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BIOGRAPHY. —No. IV. JAMES FERGUSON.
ONE of the most extraordinary instances of self-culture presented to us in the annals of biography, is that of James Ferguson, who was born in the year 1710, a few miles from the village of Keith, in Banffshire, Scotland. It was the practice of his father, who was merely a day labourer, to teach his children to read and write, as they successively reached what he considered to be the proper age. But while he was instructing one of his elder children, James was secretly occupied in listening to what was going on ; and it was his practice, as soon as he was left alone, to get the book and master the lesson that had thus been given. As he felt ashamed to let his father know what he was doing, he applied to an old woman who lived in a neighbouring cottage, to solve the difficulties that arose; and in this way he actually learned to read tolerably well. His father did not find out his little son's secret, till one day, to his great surprise, he caught him in the act of reading to himself. The roof of the cottage having partly fallen in, Mr. Ferguson applied to it a beam, resting on a prop, in the manner of a lever, and thus raised the roof again to its place. James was now about seven or eight years of age, and this circumstance set his mind to work. Again and again did he think of what had been done; and, after a while, it struck him that his father, in using the beam, had applied his strength to its extremity, and that this had, probably, much to do with the matter. He now thought he would see if this were so, and, having made several bars as he called them,-levers in fact, he discovered not only that he was right in supposing it to be important to apply the moving force at the point most distant from the fulcrum; but the rule or law, that the effect of any weight made to bear on a lever, is always exactly proportioned to the distance of the point on which it rests from the fulcrum. He says, in the highly-interesting and instructive narrative of his life, “I then thought that it was a great pity that by means of this bar, a weight could only be raised a very little way. On this, I soon imagined that by pulling round a wheel, the weight might be raised to any height, by tying a rope to the weight, and winding the rope round the axle of the wheel; and that the power gained must be just as great as the wheel was broader than the axle was thick; and found it to be exactly so, by hanging one weight to a rope put round the wheel, and another to the rope that coiled round the axle." Here, then, we see a mere child, by the solitary and independent movements of his own mind, not only discovering, but verifying by practical experiments, two of the most important elementary truths in the science of mechanics: the lever, and the wheel and axle. Such a child could not fail to hit on others; though he was without either book or teacher, and all the tools he had to fashion his blocks and wheels, were a little knife and a simple turning-lathe of his father's. He now pro•eeded to write an account of his discoveries, and to sketch his different machines with a pen; concluding, naturally enough, that they were the first of the kind that had ever been invented. Some time after, however, he was shown them all in a printed book; when, though he found that his schemes had been anticipated, he could not fail to be gratified by their coincidence with well-established and highly-important principles. The honour that encircles the brow of this young philosopher is as great and indisputable, as it would have been had he stood absolutely alone in reaching such results. The same tendencies and feelings were displayed when as a boy, far from robust, he was employed as a shepherd in the neighbourhood of his birthplace; making models of mills, spinning-wheels and othermachines by day, and, like those who kept flocks beneath the clear skies of Chaldaea, studying the starsby night. He was afterwards engaged in the service of Mr. Glashan, arespectable farmer; when he used to go at night into the fields, with a blanket about him, and a lighted candle, and there, lying down on his back, he pursued his observations on the heavenly bodies, for many successive, yet happily spent hours. “I used to stretch,” he says, “a thread with small beads on it, at arms-length, between my eye and the stars; sliding the beads upon it, till they hid such and such stars from my eye, in order to take their apparent distance from one another; and then, laying the to: down on a paper, I marked the stars thereon #i. beads,”
