin of our arithmetic; but if we suppose that the Arabians derived their knowledge of it from the Indians, it is more probable that it was one of the inventions which Pythagoras spread among the Indians, than that those persons should have obtained it from the Greeks.

The introduction of the Arabian or Indian notation into Europe, about the tenth century, made a material alteration in the state of arithmetic; and this, indeed, was one of the greatest improvements which this science had received since the first discovery of it. This method of notation, now universally used, was probably derived originally from the Indians by the Arabians, and not, as some have supposed, from the Greeks; and it was brought from the Arabians into Spain by the Moors or Saracens, in the tenth century. Gerbert, who was afterwards Pope, under the name of Silves.

ter II. and who died in the year 1,003, brought this notation from the Moors of Spain into France, long before the time of his death, or, as some think, about the year 960; and it was known among us in Britain, as Dr. Wallis has shewn, in the begin ning of the eleventh century, if not somewhat sooner. As literature and science

advanced in Europe, the knowledge of

numbers was also extended, and the writers in this art were very much multiplied. The next considerable improvement in this branch of science, after the introduction of the numeral figures of the Arabians or Indians, was that of decimal parts, for which we are indebted to Regiomontanus; who about the year 1464, in his book of "Triangular Canons," set aside the sexagesimal subdivisions, and divided the radius into 60,000,000 parts; but afterwards he altogether waved the ancient division into 60, and divided the radius into 10,000,000 parts; so that if the radius be denoted by 1, the sines will be expressed by so many places of decimal fractions as the cyphers following 1. This seems to have been the first introduction of decimal parts. To Dr. Wallis we are principally indebted for our knowledge of circulating decimals, and also for the arithmetic of infinites. The last, and perhaps, with regard to its extensive application and use, the greatest improvement which the art of computation ever received, was that of logarithms, which we owe to Baron Neper or Napier, and Mr. Henry Briggs. See LOGARITHMS.

ARITHMETIC, theoretical, is the science of the properties, relations, &c. of numbers, considered abstractedly, with the reasons and demonstrations of the several rules. Euclid furnishes a theoretical arithmetic, in the seventh, eighth, and ninth books of his elements.

ARITHMETIC, practical, is the art of numbering or computing; that is, from certain numbers given, of finding certain others, whose relation to the former is known. As, if two numbers, 10 and 5, are given, and

ADDITION.

Addition is that operation by which we find the amount of two or more numbers. The method of doing this in simple cases is obvious, as soon as the meaning of number is known, and admits of no illustration. A young learner will begin at one of the numhers, and reckon up as many units separately

as there are in the other, and practice will enable him to do it at once. It is impossible, strictly speaking, to add more than two numbers at a time. We must first find the sum of the first and second, then we add the third to that number, and so on. However, as the several sums obtained are easily retained in the memory, it is neither necessary nor usual to mark them down. When the numbers consist of more figures than one, we add the units together, the tens together, and so on. But if the sum of the units exceed ten, or contain ten several times, we add the number of tens it contains to the next column, and only set down the number of units that are over. In like manner we carry the tens of every column to the next higher. And the reason of this is obvious from the value of the places; since an unit in any higher places signifies ately lower. the same thing as ten in the place immedi

Rule. Write the numbers distinctly, units under units, tens under tens, and so on. Then reckon the amount of the right-hand column; if it be under ten mark it down; if it exceed ten mark the units only, and carry the tens to the next place. In like manner carry the tens of each column to the next, and mark down the full sum of the left-hand column.

we are to find their sum, which is 15, their difference 5, their product 50, their quotient 2.

The method of performing these operations generally we shall now proceed to shew, reserving for the alphabetical arrangement those articles which, though dependent on the first four rules, do not necessarily make a fundamental part of arithmetic.

Ans. 3833

As it is of great consequence in business to perform addition readily and exactly, the learner ought to practise it till it become

It is

quite familiar. If the learner can readily add any two digits he will soon add a digit to a higher number with equal ease. only to add the unit place of that number to the digit, and if it exceed ten, it raises the amount accordingly. Thus, because 8 and 6 are 14, 48 and 6 are 54. It will be proper to mark down under the sums of each column, in a small hand, the figure that is carried to the next column. This prevents the trouble of going over the whole operation again, in case of interruption or mistake. If you want to keep the account clean, mark down the sum and figure you carry on a separate paper, and after revising them, transcribe the sum only. After some practice we ought to acquire the habit of adding two or more figures at one glance. This is particularly useful when two figures which amount to 10, as 6 and 4, or 7 and 3, stand together in the column. Every operation in arithmetic ought to be revised, to prevent mistakes; and as one is apt to fall into the same mistake if he revise it in the same manner he performed it, it is proper either to alter the order, or else to trace back the steps by which the operation advanced, which will lead us at last to the number we began with. When the given number consists of articles of different value, as pounds, shillings, and pence, or the like, which are called different denominations, the operations in arithmetic must be regu lated by the value of the articles. We shall give here a few of the most useful tables for the learner's information, referring for other information to the articles, MEASURES, WEIGHTS, &c.

VII. CLOTH MEASURE.
2 Inches 1 nail.
4 Nails 1 quarter.
4 Quarters = 1 yard,

5 Quarters 1 English ell.

quantities under like, and carry according Rule for Compound Addition. Arrange like

to the value of the higher place. When you add a denomination which contains more columns than one, and from which you carry to the higher by 20, 30, or any even number of tens, first add the units of that column and mark down their sum, caradd the tens and carry to the higher denorying the tens to the next column; then mination, by the number of tens that it contains of the lower. For example, in adding shillings carry by 10 from the units to the tens, and by 2 from the tens to the pounds. If you do not carry by an even number of tens, first find the complete sum of the of the higher that sum contains, and carry lower denomination, then inquire how many accordingly, and mark the remainder, if any, under the column. For example, if the sum of column of pence be 43, which is three shillings and seven-pence, mark 7 under the pence column, and carry 3 to that of the shillings.