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the beginning, immersion, and e thus obtaining a rule for finding mersion of several spots, and the the remainder of the root, the au. end were observed, and the times thor deduced his theorem by mak, of the phenomena respectively de- ing the unknown quantity itself a termined.

part of the divisor. Hence arises Of the solar eclipse the begin the difficulty, which learners expe. ning and end were seen, and the rience in finding the divisors in times noted by Dr. Cutler, and this method. The excess of this two other gentlemen, who obsery. difficulty above the degree of it, ed in company with him.

which belongs to the common

method of extracting the square XV. On the extraction of roots root, Dr. West, we think, has aBy Benjamin West, Esq. F.A.A. voided in his rules, which he ob

The author's design in this per- tained, as an algebraist will readily formance we shall give in his own perceive, by a process differing words. “ What I' chiefly aimed from that of Ward in the solution at was, to render the method of of the aforesaid equations, which extracting the roots of the odd are treated as affected quadratick powers easier, and less burthen- equations. some to the memory; and, I think, In a similar manner a general I have not failed in my attempt. theorem for the extraction of roots The method, followed by Ward, may be investigated, from which and others, is excellent, but is ate these and other particular rules are tended with too much difficulty in easily deduced by only substituting getting the divisors ; especially particular for general and distinfor learners, who are not acquaint. guishing quantities. But the gene ed with the reason of the rules. eral rule of approximation for the That difficulty I have striven to extraction of roots, which we preremedy in the following work." fer to any that we have seen, was

Dr. West here gives the inves- discovered by Dr. Hutton, and is tigation and exemplification of in his arithmetick, and in the Matha rules for extracting the third, fifth, ematical Text-Book, used in the and seventh roots ; and observes, University. that similar methods may be found for extracting the roots of the even XVI. A new and concise methe powers, and that he has not met od of computing interest at six per with an instance, where the ap. cent. per annum. By Philomath. proximation is not as rapid by his This memoir contains two con. rules, as by those of Ward. cise rules for computing the inter

It may be seen by looking into est of any principal, expressed in Ward's Algebra, in his “ Young pounds and parts of a pound, for Mathematician's Guide," that in any time, expressed in months and the process of forming theorems parts of a month, at the rate of 6 for extracting the roots of simple per centum. They are obtained by or pure powers, the equation im, contracting the operation for finds, mediately preceding each theorem ing the answer to a single examis of the affected quadratick kind, ple, stated in compound propore representing the part of the root tion. The conclusions however to be found or the unknown quan- depend on general principles, and tity. But instead of solving this their truth is sufficiently apparent, equation in the usual manner, and These rules are not given as news

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discoveries, but probably with a cause every thing is new, strange, view to extend the knowledge of and confused. All his former them, and to shew their truth. anxieties, duties, and habits he And to facilitate their application leaves at the sill of his own door, tables of decimal parts of a pound and, as he departs from it into disand of a month, with the manner tance, he amuses the weariness of of deducing the interest at any his many footsteps with the new other rate from that at 6 per motion of physical change, and cent. are annexed.

enlivens the solitude of his mind

with the strange operations of XVII. Several ways of deter, moral alteration. That our au. mining what sum is to be insured thor is eminently of this character on an adventure, that the whole in and spirit, we shall have occasion terest may be covered. By Mer

to show hereafter. calor.

The book is two stout volumes, Three methods are here given. The first is said to be most com

anonymous in the title page ; but

we find that vanity gets the better mon. It is therefore probable, that of the author's prudence, and he the last is less extensively known. For we think no person, acquaint that he cannot help hinting to the

grows so charmed with himself, ed with this, would ever make use

eager world, in the second volume, of that. To extend the knowl- who he is. It is dedicated to a edge of the last method, and to Mr.Hamilton,“ of the woodlands," show its advantage relatively to the partly on account of his libothers by comparison we suppose eral application to horticulture.” to have been the object of the com- No book was ever less wanted,than munication.

the Pennsylvanian's, and none To be continued,

ever deserved type and paper less. But hear his reason for publish

ing;“he is the first American,wło ART. 4.

ever wrote his travels.” His columLetters from Europe, during a bianisms are sufficient credentials

tour through Switzerland and to prove to us whence he came, Italy, in the years 1801 and and whither he is going. “ Debe1802, by a Native of Pennsyl mur nos nostraque morti.” vania. Philadelphia, 1805, Bar, We will now perform a little of tram. 2 vols, syo. Price $6,50, our itinerant duty with our litera

ry traveller.

