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just notions concerning the inferior orders of society. And I am the more emboldened to expect the public approbation on this occafion, from the confideration, that in my endeavours to promote those prime' views, no new burthen has been imposed, or any very considerable encroachment made on the time of the pupil, the information in question being incorporated with a branch of education in which ALL must be conversant.

The title announces this small treatise to be designed for the use of YOUNG LADIES, because the author's department of teaching is solely confined to them. Perhaps, however, it may be thought equally adapted to the other sex, when it is considered that'a youth, capable of working through the whole book, and of delivering a satisfactory account of each operation, would be qualified for almost any of the common concerns of business. Vulgar and decimal fractions, and the extraction of roots are of little utility, except in a few particular employments; and as to interest, profit and loss, barter, fellowship, exchange, and fome other rules which have distinct heads in the ordinary treatises of arithmetic, they all belong to the rule of three, and the questions in each may be worked with the greatest facility, by any one well versed in that and practice.

The generality of the questions being too long for the learner's transcription, they have all been numbered. Accordingly, the number, with a word or two of the sum (for instance, No. 1, Chronology, No. 2, Solar Systern) will be a suficient reference to the operation at large, at any future period. The pupil, however, if sufficiently qualified in writing, should by no means omit copying the whole process of each sum in a common fumbook. To prevent the possibility of plagiarism, and to perfect the students completely in this important branch of education, they should, on presenting a sum, be constantly made to aflign a reason for every part of the operation, and, moreover, occafionally be exercised with a variety of manuscript fums in each rule.

WILLIAM BUTLER.

Oxford-Court, Cannon-Street,

August 3, 1795.

ADVER

ADVERTISEMENT.

Published by the same Author, for the Use of Young Ladies. A

N engraved INTRODUCTION to ARITHMETIC, consisting

of examples in the four principal rules, and a collection of tables : defigned to facilitate the progress of young beginners, and to diminish the labour of the tutor.

Ready for the Press, and speedily to be Published. An Easy INTRODUCTION to the Use of the GLOBEs, in which will be incorporated some Miscellaneous Matter which the Author has found to be entertaining and useful to his own pupils.

The above little manual will be immediately succeeded by a small tract of Scripture Geography, with maps: to which will be annexed, a brief sketch of the different principles maintained by the chief Christian fects, and other introductory information.

On the completion of this laft-mentioned work, which is already nearly prepared for the press, the Author means to resume the printing of his larger geographical and biographical performance (advertised in his Introduction to Arithmetic) which will be accompanied with a general ATLAS.

ADDRESS TO THE PUBLIC.

M

R. BUTLER, Teacher of WRITING, ACCOUNTS, and GEOGRAPHY,

respectfully informs his friends and the public, that, having frequently found himself prevented, by prior engagements, from attending LADIES Schools and priVATE FAMILIES, which had honoured him with applications for that purpose, he has engaged as partner, Mr. THOMAS Bourn, Jun. of Mare-Street, HACKNEY. This connection will not only better enable Mr. B. to avail himself of the kind partiality of his friends, but, by introducing to their acquaintance, will recommend to their protection, a much-esteemed pupil of exemplary moral conduct, and great professional ability, with the happy talent of communicating instruction, united to indefatigable affiduity and zeal in the discharge of his engage

ments.

ARITHMETICAL QUESTIONS.

A A RITHMETIC

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a science, which explains the properties of numbers, and shows rules, namely, NUMERATION, Addition, SUBTRACTION, MulTIPLICATION, and Division; and these are the foundation of all arithmetical operations.

We have very little information respecting the origin and invention of arithmetic; hiftory neither fixes the author of it, nor the time of its discovery. Some imagine, that it must have taken its rise from the introduction of commerce, and ascribe its invention to the Tyrians. That, however, it had a much earlier introduction into the world, even before the deluge, we may gather from the following expression in the prophecy of Enoch, as mentioned by Jude : “ Behold the Lord cometh with ten thousand of his saints." This shows that, even at that time, men had ideas of very high numbers, and computed them also in the same manner that we do, namely, by tens. "The directions also given to Noah, concerning the dimensions of the ark, leave us no room to doubt that he had a knowledge of numbers, and likewise of measures. · When Rebecca was sent away to Isaac, Abraham's son, her relations wished that she might be the mother of thousands of millions; and if they had been totally unacquainted with the rule of multiplication, it is impossible to conceive that they could have formed such a wish. It appears, therefore, certain, that the four fundamental rules of arithmetic were known, in some nations, in very early ages of the world; though at what time they were discovered or invented cannot now be exactly ascertained.

