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325. Arius acknowledged Christ to be about the sun, at the same time that it reGod, in a subordinate sense, and considered volved about its own axis. He determined his death to be a propitiation for sin. The that the annual orbit of the earth, compared Arians acknowledge, that the Son was the with the distance of the fixed stars, is but word, though they deny its being eternal, as a point. For these his opinions, which contending only that it had been created time has proved to be undeniably true, he prior to all other beings. They maintain was censured by his contemporaries, some that Christ is not the eternal God; but, in of whom went about to prove that Greece opposition to the Unitarians, they contend ought to have punished Aristarchus for his for his pre-existence, a doctrine which they heresy. This philosopher invented a pecufound on various passages of scripture, par. liar kind of sun-dial, mentioned by Vitryticularly these two, “before Abraham was, vius. There is now extant only a treatise I am;” and “glorify me with the glory upon the magnitude and distance of the sun which I had with thee before the world and moon, which was translated into Latin, was.” Arians differ among themselves as and commented upon by Commandine, who to the extent of the doctrine. Some of published it with Pappus's explanations in them believe Christ to have been the Crea. 1572. tor of the world, and on that account has a ARISTEA, in botany, a genus of plants claim to religious worship; others admit of of the Triandria Monogynia class and order. his pre-existence simply. Hence the ap- Petals six ; style declined; stigma funnelpellations, high and low Arians. Dr. form, gaping; capsule inferior, many-seeded. Clarke, Rector of St. James, in his “ Scrip. There is but one species : a Cape plant, ture Doctrine of the Trinity;" Mr. Henry low ; leaves veined and narrow ; flowers in Taylor, Vicar of Portsmouth, in a work downy heads. entitled, “Ben Mordicai's Apology;" Mr. ARISTIDA, in botany, a genus of the Tomkins, in his “Mediator;" and Mr. Triandria Digynia class of plants, the calyx Hopkins in his “ Appeal to the Common of which is a bivalve subulated glume, of Sense of all Christian People,” have been the length of the corolla ; the corolla is a deemed among the most able advocates of glume of one valve, opening longitudinally, Arianism. Dr. Price has been one of the hairy at the base, and terminated by three last writers in behalf of this doctrine : in his sub-equal patulous aristæ ; the fruit is a

On the Christian Doctrine,” will connivent glume, containing a naked filibe found an able defence of low Arianism. form single seed, of the length of the coSee also a tract published in 1805, by Ba- rolla. There are ten species. sanistes.

ARISTOCRACY, a form of government ARIES, in astronomy, a constellation of where the supreme power is vested in the fixed stars, drawn on the globe in the figure principal persons of the state, either on acof a ram.

It is the first of the twelve signs count of their pobility, or their capacity of the zodiac, from which a twelfth part of and probity. the ecliptic takes its denomination. It is

Aristocracies, says Archdeacon Paley, marked thus p, and consists of sixty-six are of two kinds ; first, where the power of stars.

the nobility belongs to them in their collecARISH, a long measure used in Persia, tive capacity alone; that is, where, although containing 3197 English feet.

the government reside in an assembly of ARISTA, among botanists, a long needle the order, yet the members of the assemlike beard, which stands out from the husk bly, separately and individually, possess no of a grain of corn, grass, &c.

authority or privilege beyond the rest of the ARISTARCHUS, in biography, a cele- community : such is the case in the constibrated Greek philosopher and astronomer, tution of Venice. Secondly, where the noand a native of the city of Samos; but at bles are severally invested with great persowhat period he flourished is not certain. It nal power and immunities, and where the must have been before the time of Archi- power of the senate is little more than the medes, as some parts of his writings and aggregate power of the individuals who opinions are cited by that author. He held compose it: such was the case in the conthe doctrine of Pythagoras as to the system stitution of Poland. Of these two forms of the world, but whether he lived before of government, the first is more tolerable or after him is not known. He maintained than the last; for although many, or even that the sun and stars were fixed in the hea- all the members of a senate, should be so vens, and that the earth moved in a circle profligate as to abuse the authority of their


stations in the prosecution of private de ARISTOTELIAN, something relating signs, yet, whilst all were not under a to Aristotle : thus we read of the Aristote. temptation to the same injustice, and hav- lian philosophy, school, &c. See PERIPAing the same end to gain, it would still be TETICS. difficult to obtain the consent of a majority ARITHMETIC, the art of numbering; to any specific act of oppression, which the or, that part of mathematics, which consiiniquity of an individual might prompt bim ders the powers and properties of numto propose: or, if the will were the same, bers, and teaches how to compute or calcithe power is more contined ; one tyrant, late truly, and with expedition and ease. By whether the tyranny reside in a single per

some authors it is also defined the science son, or a senate, cannot exereise oppression of discrete quantity. It consists chiefly in in so many places at the same time, as may