We should not be EVERY traveller, when he able to follow him in very close suçbreaks from the comforts of his cession, however, if the path had own home, and is beginning to not been so well trodden before estrange himself from the bless him, for his own track is so faint, ings and habits of his country, that we are half the time out of creates himself, at once, a kind of sight of our guide. bero of adventure. His fancy is The Pennsylvanian begins now chivalrous in its wanderings, and to show himself the hero we deis already blazoning in the tilts scribed. He drives off full tilt and tournaments of the sublime along the gay « Boulevards de passions of men. He rushes, with Paris," and in his erratick ardour all the impetuosity of vain enter- he declares to us, that “ he happily prise, into the romance of life, be missed running over any body in

the Rue St. Dennis, or on the beneath. It was in these solemnts Pont neuf ;" and he rattles the and silent recesses of nature, that reader to Basil, though distant the Swiss heroes held their secret fronı Paris some hundred miles, revolutionary meetings for the in the hurry of one short letter. freedom of their country. It wag

From Basil he proceeds to Zu. along these cliffs and glens, that rich, and from Zurich to Berne. the wild Tell leapt after the thin Though Berne is the capital of all and fleeting form of liberty. the Swiss cantons, and has so The reader is now carried much to interest the traveller, our through the picturesque valley of author has not said a word on the Schellenen, without knowing it ; peculiar neatness and style of this and he is transported over the stucity, nor even informed us, whethe pendous mountain of St. Gothard er the French, or German lan- by the most turgid swell of cone guage is spoken here. He says ceited description. Those, who nothing of the cathedral, which have not experienced the hardis the most imposing and solemn ships and terrours of the Alpine Gothick pile in Europe ; nor of the regions, will know nothing of western part of the city, which them in the heroicks of the Pennhangs so strangely so many hun. sylvanian, though he may feel dred feet over the rushing torrent them in the lines of Pope. of the Aar. The following paragraph contains every word, our

At first the towering Alps we try,

Mount o'er the rocks, and seem to tread the sky, author says of Berne. “ The next

TH' eternal snows appear already past, morning we rose with the lark, And the first clouds and moantains seem the last ; before the easy cits had left their

But these attained, we tremble to survey

The growing labours of the length'ned way; beds, breakfasted on the banks

Th' increasing prospect tires our lab'ring eyes, of the Aaron a loaf of bread Hills peep o'er hills, and Alps on Alps arise. and bottle of wine, and brandishing our oaken staffs went on again We now leave these sublime with fresh spirits for Thun."

altitudes, where we have overWe next find our guide at Al- looked the world, and descend torf

, the capital of the canton of from that cold elevation, where we Uri

, situated nearly on the Lake forcibly felt our proximity to the of the four cantons. The next ob- other planets, to the smooth surjects of grandeur in Swisserland, face of the lake Maggiore, and to the Alps, surround this the still plains of Lombardy, lake.

Mr. S. has passed it, and “ diis patriis Italoque cælo." passed it without observation. The writer's first letter on Italy Its borders are the extent of the (Let. 6) begins with the different sublimest scenery. The imagina. modes of travelling in that countions is here under a new and try, by voiture, (better known strange operation of nature. It there by the name of vetturino) sometimes rises to sublimity on brocache, and post. He does not the wild surfaces of its eternal approve of travelling by post, mountains, whose frozen summits which is indeed the only mode, by stand steadfastly in the heavens, which a gentleman can travel and glitter with a faint and distant with any convenience or advanlight, which has yet to reach our tage in this country, on account sight; and it sometimes sinks to of “ being obliged to travel with a the profoundest horrour, in the lacquey," or in other words, with deep and dark vallies, which stretch a courier avant. This, however,

is not the case ; for, if travellers do and so dark, as that of Michael not speak Italian, they can gener- Angelo ! ally make themselves current, in In his letter on Florence, our auany part of Italy, with a very moda thor has said little of this intellecerate share of the French language. tual prodigy ; little of the bright

