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has another reply in hand, which we bath in reading, spelling, writing, arith. hope will shortly appear.
metic, and the leading doctrines of the SALISBURY.—The society and friends church, by twelve teachers. The object of the church in Salisbury celebrated thus achieved will, if duly persevered in, their anniversary on Monday, January be found to be productive, through the 3, 1842, by a tea meeting, at which Divine blessing, of much lasting good to forty-five persons were present. On the the church in that city. removal of the tea equipage, the society's THE MAGAZINE FOR THE CHILDREN leader, Mr. D. T. Dyke, was called to OF THE NEW JERUSALEM Church. the chair, who, after a short preliminary This little periodical is making its way address, read the report of the committee in the world even better than its most for the past year. Several other friends sanguine friends could have anticipated. also addressed the meeting on various in. Wherever it comes it appears to gladden teresting topics ; and conversation on the and charm all who read it. An edition doctrines was continued until nine o'clock, of more than 3,000 copies is now rewhen the proceedings were brought to a quired to satisfy the increasing demand. conclusion by singing an appropriate The Editors request us to state, in reply hymn. The report of the society, as to the observations of a “Member" in read to the meeting, abounds in incidents our last, that so far as they are conof a satisfactory nature, which could not cerned, the title of their little work is fail of giving pleasure to the friends as- not of their selection, but that it was sembled ; and there is one particular adopted at the annual meeting of the alluded to which will, we are perfectly Sunday School Union, and that it can sure, give pleasure to every member of only be altered at a similar meeting. the whole church,—the establishment by They also think that the title, by which the society of a Sunday school. This the church should be designated, is useful institution was commenced on worthy of the consideration of the Ge. Sunday, September 12, and its progress neral Conference. and present prospects have far exceeded ERRATUM.-In our February Numthe most sanguine expectations of our ber, p. 72, second column, line 12, from friends. It new contains twenty-five the top, for acquirements read requirechildren, who are instructed every Sab- ments.
naminminmann DIED, January 3, 1842, in the 74th happy life together upon earth, an examyear of her age, SARAH, widow of the ple of conjugial love and Christian conlate Mr. GEORGE ARTINGSTALL, of duct to their children, whom they careWorsley, whose obituary appeared in our fully instructed in the truths and docperiodical for July, 1837. She had been trines, they themselves had so affectiona sincere receiver of the heavenly doc- ately embraced. In all the relations of trines of the New Church from her early life, as a wife, a mother, a friend, and a years, being one of the little flock who neighbour, she was greatly respected and attended Mr. Clowes's ministry, when beloved. She endured sufferings with he visited that village. She introduced patience and resignation, and her confithe doctrines to her husband, who from dence and trust in her Saviour God daily the sincere affection and exemplary con- increased. Her mind was greatly enduct of his beloved partner, was induced lightened, strengthened, and consoled, by to read them with diligence; and he soon the doctrines of the Holy Word, which became sensible of their great superiority had been so long the delight of her life. and importance. Being thus united in Her end was peace, and a happy eternity, religious principles, they spent a long and will, no doubt, be her blissful portion.
New Jerusalem Magazine.
No. 29. — MAY, 1842.
LETTER OF EMANUEL SWEDENBORG.
"AMONGST other witnesses whom I might here produce, I shall mention the learned M. Swedenborg, Assessor of the Board of Mines, whose name is known not only in Sweden, but in foreign countries, by several approved works. Understanding that I intended to publish the History of Charles XII., he wrote to me a letter containing many particulars relative to that king's love for mathematics, particulars no one was so well able to communicate, having often had the honour of conversing upon the subject with the king, when at Lund, in 1716, whither he had accompanied M. Polheim, the Minister of Commerce, who had been summoned there by his majesty, This letter, which will be found in the Appendix, merits a careful perusal, as being founded on memoranda made by the king himself, and as giving us the opinion of an able mathematician upon the new mode of calculating invented by that prince, entitled Calculus Sexagenarius, upon his skill in the solution of problems in Analytical Geometry (Calcul Analytique), his just reasoning on mechanics, and the undertakings contemplated by him in connexion with this subject,” &c. Nordberg's Histoire, vol. 3, pp. 278, 279. “ No. CCXXI. Letter of M. Swedenborg, Assessor of the Board of
Mines, to M. Nordberg, Author of the ' History of Charles XII.'