the four great rules or operations of Addibe carried on by the dominion of a nume

tion, Subtraction, Multiplication, and Divirous nobility over their respective vassals sion. Concerning the origin and invention and dependents. Of all species of domina- of arithmetic we have very little information, this is the most odious ; the freedom tion ; history fixes neither the author nor and satisfaction of private life are more re the time. Some knowledge, however, of strained and harassed by it, than by the numbers must have existed in the earliest most vexatious laws, or even by the lawless ages of mankind. This knowledge would will of an arbitrary monarch, from whose be suggested to them, whenever they knowledge, and from whose injustice, the opened their eyes, by their own fingers, and greatest part of his subjects are removed by by their flocks and herds, and by the vatheir distance, or concealed by their obscu- riety of objeets that surrounded them. At rity. An aristocracy of this kind has been first, indeed, their powers of numeration productive, in several instances, of disas. would be of very limited extent ; and be trous revolutions, and the people have con- fore the art of writing was invented, it must curred with the reigning prince, in ex- have depended on memory, or on such artichanging their condition for the miseries ficial helps, as might most easily be obtainof despotism. This was the case in Den- ed. To their ten fingers they would, withmark about the middle of the seventeenthout doubt, have reconrse in the first incentury, and more lately in Sweden. In stance ; and hence they would be naturally England, also, the people beheld the de- led to distribute numbers into periods, each pression of the barons, under the house of of which consisted of ten units. This prace Tudor, with satisfaction, although they saw

tice was common among all nations, the anthe crown acquiring thereby a power which cient Chinese, and an obscure people men. no limitations, provided at that time by the

tioned by Aristotle, excepted. But though constitution, were likely to confine.

some kind of computation must have comFrom such events this lesson may be menced at a very early period, the introducdrawn : « That a mixed government, which tion of arithmetic as a science, and the imadmits a patrician order into the constitu- provements it underwent, must, in a great tion, ought to circumscribe the personal degree, depend upon the introduction and privileges of the nobility, especially claims establishment of commerce: and as comof hereditary jurisdiction and local autho

merce was gradually extended and improve rity, with a jealousy equal to the solicitude ed, and other sciences were discovered and with which it provides for its own preserva- cultivated, arithmetic would be improved tion.” Paley's Princ. of Philos.

likewise. It is therefore probable, that if it ARISTOLOCHIA, in botany, birth. was not of Tyrian invention, it must have wort, a genus of plants of the Gynandria been much indebted to the Phænicians or Hexandria class and order. Stigmata six ; Tyrians. Proclus, indeed, in his commenno calyx; corolone-petalled, tubular, tongue. tary on the first book of Euclid, says, that shaped; capsule inferior, six-celled. There the Phænicians, by reason of their traffic are 27 species, most foreign.

and commerce, were the first inventors of ARISTOTELIA, a genus of the Dode. arithmetic ; and Strabo also informs us, candria Monogynia class and order : calyx that in his time it was attributed to the five-leaved; petals five ; style three-cleft; Phænicians. Others have traced the ori. berry-three-celled, with two seeds in each. gin of this art to Egypt; and it has been a One species, found in Chili, a shrub, leaves general opinion, sanctioned by the authoriever-green; flowers wbite in axillary ra- ties of Socrates and Plato, that Theut or cemes,

Thot was the inventor of numbers; that

from hence the Greeks adopted the idea of of progression used by the Arabians, wiio ascribing to their Mercury, corresponding acknowledge, as some have said, that they to the Egyptian Theut or Hermes, the su- received it from the Indians. Archimedes perintendance of commerce and arithmetic. also in his “Arenarius,” used a particular With the Egyptians we ought also to asso scale and notation of his own. In the seciate the Chaldeans, whose astronomical cond century of the christian era, Ptolemy disquisitions and discoveries, in which they is supposed to have invented the sexagesitook the lead, required a considerable ac mal numeration and notation, and this mequaintance with arithmetic. From Asia it thod is still used by astronomers and others, passed into Egypt, as Josephus says, by for the subdivision of the degrees of circles. means of Abraham. Here it was greatly These several modes of notation above recultivated and improved ; insomuch that a cited, were so operose and inconvenient, large part of the Egyptian philosophy and that they limited the extent, and restrained theology seems to have turned altogether the progress of arithmetic, so that it was apupon numbers. Kircher shews, that the plicable with great difficulty and embarrassEgyptians explained every thing by num ment to the other sciences, which required bers ; Pythagoras himself affirming, that the its assistance. The Greeks, if we except nature of numbers pervades the whole uni- Euclid, who in his elements furnished many verse, and that the knowledge of numbers is plain and useful properties of numbers, the knowledge of the deity. From Egypt, and Archimedes in his Arenarius, contriarithmetic was transmitted to the Greeks buted little to the advancement of this sciby Pythagoras and his followers; and among ence towards perfection. From Boethius them it was the subject of particular atten we learn, that some Pythagoreans had intion, as we perceive in the writings of Eu- vented and employed, in their calculations, clid, Archimedes, and others; with the im. nine particular chiaracters, whilst others provements derived from them, it passed to used the ordinary signs, namely, the letters the Romans, and from them it came to us. of the alphabet. These characters le calis The ancient arithmetic was very different apices; and they are said greatly to resemfrom that of the moderns in various respects, ble the ancient Arabic characters, which and particularly in the method of notation. circumstance suggests a suspicion of their The Indians are at this time very expert in authenticity. Indeed, the MSS. of Boethius, computing, by means of their fingers, with in which these characters, resembling those out the use of pen and ink ; and the of the Arabian arithmetic, are found, not natives of Peru, by the different arrange, being more ancient than three or four cenments of their grains of maize, surpass the turies, confirm the opinion that they are the European, aided by all his roles, with re works of a copyist. Upon the whole, this gard both to accuracy and dispatch. The treatise of Boethius does not warrant our reHebrews and Greeks, however, at a very jecting the commonly received system with early period, and after them also the Ro. regard to the origin of our arithmetic ; but mans, had recourse to the letters of their al- if we suppose that the Arabians derived phabet for the representation of numbers, their knowledge of it from the Indians, it is The Greeks, in particular, had two different