He thus paints himself before us, as engaged in the most sublime and astounding of sciences, and not only as employed in astronomical observations, but in actually making a map of the heavens. “My master,” he adds, “first laughed at me; but when I explained my meaning to him he encouraged me to go on; and that I might make fair copies in the day-time of what I had done in the night, he often worked for me himself.” On Ferguson being employed by his master to carry a message to Mr. Gilchrist, the minister of Keith, he showed that gentleman the drawings he had been making. Mr. Gilchrist, in consequence, put a map into his hands, and desired him to make a copy of it, supplying him at the same time with compasses, ruler, pens, ink, and paper. “For this pleasant employment,” he says, “my master gave me more time than I could reasonably expect, and often took the threshing flail out of my hands, and worked himself, while I sat by him in the barn, busy with my compasses, ruler, and pen.” No wonder he remarks, “I shall always have a respect for the memory of that man.” Nor do we envy the mind that does not sympathise with him; Mr. Glashan presents a very rare example of sincere interest in the intellectual efforts of his servant, and of real concern for his advancement in life. Having completed his map, Ferguson carried it to Mr. Gilchrist, where he met Mr. Grant, of Acho ey, who offered to take him into his house, and promised that he should have lessons from his butler. He replied that he should rejoice in being at the house of Mr. Grant, as soon as his engagement with his master expired, and respectfully declined Mr. Grant's kind offer to put some one for the time in his place. Ferguson was in his twentieth year when he went to for. Grant's, whose butler, Cantley, was what might be generally termed a selftaught, and, at the same time, an extraordinary man. He was profoundly conversant with mathematics; understood Greek, Latin, and French; could play on every known instrument, except the harp; and, moreover, could prescribe for diseases, and let blood. Ferguson, who had mastered vulgar arithmetic by the aid of books, received instructions from him in Decimal Fractions and Algebra, and he was about to commence geometry when Cantly removed from his situation to one in the establishment of the Earl of Fife, and Ferguson returned home. It will be remembered by those who have read the biographical sketch of Alexander Murray," how much he was indebted to “Salmon's Geographical Grammar;” and it is remarkable that a similar work by Gordon, a parting gift of his friend Cantley, was of great service to James Ferguson. The book contains a description of an artificial globe, and though it was not accompanied by any o Ferguson made a globe in three weeks, having turned the ball out of a piece of wood, cóvered it with paper, and delineated on it a map of the world; he also made the meridian ring and horizon of wood, covered them with paper, and traced upon them the proper degrees; and was delighted to find that by the globe he had corstructed—the first he ever saw—he could solve the problems which the book contained. That he might not remain idle at home, he engaged himself to a neighbouring miller, who, finding he could confide in his servant, spent his time at the alehouse, leaving Ferguson everything to do, while a little oatmeal mixed with coid water was often all he was allowed. At the close of a year he returned home, much the weaker for his privations. He suffered greatly also in the service of a medical man, who promised him instruction, but broke his engagement, and treated him tyrannically. A severe hurt which he had received, to which the doctor was too busy to attend, confined him to his bed after his return home. In order to amuse himself in his low state, he made a wooden clock, the frame of which was also of wood, and it kept time pretty well. The bell on which the hammer struck the hours was the neck of a broken bottle. On recovering his health, Ferguson accomplished an extraordinary work, which he thus describes:—“Having noidea how any timepiece could go but by a weight and line, Lywondered how a watch could go in all positions, and was sorry I had never thought of asking Mr. Cantley, who could very easily have informed me. But happening one day to see agentleman ride by my father's house (which was close by a public road), I asked him what o'clock it then was He looked at his watch, and
• Popular Educator, No.3, p. 47.