“Sir,—As you are now actually engaged upon the Life of Charles XII., I avail myself of the opportunity to give you some information concerning that monarch, which is, perhaps, new to you, and worthy of being transmitted to posterity. I have already touched upon the subject, in the fourth part of my Miscellanea, * treating de Calculo
* Pars Quarta Miscellanearum Observationum, circa res naturales et præcipue circa Mineralia, Ferrum, et Stalactitas in Cavernis Baumannianis,” Naupotami, typis H. H, Hollii, 1722, 8, p. 1. The account in this work, is probably that of which a translation is given in the Gentleman's Magazine, (vol. 21, an. 1754, pp. 423—4,) under the title “ A curious Memoir of M. Eman. Swedenborg, concerping Charles XII., of Sweden.”
NEW SERIES. NO. 29.--VOL. 3.
gly did, proo rule, to use on, and after af
as flection, behat was onetly with
novo Sexagenario, fc., whence M. Wolff has derived what he has said in his Elementa Matheseos Universe, relative to this new Calculus.*
“In 1716, when M. Polheim received the king's orders to repair to Lund, he engaged me to accompany him thither. Having been presented to his majesty, he often did us the honour of conversing with us upon the different branches of mathematics, and particularly upon mechanics, the mode of calculating forces, and other problems of geometry and arithmetic. He seemed to take remarkable pleasure in these conversations, and often put questions, as if he merely proposed to gain some slight elucidation from us; but we soon found that these things were not strange to him, which put us, subsequently, more upon our guard, not to speak to him of common or unimportant matters, nor to advance any thing doubtful in which he might have shewn us to be mistaken. The conversation turning upon analytical and algebraical calculation, as well as upon what is called the regula falsi, (rule of false position,) he desired us to bring forward examples, which we accordingly did, proposing such as made it incumbent, in order to proceed agreeably to rule, to use signs or symbols, as well as equations. The king did not require them, and after a few minutes reflection, he told us, without any other aid than his own superior genius, in what way our examples might be solved, which we always found to agree perfectly with our calculations. I confess, that I have never been able to understand, how, by mere reasoning, and without the aid of Algebra, he was enabled to solve problems of this kind. It seemed, indeed, that the king was not sorry to display before M. Polheim,—a competent judge in these things,—a penetration and power of reasoning, equalling those of the ablest mathematicians.
“I will now relate to you, as I am peculiarly able to do, what arose from this learned amusement, which is as follows:--Conversing one day with the king upon arithmetic, and the mode of counting, we observed, that almost all nations upon reaching 10, began again; that those figures which occupy the first place, never changed their value, while those in the second place, were multiplied ten-fold, and so on with the others; to which we added, that men had apparently begun by counting their fingers, and that this method was still practised by the people; that arithmetic having been formed into a science, figures had been invented, which were of the utmost service; and, nevertheless, that the ancient mode of counting had been always re
* Christ. Wolf's Elementa Matheseos Universe, Tom. 1, p. 21, Genevä, 1743. The passage is as follows :-—" Et Carolus XII., Rex Sueciæ, calculum Sexagenarium excogitavit, referente Emanuele Swedenborgio, novis characteribus et numeris, novisque denominationibus adinventis."
