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a train of ideas, the archetypes of which are not the objects of sense, and are, therefore, of difficult recollection, to another train which we cannot miss to recollect, because the archetypes are not only objects of sense, but objects of sight, with which archetypes we are perfectly familiar; or which may be placed actually before our eyes. Suppose then Simonides were to commit to memory a discourse, consisting of speculations concerning government, finances, naval affairs, or wisdom, none of the archetypes of which could be made objects of sense, at least, at the time of delivery; and, to assist his recollection, he were to connect the series of ideas, in that discourse, with a series of objects, which he could either place in sight, or with which he was so familiar, that he could not fail to recollect them; he would proceed in the following manner. He would take a house, for instance, either the one in which he might deliver the discourse, or another; with every part of which he was perfectly acquainted. He would begin at some fixed point of that house, suppose the right side of the door, and he would proceed round it, in a circular line, till he arrived at the point from which he set out. He would divide the circumference of the house into as many parts as there were different topics, or paragraphs, in the discourse. He would distinguish each paragraph by some symbol of the subject it contained; that on government, by the symbol of a crown, or a sceptre; that ou finances, by the symbol of some current coin; that on naval affairs, by the figure of a ship; that on wisdom, by the figure of the goddess who presided over it. He would either actually transfer, or suppose transferred, these symbols to the different compartments of the house, and then all he had to do, in order to recollect the subject of any paragraph, was, either to cast his eye on the symbol during delivery, or to remember upon what division the symbol was placed. The memory, by this contrivance, easily recalled the discourse. The orator either saw, or could not fail to remember the compartments, because he was perfectly familiar with them. Neither could he forget the symbols of each paragraph, because they were no more than hieroglyphical paintings of the sense.

9. In the place of a house, we may assume, according to Quinctilian, a public building, the walls of a city, a well

known road, or a picture, to divisions of which we may refer our symbols. Metrodorus assumed the circle of the zodiac, which he divided into 360 compartments, equal to the number of degrees of which it consists, making a compartment of each degree.

10. Some people carried this art so far as to comprehend the words of a discourse, by constructing symbols for each of them, and referring, in like manner, these symbols to compartments. This seems to have constituted nearly what we call short-hand writing, except that our shorthand writers oblige themselves to commit to memory the meaning of their symbols, and pretend not to refer these to any more familiar objects. Quinctilian accordingly observes, that this pretended improvement terminated in confusion, and embarrassed, much more than it assisted, recollection. However much, therefore, he might prize the scheme of Simonides, he rejected this supplement as nugatory, or detrimental.

11. This system of Mnemonics was a favourite pursuit with the Greeks; and was cultivated with success by the Romans, among whom Crassus, Julius Cæsar, and Seneca, are said to have particularly excelled in this art. Such were the origin and principles of the celebrated topical memory of the ancients: from which source are derived all the various modern systems of local and symbolical memory, that have been promulgated, from the thirteenth to the eighteenth century.

12. The system of M. Feinaigle is founded upon these principles, and is applied by him to facilitate the acquisition of chronology, history, geography, languages, systematic tables, poetry and prose, arithmetic, and algebra. Other lecturers have appeared, in different parts of the kingdom, and much curiosity has been excited on this subject. The power of association, (the principal key-stone in the mnemonic arch) may be easily tried by making use of a succession of rooms, staircases, closets, and other remarkable divisions of a house, with which the person is familiar; If he applies any word or idea to the several parts of the

* In allusion to the different divisions of a house, &c. we still call the parts of a discourse, places or topics, and say in the first place, the second place, &c. &c.

house, in successive order, it will be almost impossible, in recalling the same order in the parts of the house, not to associate the idea or word, which had been previously annexed to each part. The succession of the kings of England may be learned, in a short time, by annexing the name of each succeeding monarch, to the successive room, closet, or part of the house; beginning either at the top or bottom. A single room, divided into many imaginary compartiments-a succession of streets--or any other permanent and familiar set of objects is equally applicable to this purpose.

Select Books on Mnemonics.

Locke on the Human Understanding, 2 vols. 8vo. or the abridgmert, 1 vol. 12mo. Watts on the Mind, 12mo. Grey's Memoria Technica, 12mo. The New Art of Memory founded upon the principles taught by M. Feinaigle (second edition), 12mo. Stewart on the Mind, svo.; to all which books this chapter is indebted. Gurney's System of Short Hand, 12mo.

CHAP. IV. -MATHEMATICS.