told me. As he did that with so much goodnature, I begged
him to show me the inside of his watch, and though he was an entire stranger, he immediately opened his watch, and put it into my hands. I saw the spring-box, with part of the chain round it, and asked him what it was that made the box turn round? He told me that it was turned round by a steel spring within it. Having then seen no other spring than that of my father's gun-lock, I asked him how a o within a box could turn the box so often round as to wind all the chain upon it? He answered, that the spring was long and thin : that one end of it was fastened to the axis of the box, and the other end to the inside of the box; that the axle was fixed, and the box was loose upon it. I told him that I did not as yet thoroughly understand the matter. “‘Well, my lad," says he, “take a long, thin piece of whalebone, hold one end of it fast between your finger and thumb, and wind it round your finger, it will then endeavour to unwind rtself, and if you fix the other end of it to the inside of a small hoop, and leave it to itself, it will turn the hoop round and round, and wind up a thread tied to the outside of the hoop.’ I thanked the gentleman, and told him that I understood the thing very well. Ithen tried to make a watch with wooden wheels, and made the spring of whalebone, but found that I could not make the wheel go when the balance was put on, because the teeth of the wheels were rather too weak to bear the force of a spring sufficient to move the balance, although the wheels would run fast enough when the balance was taken off. I enclosed the whole in a wooden case, very little bigger than#. teacup; but a clumsy neighbour, one day looking y watch, happened to let it fall, and turning hastily about to pick it up set his foot upon it, and crushed it all to pieces; which so provoked my father that he was almost ready to beat the man, and discouraged me, so much that I never attempted to make such another machine again, especially as I was thoroughly convinced I could never make one that would be of any real use.” Ferguson's attention to timepieces, however, was turned to some account; for he made some money in the neighbourhood, as a cleaner of clocks. He was now invited to reside in the house of Sir James Dunbar, of Durn, where he usefully employed his ingenuity. He converted two round stones upon the gateway into a pair of stationary globes, by painting a map of the earth on one, and a map of the heavens on the other. “The poles of the painted globes,” he states, “stood towards the poles of the heavens; on each the twenty-four hours were placed around the equinoctial, so as to show the time of the day when the sun shone out, by the boundary where the half of the globe at any time * by the sun, was parted from the other half in the shade; the enlightened parts of the terrestrial globe answering to the like enlightened parts of the earth at all times. So that, whenever the sun shone on the globe, one might see to what places the sun was then rising, to what places it was setting, and all the places where it was then day or night, throughout the earth.” Lady Dipple, the sister of Sir James, induced him to attempt the drawing of patterns for ladies' dresses, in which he soon became an adept. He afterwards made them for other ladies, copied pictures and prints with pen and ink, and even took portraits in Edinburgh with great success. Sometimes, too, he pursued his astronomical observations; employing his beaded threads, and delineating on S.P. the apparent facts of the planets as thus ascertained. On such occasions he describes himself as conceiving that he saw the ecliptic lying like a broad highway across the firmament, and the planets making their way in parts like the narrow ruts made by cartwheels, sometimes on one side of a plain road, and sometimes on the other, crossing the road at small angles, but never going far from either side of it. His circumstances were now greatly improved by his artistic labours; and in a short time, he made so much money as not only to defray his own expenses, but to gratify the affectionate dispositions he constantly cherished, by contributing largely to the support of his aged parents. After Ferguson had been about two years in Edinburgh, he was seized with such a passion for the practice of medicine, that he returned to his father's, intending to carry out his design in his native village. But, not succeeding as he hoped, he went to Inverness, “When I was there,” he says, “I began to think of astronomy again, and was heartily sorry