The Greeks were the first European nation among whom arithmetic arrived at any great degree of perfection, and they made ufe of the letters of the alphabet to represent their numbers.' The Romans followed a like method, and, besides characters for each rank of classes, they introduced others for five, fifty, and five hundred. Their method is still used for distinguishing the chapters of books and some other purposes. From the Romans arithmetic came to us; but the

B

common

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common arithmetic among us, which makes use of the ten Arabic figures 1, 2, 3, 4, 5, 6, 7, 8, 9, o, was utterly unknown to the Greeks and Romans, and came into Europe from the Arabians by way of Spain. The Arabians are said to have received them from the Indians. This most perfect method of supputation is supposed to have taken its origin from the ten fingers of the hand, which were made use of in computations before arithmetic was brought into an art. The Eastern missionaries assure us, that to this day the Indians are very expert at computing on their fingers without any use of pen or ink. And the natives of Peru in South America, who do all by the different arrangement of grains of maise, are said to excel any

European both for certainty and dispatch with all his rules.

Ν Ο Μ Ε R Α Τ Ι Ο Ν

"EACHES to read or write any proposed sum, and to find the

figures.

E X A M P L E S. No. 1. CHRONOLOGY. Chronology is the art of measuring and diftinguishing time past, and referring each event to the proper year. Its use is very great, being called one of the eyes of history. Epocha, in chronology, is a term or fixed point of time, whence fucceeding years are numbered or computed. That principally, regarded among Christians is the epocha of the nativity of our Saviour; that of the Mahometans the hegira; that of the Jews the creation of the world ; that of the ancient Greeks the Olympiads; that of the Romans the building of their city, and that of the ancient Persians and Assyrians, the epocha of Nabonaffar king of Babylon, its institutor, 746 years B. c. The building of Rome took place 753 years B. C. The Olympics or Olympic games, fo famous among the Greeks, were inftituted in honour of Jupiter. They were holden at the beginning of

year, on the banks of the Alpheus, near Olympia, to exercise their youth in five kinds of combats. Those who were conquerors in these games were highly honoured by their countrymen. The prize contended for was a crown made of a peculiar kind of wild olive, appropriated to this use. The Olympiads ended with the year of Christ 440, making in all 364. The hegira, or flight of the impoítor Mahomet, the founder of the Mahometan religion, from Mecca to Medina, happened A. D. 622. The computation of years from the birth of Christ did not begin to be used in history till the year 748. The current year of the Christian æra is 1795.

N.B. A. M. denote Anno Mundi, the year of the world; U. C. Urbe conditâ (ab, from, being understood) the building of the city, i. e. of Rome; B. C. Before Chrift; A. C. Ante Chriftum, before Chrift; A. D. Anno Domini, in the year of our Lord.

every fifth

No. 2.

SOLAR SYSTEM. By the solar system is meant the order and disposition of the several heavenly bodies, which revolve round the Sun, as the centre of their motion, and receive from it their light and heat. These celestial spheres consist of planets and comets. Under the denomination of planets are comprised Mercury, Venus, the Earth, Mars, Jupiter, Saturn, and the Georgium Sidus.

Mercury is said to be about 37,000,000 of miles from the fun; Venus 68,000,000; the Earth 95,000,000 ; Mars 145,000,000 ; Jupiter 495,000,000 ; Saturn 908,000,000 ; and the Georgium Sidus about 1,800,000,000 of miles diftant from the sun.

The hourly motion of Mercury in its orbit is about 109,000 miles ; Venus 80,000; the Earth 68,000; Mars 55,000; Jupiter 29,000; Saturn 22,000. Saturn is supposed to be more than go times as big as the globe which we inhabit. According to the fame calculation, Jupiter is above 200 times larger than the earth.

It has been remarked, that the planets, and all the innumerable hoft of heavenly bodies, perform their courses and revolutions with so much certainty and exactness, as never once to fail; but, for almost 6000 years, come constantly about to the same period, without the difference of the hundredth part of a minute. It is also observed by Mr. Hervey, that “ it may

seem unaccount. able, to an unlearned reader, that aftronomers should speak fuch amazing things, and speak them with such an air of assurance, concerning the distances and magnitudes, the motions and relations of the heavenly bodies. I would defire, continues the same ingenious writer, such a person to consider the case of ECLIPSES, and with what exactness they are calculated. They are not only foretold, but the very inftant of their beginning is determined. The precise time of their continuance is assigned ; alligned almost to the nicety of a moment, and what is still more surprising, for the space of hundreds or thousands of years to come. As this

is a matter of fact absolutely indisputable, it is also a very obvious yet solid demonstration, that the principles of science, on which those calculations proceed, are not merely conjecture, or precarious supposition, but have a real, a certain foundation in the nature and constitution of things.”

US.

No. 3. Comets. Comets are defined to be folid compact bodies, like other planets, and regulated by the same laws of gravity. They move about the fun in very eccentric orbits, and are of a much greater density than our earth; for some of them are heated, in every period, to such a degree as would vitrify or dissipate any substance known to

Comets are always attended with long transparent trains, or tails, issuing from that side of them which is turned away from the sun : that which appeared in 1680 drew after it a tail of fire that was computed to be 80,000,000 of miles in length. There are supposed to be 450 comets belonging to the solar fyltem; but the periods of three of them only are known with any certainty. These return at intervals of 75, 129, and 575 years. Dr. Halley, at first, supposed the comets of 1532 and 1661, to be one and the fame; and though he afterwards seemed to retract this opinion, it hias been generally adopted

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