1. MATHEMATICS denotes that science which teaches or contemplates whatever is capable of being numbered or measured, and, accordingly, includes arithmetic and geometry. Without a knowledge of mathematics, architecture and the principles of optics and perspective can never be understood. All our reasonings on the magnitudes, motions, and distances of the heavenly bodies, and of our own globe; in other words, our knowledge of geography and astronomy are founded on this interesting science. The same may be said of pneumatics, hydrostatics, and music.

Mathematics are commonly divided into pure and speculative, which consider quantity abstractedly; and mixed, which treat of magnitude, as subsisting in material bodies.

2. The mathematics (observes Dr. Barrow) effectually exercise, not vainly delude, nor vexatiously torment, studious minds with obscure subtilties; but plainly demonstrate every thing within their reach, draw certain conclusions, instruct by profitable rules, and unfold pleasant questions. These disciplines likewise enure, and corroborate the mind to a constant diligence in study; they wholly deliver us

from a credulous simplicity, most strongly fortify us against the vanity of scepticism, effectually restrain us from a rash presumption, most easily incline us to a due assent, perfectly subject us to the government of right reason. While the mind is abstracted and elevated from sensible matter, it distinctly views pure forms, conceives the beauty of ideas, and investigates the harmony of proportions. The manners themselves are sensibly corrected and improved, the affections composed and rectified, the fancy calmed and settled, and the understanding raised and excited to more divine contemplations.

SECT. I.-ARITHMETIC.

Arithmetic teaches the method of computing numbers, and explains their nature and peculiarities. The four first fundamental principles, viz. addition, subtraction, multiplication, and division have always, in a certain degree, been practised by different nations.

1. Numbers, as a science, must, in a great measure, have depended on the advancement of commerce, because arithmetical calculations becoming, then, more necessary would receive a greater degree of attention. Thus arithmetic is, with great probability, supposed to have been of Tyrian or Phoenician invention. From Asia it is said to have passed into Egypt. From Egypt, arithmetic was transmitted to the Greeks; thence, with its improvements, it proceeded to the Romans, and from the Romans it has been dispersed over the modern nations of the world. The symbols or characters of numbers, and the scale of numerical calculations have been considerably diversified in different ages. The Hebrews and Greeks, and after them the Romans, had recourse to the letters of their alphabet for the representation of numbers. The Mexicans adopted circles for cyphers, and the ancient Peruvians coloured knotted cords, called quipos. The Indians are, at this time, very expert in computing by means of their fingers; and the modern natives of Peru are said by the different arrangements of their grains of maize, to surpass Europeans, aided by all their rules.

2. The Arabian or Indian notation, which is now universally practised, was originally derived from the Indians,

and was, in the tenth century, brought by the Moors or Saracens from Arabia into Spain. Its improvements principally consist in its brevity and precision; instead of employing twenty-four characters, only nine digits and a cypher are wanted. The symbols also are more simple, more appropriate, and determined; and therefore the powers of them are less liable to inaccuracy or confusion. With the symbols too, the scale of numerical calculations has been varied. The first improvement was the introduction of reckoning by tens, which, no doubt, took its rise from the obvious mode of counting by the fingers, as that was customary in the primary calculation of every nation except the Chinese.

3. The Greeks had two methods of marking the advance of numbers; one on the plan which was afterwards adopted by the Romans, and which is still used to distinguish the chapters and sections of books; and in the other, the first nine letters of the alphabet represented the first numbers from 1 to 9, the next nine so many tens, from 10 to 90. The number of hundreds were expressed by other letters, supplying what was wanting either by other marks or characters, or by repeating the letters with different signs in order to describe thousands, tens of thousands, &c.

4. About the year of Christ 200, a new kind of arithmetic, called sexagesimal, was invented by Ptolemy. Every unit was supposed to be divided into 60 parts, and each of these into 60 others, &c. Thus from 1 to 59 were marked in the common way: then 60 was called a sexagesima, or first sexagesimal integer, and had one single dash overit, as I'; 60 times 60 was called 'sexagesima secunda,' and marked I", &c. These methods of calculation are continued by astrologers in the subdivisions of the degrees of circles. The decuple, or Arabian scale, substitutes decimul instead of sexagesimal progression, and by this single process removes the difficulties and embarrassments of the preceding modes. Thus the signs of numbers, from 1 to છે, are considered as simple characters, denoting the simple numbers subjoined to the character; the cypher, 0, by filling the blanks, denotes the want of a number, or unit, in that place; and the addition of the columns in a ten-fold ratio, always expressing ten times

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