for having neglected it at Edinburgh, where I might have improved my knowledge by conversing with those who were able to assist me. I began to compare the ecliptic with its twelve signs, through which the sun goes in twelve months, to the circle of twelve hours on the dialplate of a watch, the hour-hand to the sun, and the minute-hand to the moon, moving in the ecliptie, the ene always overtaking the other at a place forwarder than it did at their last conjunction. On this I contrived and finished a scheme on paper, for showing the motions and places of the sun and moon in the ecliptic on each day of the year, perpetually; and, consequently, the days of all the new and full moons. “To this I wanted to add a method for showing the eclipses of the sun and moon, of which I knew the cause long o: by having observed that the moon was for one half of her period on the north side the ecliptic, and for the other half on the south. But not having observed her course long enough among the stars by my above-mentioned thread, so as to delineate her path on my celestial map, in order to find the two opposite points of the ecliptic in which her orbit crosses it, I was altogether at a loss how and where in the ecliptic, in my scheme, to place these interesting points. This was in the year 1739. “At last, I recollected that when I was with "Squire Grant, of Auchoynaney, in the year 1730, I had read, that on the 1st of January, 1690, the moon's ascending node was in the 10th minute of the first degree of Aries, and that her nodes" moved backward through the whole ecliptic in 18 years and 224 days, which was at the rate of three minutes 11 seconds every 24 hours. But as I scarce knew in the year 1730 what the moon's nodes meant I took no further notice of it at that time. “However, in the year 1739, I set to work, at Inverness, and after a tedious calculation of the slow motion of the nodes from January 1690 to January 1740, it appeared to me that (if I was sure I remembered right) the moon's ascending node must be in 23 degrees 25 minutes of Cancer at the beginning of the year 1740. And so I added the eclipse part to my scheme, and called it the Astronomical Rotula. “When I had finished it I showed it to the Rev. Alexander Macbean, one of the ministers at Inverness; who told me he had a set of almanacks by him for several years past, and would examine it by the eclipses mentioned in them. We examined it together, and found that it agreed throughout with the days of all the new and full moons and eclipses mentioned in these almanacks, which made me think I had constructed it upon true astronomical principles. On this Mr. Macbean desired me to write to Mr. Maclaurin, professor of mathematics, at Edinburgh, and give an account of the methods by which I had formed my plan, requesting him to correct it where it was wrong. He returned me a most polite and friendly answer, although I had never seen him during my stay at Edinburgh, and informed me that I had only mistaken the radical mean place of the ascending node by a quarter of a degree." Maclaurin was indeed so much pleased with the result that he had the scheme engraved, and Ferguson was once more induced to return to Edinburgh. One day, having asked the professor to show him his orrery, Maclaurin immediately complied with his request, so far as the outward movements of the machine were concerned, but would not venture to open it—which indeed he had never done, being afraid that if he should displace any part of it, he should not be able to put it to rights again. But Ferguson saw enough to set his mind again in vigorous action. After a good deal of thinking and calculation, he found he could contrive the wheel-work for turning the planets in such a machine, and giving them their progressive motions; but considered he should be very well satisfied if he could make an orrery to show the motions of the earth and moon, and of the sun round its axis. He then employed a turner to make him a sufficient number of wheels and axles, according to patterns which he gave him in drawing; and after having cut the teeth in the wheels by a knife, and put the whole together, he
• Nodes in Astronomy are the two points in which the orbit of a planet intersects the plane of the ecliptic,+the great circle of the heavens which the sun appears to describe in his annual revolution. The point in which the centre of a planet passes from the south to the north side of the ecliptic is called the o node; the opposite point, or that in which the planet passes to the south side of the ecliptic is called the descending node.