thout anequire them ons op
tained, in beginning again after arriving at 10, and which is observed by putting each figure in its proper place. The king was of opinion, that had such not been the origin of our mode of counting, a much better and more geometrical method might have been invented, and one which would have been of great utility in calculations, by making choice of some other periodical number than 10. That the number 10 had this great and necessary inconvenience, that when divided by 2, it could not be reduced to the number 1 without entering into fractions. Besides, as it comprehends neither the square, nor the cube, nor the fourth power of any number, many difficulties arise in numerical calculations. Whereas, had the periodical number been 8 or 16, a great facility would have resulted, the first being a cube number, of which the root is 2, and the second a square number, of which the root is 4, and that these numbers being divided by 2, their primitive, the number 1 would be obtained, which would be highly useful with regard to money and measures, by avoiding a quantity of fractions. The king, after speaking at great length on this subject, expressed a desire that we should make a trial with some other number than 10. Having represented to him, that this could not be done, unless we invented new figures, to which, also, names altogether different from the ancient ones must be given, as, otherwise, great confusion would arise, he desired us to prepare an example in point.
“We chose the number 8, of which the cube root is 2, and, which, being divided by 2, is reduced to the primitive number 1. We also invented new figures, to which we gave new names, and proceeded according to the ordinary method; after which we applied them to cubic calculations, as well as to money and to measures. The essay having been presented to the king, he was pleased with it; but it was evident that he had wished something more extended, and less easy, in order that he might display the superiority of his genius and his great penetration. To this end he proposed to adopt some number which should contain a square as well as a cube, and, which, when divided by 2, might be reduced to the primitive number 1. He made choice of 64; but we observed to him that it was too high a number, and, consequently, very inconvenient, and, indeed, that it was almost impossible to employ it; that, besides, if we were obliged to reckon up to 64, before recommencing, and that upon reaching 64 times 64, or 4096, only three figures were used, calculation would be rendered immensely difficult, especially with regard to multiplication and division ; because it would be necessary to commit to memory a multiplication table composed of 4096 numbers, while the common table comprised only 80 or 90 numbers. However, the more we urged our difficulties, the more he was determined to put his idea into practice : and to shew the possibility of what appeared to us to require long and profound reflexion, he undertook to devise this method himself, and to lay down the plan of it, which he sent to us the next morning. He had invented new figures, each with its particular name. The 64 figures were divided into 8 classes, each being designated by a particular symbol. Upon a closer inspection, I found that these symbols or signs were composed of the initial and final letters of his own name, in a manner at once so clear and exact, that when the first 8 numbers were known, all the rest up to 64 were attainable without the least difficulty. The names of the 8 numbers of the first class were very simple, and those of the others so well contrived, that one could easily remember them, without fear of confusion. Having arrived at the number 64, when it became necessary to proceed with three figures, up to 64 times 64, he had invented new names, admirably arranged, and so easily and naturally varied that there was not any number, however high, for which there was not a name; and this might be carried on ad infinitum, following the principles and rules laid down.
" It was to me that the king committed this plan, in his own handwriting, [the original of which I still preserve,] in order to arrange from it a table shewing the difference between this and the common mode of counting, both with regard to the names and the figures. ..
“The king had also added to his plan an example in multiplication and in division; two operations in which I had contemplated so much difficulty. As it was my place to undertake the perfecting of his method, I examined it thoroughly, in order to discover whether it might not be rendered yet more easy and more convenient of application than it was. My attempts, however, were in vain; and I much doubt whether the greatest mathematicians would have succeeded. What I chiefly admire, is, the ingenuity shewn by the king in the invention of the figures and the names, and the ease with which the signs may be varied ad infinitum. I was also greatly struck with his example in multiplication; and when I consider the short time in which he accomplished this, I cannot but regard him as a prince endowed with a genius and a penetration much above those of other men; whence I have been led to believe that, in all his other actions, he was guided by greater wisdom than apparently belonged to him. Certain it is, that he thought it beneath him to assume the air of a learned man, by affecting an imposing exterior. What he said to me, one day, regarding mathematics, expressed a sentiment truly worthy