more probable that it was one of the inven. methods : the first resembled that of the tions which Pythagoras spread among the Romans, which is sufficiently known, as it is Indians, than that those persons should have still used for distinguishing the chapters obtained it from the Greeks. and sections of books, dates, &c. They af The introduction of the Arabian or Interwards had a better method, in which the dian notation into Europe, about the tenth first nine letters of the alphabet represented century, made a material alteration in the the first numbers from 1 to 9, and the state of arithmetic; and this, indeed, was next nine letters represented any number one of the greatest improvements which of tens, from 1 to 9, that is, 10, 20, &c. this science had received since the first disto 90. Any number of hundreds they ex covery of it. This method of notation, now pressed by other letters, supplying wliat they universally used, was probably derived oriwanted by some other marks or characters: ginally from the Indians by the Arabians, and in this order they proceeded, using the and not, as some have supposed, from the same letters again, with different marks to Greeks; and it was brought from the Ara. express thousands, tens of thousands, hun- bians into Spain by the Moors or Saracens, dreds of thonsands, &c. ; thus approaching in the tenth century. Gerbert, who was very near to the more perfect decuple scale afterwards Pope, under the name of Silves.

ter II. and who died in the year 1,003,

ADDITION, bronght this notation from the Moors of

Addition is that operation by which we Spain into France, long before the time of find the amount of two or more numbers. his death, or, as some think, about the year

The method of doing this in simple cases is 960 ; and it was known among us in Bri- obvious, as soon as the meaning of number tain, as Dr. Wallis lias shewn, in the begin. is known, and admits of no illustration. A ning of the eleventh century, if not some

young learner will begin at one of the numwhat sooner. As literature and science advanced in Europe, the knowledge of bers, and reckon up as many units separately

as there are in the other, and practice will numbers was also extended, and the writers

enable him to do it at once. It is impossiin this art were very much multiplied. The ble, strictly speaking, to add more than next considerable improvement in this

two numbers at a time. We must first find branch of science, after the introduction

the sum of the first and second, then we of the numeral figures of the Arabians or

add the third to that number, and so on. Indians, was that of decimal parts, for

However, as the several sums obtained are which we are indebted to Regiomontanus ; who about the year 1464, in his book of easily retained in the memory, it is neither “ Triangular Canons," set aside the sexage

necessary nor usual to mark them down.

When the numbers consist of more figures simal subdivisions, and divided the radius into

than one, we add the units together, the 60,000,000 parts ; but afterwards he alto

tens together, and so on. But if the sum of gether waved the ancient division into 60,

the units exceed ten, or contain ten several and divided the radius into 10,000,000 parts ; times, we add the number of tens it contains so that if the radius be denoted by 1, the sines will be expressed by so many places number of units that are over. In like

to the next column, and only set down the of decimal fractions as the cyphers follow

manner we carry the tens of every column ing 1. This seems to have been the first

to the next higher. And the reason of this introduction of decimal parts. To Dr.

is obvious from the value of the places; Wallis we are principally indebted for our

since an unit in any higher places signifies knowledge of circulating decimals, and also

the same thing as ten in the place immedifor the arithmetic of infinites. The last, ately lower. and perhaps, with regard to its extensive ap

Rule. Write the numbers distinctly, units plication and use, the greatest improvement under units, tens under tens, and so on. which the art of computation ever received, Then reckon the amount of the right-hand was that of logarithms, which we owe to Baron Neper or Napier, and Mr. Henry if it exceed ten mark the units only, and

column ; if it be under ten mark it down; Briggs. See LOGARITHMS.

carry the tens to the next place. In like ARITHMETIC, theoretical, is the science

manner carry the tens of each column to the of the properties, relations, &c. of numbers, next, and mark down the full sum of the considered abstractedly, with the reasons left-hand column. and demonstrations of the several rules. Euclid furnishes a theoretical arithmetic, in

Ex. 1. Ex 2.