found that it answered all his expectations. It showed the sun's motion round its axis, the diurnal and annual motions of the earth on its inclined axis, keeping its parallelism in its whole course round the sun; the motions and phases of the moon, with the retrograde motion of the nodes of her orbit; and, consequently, all the variety of her seasons, the different lengths of days and nights, as well as the days of the new and full moons and eclipses. He now had the honour of reading a lecture on the orrery, to Maclaurin's pupils. He subsequently made an orrery of ivory, and, in the course of his life, he constructed six more, all unlike each other. Ferguson now resolved to visit London, hoping to find employment as a teacher of mechanics and astronomy. After his arrival, he was introduced to the Royal Society. He soon after published his first work, “A Dissertation on the Phenomena of the Harvest Moon, with the description of a new Orrery, having only four wheels.” Of this work he modestly says, “Having never had a grammatical education, nor time to study the rules of just composition, I acknowledge I was afraid to put it to press; and for the same cause, I ought to have the same fears still.” It was, however, well received, and this very ingenious man sent forth various other works, most of which attained high popularity. In 1748 he began to give public lectures on his favourite themes, to numerous and fashionable admirers, among whom when a boy occasionally was George III., who, soon after his accession to the throne, granted him a pension from the privy purse, of £50 per annum. Henow ceased to paint portraits, in which he had been engaged for twenty-six years. In 1763 he was elected a Fellow of the Royal Society; the usual fees being remitted, which had only been done in two other instances—those of Newton and Thomas Simpson. He died in 1776. “Ferguson,” says Dr. Hutton, “must be allowed to have been a very uncommon genius, especially in mechanical contrivances and inventions. . . . . . His mathematical knowledge was little or nothing. Of algebra he understood little more than the notation; and he often told me he could never demonstrate one proposition of Euclid, his constant method being to satisfy himself as to the truth of any problem with a measurement by scale and compasses.” We can now only remark that Sir David Brewster has pronounced on Ferguson the following high but just eulogium:“He possessed a clear judgment, and was capable of thinking and writing on philosophical subjects with great accuracy and precision. He had a peculiar talent for simplifying what is complex, for rendering intelligible what is abstract, and for bringing down to the lowest capacities what is naturally above them. His unwearied assiduity in the acquisition of knowledge may be inferred from the great variety of his publications; and when we reflect upon the very unfavourable circumstances in which he was educated, and the little assistance he received from others, we cannot fail to wonder at the style in which all his works were composed. On some occasionshis style is uncommonly correct and animated. When admiring the displays of wisdom and beneficence in the accuracy of nature, he often rises into a species of ‘. characterised by the most artless simplicity, and infinitely more affecting than the laboured and polished periods of the professed orator. In his manners he was affable and mild; in his dispositions communicative and benevolent. He was distinguished by none of those peculiarities of temper, and eccentricities of conduct, which we generally observe in literary men. . If Mr. Ferguson had any foibles, they “leaned to virtue's side;’ and even his wonderful simplicity of character, which, in a state of artificial manners, is too apt to be regarded as a off: and exposed to ridicule and scorn, tended only to heighten the respect in which he was constantly held.”
LESSONS IN ENGLISH.—No. VI. By John R. BEARD, D.D. SAXON ELEMENT OF THE ENGLISH LANGUAGE. Having shown how the constituents of the English language enter into and form simple propositions, I might now speak of sentences in relation to the laws of their constitution, and exhibit the manner in which simple sentences may be expanded into compound sentences, and how compound sentences may be reduced to simple
ones. But there is much, very much, to be learnt respecting the subject-matter already set forth. . For instance every separate part of speech has to be more minutely investigated. Besides there are general facts which more or less bear on all the constituent elements of speech. These facts must be set forth, and this investigation must be gone through, before we treat of the formation of compound sentences, if only, because in proceeding in this way I shall conduct the learner onward by easier steps. Before, then, we formally set about building the house, it may be desirable to consider the materials which we shall have to em. ploy, in order that we may become familiar with their qualities and character. Let us then take what is commonly called “The Lord's Prayer,” and look a little closely into the words of which it is made up. “Qur Father which art in Heaven, hallowed be thy name. Thy kingdom come. Thy will be done in earth, as it is in Heaven. Give us this day our daily bread. And forgive us our debts as we forgive our debtors. . And lead us not into temptation; but deliver us from evil. For thine is the kingdom, and the power, and the glory, for ever. Amen.”—Matt. vi. 9–13.
Now at the first glance I see that here there are words of diverse origin. Father I recognise as of Saxon birth; temptation, I know to be a Latin word slightly altered; and amen is a Hebrew term in English letters. Hence, I am led to see that if I would know my mother-tongue I must study it in relation to the diverse materials which enter into its composition. You are not yet sufficiently advanced to assign each word in the preceding quotation to the family to which it belongs in the great community of languages. I must, therefore, be satisfied at present with a somewhat rough division of these words into the three classes already indicated,—namely, words of Saron origin, words of Latin origin, and words derived from other sources. In all, there are in the Lord's Prayer 66 words. Of these 66 only eight are from sources that are not Saxon. More than seven-eighths of the words in the Lord's Prayer come from the Saxon. You may now judge to what extent the Saxon prevails in the English tongue. Of the eight words that are not Saxon, six are from the Latin, one from the French, and one from the Hebrew, as seen in this view :Jatin. Ilaine debts debtors temptation wer glory The one French word might be added to the Latin column for deliver, though it comes into the English directly from the French, is Latin by extraction. This analysis, however, shows that the materials of the English language may be arranged into two great classes; namely, the Saxon and the Latin. These classes have reference to the origin of the words. Another view may direct our attention to the condition in which the words are. Some of the words are very short, others are somewhat long. Our has only three letters; kingdom has seven; and temptation has ten letters. Our is a word of one syllable; kingdom a word of two syllables; and temptation is a word of three syllables. Observing that all the words are Saxon, except the eight specified above, you will see that the Saxon words for the most part are short words, and words of one syllable. Of words, however, having more than one syllable, two kinds must be noticed. Take, as an instance, father and kingdom. Now father, though consisting of two syllables, is a simple word; while kingdom is a compound word. Hence arises another division. Words, whether of Saxon or of Latin origin, are either-1, simple; or 2, com
- Hebrew. deliver
The two compound words here presented, from the Lord's Prayer, may be resolved into their elements thus: forgive is made up of for and gire, in German vergeben; deliver comes originally from de, down, from, and liber, free. Now observe, I do not put down the import of the component parts of Jorgive, for they are known. Words of Saxon origin are known to every Englishman. But I do assign their signification to the terms
which combine to make up deliver, since those terms awaken no
energetic that any language can supply; for the same reason that
this is a good reason for the advice. But it is not the only reason. The great object of the orator and the poet is to make their meaning felt; to stimulate the imagination, and thence excite emotion. They, therefore, seek the most special terms they can find. Again, the terms which, cateris paribus (other things being equal), most vividly recall the objects or feelings they represent, are those which have been earliest, longest, and most frequently used, which are consequently covered with the strongest associations, the sign and the thing signified having become so inseparably blended that the one is never suggested without the other. And thus it is that of two synonymes (words having nearly the same meaning) derived respectively from Latin and the Anglo-Saxon, both equally well understood, the one shall impart the most vivid, and the other the most tame conception of the meaning. It is precisely for the same reason that the feelings with which we read beautiful passages in foreign lo are so faint and languid, compared with those which are exerted by parallel passages in Shakspeare, Milton, or Burns.
SOLUTIONS OF PROBLEMS AND QUERIES. (From No. 7, page 111.) 5. Show how the squares described on the two legs of a right angled triangle must be cut so that the pieces may be laid upon the square described on the hypotenuse. In this solution by ocular demonstration, the pieces of the two smallersquares marked l, 2, 3, 4, 5, 6, 7, when cut out and laid upon the parts of As the larger square marked with the same figures, will exactly cover the same. The author of the preceding solution remarks that the sides of all the figures which form the pieces of the smaller f squares, make exactly the same angles with the base of the larger, which the sides of the corresponding figures of that square make with its base. Accordingly, those pieces may be made to slide into their proper places on the larger square, by merely moving them downwards, aid preserving the parallelism of their original position. We are indebted to Mr. Henderson, the Astronomer, at Liverpool, for his kindness in recommending this solution to besent tous by the author, Henry Dugdale, of Slaidburn. in the interesting biography of James Ferguson contained in this Number, it appears that this wonderful genius was theoretically unacquainted with Euclid's geometry, and that when he had occasion for any proposition contained in that storehoose of valuable facts he consulted it, and tested the accuracy of the fact he wanted to employ in his own pursuits, by scale and composes. We have someohere read concerning this same Ferguson, that he satisfied himself of the truth of the 47th Proposition of the First Book of Euclid, by some method of ocular demonstration similar to the preceding. We do not know the exact mode in which he cut out the parts of the smaller squares and applied them to the larger