Ex, 3. the seventh, eighth, and ninth books of his

432 10467530 457974683217 elements.

37604 2919792935 ARITHMETIC, practical, is the art of num

394 63254942 47374859621 bering or computing ; that is, from certain


24354642 numbers given, of finding certain others,

109 856757 925572199991 whose relation to the former is known. As,

245 2941275

473214 if two numbers, 10 and 5, are given, and


459 499299447325 we are to find their sum, which is 15, their

694 41210864

10049431 difference 5, their product 50, their quo 317 52321975

41 tient 2.


4686 5498936009 The method of performing these opera

243 43264353 943948999274 tions generally we shall now proceed to

Ans. 3833 shew, reserving for the alphabetical arrangement those articles which, though dependent on the first four rules, do not ne As it is of great consequence in business to cessarily make a fundamental part of arith. perform addition readily and exactly, the metic.

learner ought to practise it till it become





quite familiar. If the learner can readily

V. LONG MEASURE, add any two digits he will soon add a digit

12 Inches = 1 foot. to a higher number with equal ease. It is

3 Feet = 1 yard. only to add the unit place of that number to the digit, and if it exceed ten, it raises

5} Yards = 1 pole.

40 Poles 1 furlong. the amount accordingly. Thus, because 8

8 Furlongs = 1 mile. and 6 are 14, 48 and 6 are 54. It will be pro

S Miles = 1 league. per 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 opera

301 Square yards = 1 pole or perch.

40 Poles = 1 rood. tion again, in case of interruption or mis

4 Roods = 1 acre. take. 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

21 Inches = 1 nail.

4 Nails = 1 quarter. practice we ought to acquire the habit of

4 Quarters = 1 yard, adding two or more figures at one glance. This is particularly useful when two tigures

5 Quarters = 1 English ell. which amount to 10, as 6 and 4, or 7 and 3, stand together in the column. Every opera

Rule for Compound Addition. Arrange like tion in arithmetic ought to be revised, to

quantities under like, and carry according

to the value of the higher place. When prevent mistakes; and as one is apt to fall into the same mistake if he revise it in the

you add a denomination which contains same manner he performed it, it is proper

more columns than one, and from which either to alter the order, or else to trace you carry to the higher by 20, 30, or any back the steps by which the operation

even number of tens, first add the units of

that column and mark down their sum, car. advanced, which will lead us at last to the number we began with. When the given rying the tens to the next colunin; then number consists of articles of different value,

add the tens and carry to the higher deno. as pounds, shillings, and pence, or the like, tains of the lower. For example, in adding

mination, by the number of tens that it conwhich are called different denominations, the operations in arithmetic must be regu

shillings carry by 10 from the units to the lated by the value of the articles. We shall

tens, and by 2 from the tens to the pounds. give here a few of the most useful tables

If you do not carry by an even number of for the learner's information, referring for tens, first find the complete sum of the other information to the articles, MEASURES,

Tower denomination, then inquire how many WEIGHTS, &c.

of the higher that sum contains, and carry

accordingly, and mark the remainder, if any, I, STERLING MONEY.

under the column. For example, if the sum 4 Farthings = 1 penny, marked d.

of column of pence be 43, which is three 12 Pence = 1 shilling, s.

shillings and seven-pence, mark 7 under the 20 Shillings = 1 pound, £.

pence column, and carry 3 to that of the

shillings. 94 Grains = 1 pennyweight, dut. 20 Pennyweights = 1 ounce, oz.

Exumples in sterling Money. 12 Ounces = 1 pound, lb.

£. d. £. d. 111, AVOIRDUPOIS WEIGHT.

215.. 3..9 169 16 .. 10 16 Drams = 1 ounce, oz.


36 .. 12 .. 16 Ounces = 1 pound, lb.

645 7..7

54.. 7.. 6 18 Pounds = 1 quarter, qr.


30 .. 0 .. 11 4 Quarters = 1 hundred weight, C.

35.. 3..9

6 20 Hundred weight = 1 ton, T.

9.. 0..7 707 .. 19.. 11

1814.. 16 .. 3 1006., 16., 8
2 Pints = 1 quart.
4 Quarts = 1 gallon.
2 Gallons = 1 peck,
4 Pecks = 1 bushel,
8 Bushels = 1 quarter.


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