one in order to cover it; but we know that there are many ways be: sides the above, and some that require fewer parts or divisions of the figures, which we consider a recommendation to any method, and a reason for its preference in general. ... In the edition: of Euclid by Lardner and Playfair different methods are exhibited, and those which are accompanied with a demonstration are to be preferred; we shall be glad to see the author’s demonstration of the preceding one. in the solution of the problem “to draw a perpendicular to a straightline at one of its extremities,” inserted in our last Number, there is an omission in the demonstration which we now supply. The omission consists in not proving that p n and Bo are in the same straight line. To prove this, it is plain that the three angles An p, a c, and c ar, are equal to the three angles of any one of the equilateral triangles, and, therefore, by the 32nd of the first Book, they are equal to two right angles. Wherefore, by the 14th of the same Book, the two straight lines D B and B e, are in one and the same straight line. This problem has been sent to us solved in various ways, which are aw well known and appreciated. The following solution, which
we give without a diagram, in order to exercise some of our younge, pupils, appears to us to be the simplest and best; and it requires nothing more than the 11th of Euclid's first Book, and some preceding propositions. From the given extremity of the straight line cut off a convenient length towards the other extremity, and from the point of section draw a perpendicular to the given straight line. From this perpendicular cut off a part equal to the part of the given straight line between the given extremity and the point of section; and from the point of section in this perpendicular draw a perpendicular to it on the side next the given extremity of the given straight line. Bisect the angle on the same side between the first perpendicular and the given straight line, and the bisecting line will meet the second perpendicular. From the point of meeting in this perpendicular draw a straight line to the given extremity of the given straight line, and it will be a perpendicular to that straight line at the point required. The proof is this: Because that the bisecting line divides the right angle between the first perpendicular and the given straight line into two equal angles, that this bisecting line is common to the two triangles thus formed, and that the part cut of the first perpendicular is equal to the part of the straight line between the first point of section and the given point; therefore, by the fourth of the first book, the two triangles are equal, their bases are equal, and the remaining angles of the one are equal to the remaining angles of the other each,-viz., those to which the equal sides are opposite. Therefore all their sides are equal, and the angle at the given point is equal to the angle at the point of section in the second perpendicular; but the angle at the latter point is a right angle. Therefore the angle at the given point is a right angle; and the straight line is drawn perpendicular to the given straight line at one of its extremities as required. N.B.-The figure formed by the four straight lines which are all equal, has all its angles, as can easily be shown, right angles, and is therefore, according to Euclid's definition, a square.
ALLow me to tell you a little story in connexion with the Populah EducAron. About two miles from where Istay, is a small village; and in that village is a tinsmith. In that Tinsmith's shop, is a little orphan-boy apprenticed, quite young—no father, no mother, to tend him, and see that his young mind does not shrivel away into nothing for lack of food Well, in this shop, a paper may be seen in a corner. On taking it up, we discover that it is the Popular Educator. In the inside of it is a little note-book which he (the boy) has made himselfosa few shreds of paper. It is neatly ruled; and he has Latin words written on the one side, and English on the other. I was perfectly struck to see the poor little fatherless and motherless boy persevering, all unaided, unless by your lessons, and learning the language of ancient Rome. You say, “The authority of such men as Macaulay, Macintosh, Addison, Dryden, Shakspeare, is in grammar paramount and supreme." I would sike to have a prose composition that you would recommend as being worthy to be studied, every word, and line for the style. Macaulay's are all too dear. Would Mackintosh’s “History of England” do? I do not see how Shakspeare can be an authority for a grammar at all, since his expressions are antiquated and stiff. I should
iike if you would recommend a book written in a fine, flowing style. Fitos.
History or THE PAINTERs of ALL NATIons.-The first part of this magnificent work, in imperial quarto, containing a portrait of Murillo, and eight specimens of his choicest works, including the “Conception of the Virgin," lately in the collection of Marshal Soult, and recently purchased by the French Government for the Gallery of the Louvre, for the sum of £28,440, is now ready. . The successive part: will appear on the first of every month, at 2s. each, and will be supplied through every bookseller in town or country.
CAsseill's SHILLING EDITIon or EucLID.—THE EuroNT*.* Geomorry, containing the First Six, and the Eleventh and Twelfth Books of Euclid, from the text of Robert Simpson, M.D., Emeritus professor of Mathematics in the University of Glasgow; with9orrections. Annotations, and Exercises, by Robert Wallace, A.M., of the same university and Collegiate Tutor of the University of London, will be ready early in July, price is. in stiff covers, or is to: meat cloth.
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