We have now to pass through Gallileo ; nothing of the intricate the old states of Milan, Lodi, Par Machiavelli ; & nothing of the dark ma, Modena, and Bologna, then unió spirit of Dante, who declares to us, ted under the futile title of the Cisal. he will often make holy visitations pine Republick,and since denomina- on the still banks of the Arno. ted the kingdom of Italy. But of the We think also, as our author is an rolitical changes and oppressions American, (and," for that reason, of these dukedoms he says noth- troubles his countrymen with his ing, and the reader is not even in travels) he might have done more, formed, that, by the articles sign• than merely to mention the name ed by Melas after the victory of of Americus Vespucius, and tho' Marengo, Buonaparte was ado nosarcophagus, proudly fretted mitted to Milan with triumphal with the history of his enterprises, entry, and placed over the whole contains his bones, still he ought of subjugated Lombardy (except- to have entered the church of Saning the Venetian state) from the ta Bourgona, where, on a rough Alps to the Appenines, and from tombstone, is this incription : the Adriatick to the Mediterranean.

8. Amerigo Vespucio suisque amicis, XXXII:. We now meet our guide at Florence, and our curiosity is highly

Mr. S. here speaks of that excited to have all the interesting to have descended from the ancient

strange order of men, who seem objects of “Firenze la bella," point- Troubadours, and who call themed out to us. We regret, that the limits of a review preclude our

selves Improvisatori, and quotes

Dr. Moore upon them ; but as filling up the deficiencies of our author's letter on this city. How has given a specimen of their pow

neither the Doctor, nor himself, cold and stupid must he be, who has gazed on the figures of “ Day

ers of impromptu, we will subjoin

the following courteous address. and Night," and of “ Morning and Evening Twilight;" resting on the Di Bartolo, e di Baldo, illustre figlio, tombs of Julio and Lorenzo of Colmo di zel, di probita, di onore

Alla tua patria accresci un gran splendore. Medici, not to mention more than

Ampio di mente, e multo piu di core, their mere names and place; who Non ti pone in sgomento alcun pen 'glio, could view these, without behold. E di prospera sorte ogni favore ing the splendour of Day break

Recevi ognor senza inarcasi il Ciglio. ing from a body of marble, or Of the Florentine Gallery, tho without feeling his whole soul instituted by Cosmo, finished by overshadowed with the thick and Lorenzo, and protected by the suca impenetrable darkness of Night ; ceeding families of the Medici, our or who would not perceive his author gives no history. Of its sight was dimmed, and that light splendid treasures he does not was mysteriously stealing away think much, though still among from every surrounding object, in them are the beautiful antiques of the effect of the figures of Twin the young Apollo; the head of Alight! These are the powers of a lexander, sighing after other worlds genius so bright, so mysterious, to conquer; and the Roman slave,

who is still listening. Among again is the same fulsome inflation thc pictures, are the Holy Family of the writer's style ; and because of Corrigeo, the young St. John his subject is more sublime, he of Raphael, a Maddalena of Guido, thinks he must become more tur. and the Venus of Titian. These gid. It will be too fatiguing to are mentioned by Mr. S. merely us, and too uninteresting to our as articles in his hotch-potch catı readers, to trace the heavy and alogue. As the corridors of this Gothick feet of our author through gallery are replete with chronolog the solemn and dark ruins of imical specimens of the fine arts, and perial Rome. We will not proas its saloons contain still so many fane its deep gloom and awful asexquisite pieces of the classical semblage of stupendous objects, painters, we would recommend the by here holding communion with reader to consult “Saggio Istoria him. della Galleria di Firenze," 8vo. 2 of St. Peter's he has said much, vols. and a more modern descrip- and much incorrectly. In his histion in French, printed at Florence, tory of it, he asserts, that it was 1804.

three hundred years in building ; We leave Florence for Siena, it was but one hundred and six. and though the country to this city Instead of its being begun in 1450, is so picturesque, we hear nothing in the time of pope Nicholas fifth, of it. At Siena, our traveller it was commenced under Julio s staid, while his horses were feed. Second, in 1506, by Bramante, on ing,” and makes not an observation, the spot where the first christian except this very sensible one, “ the church was built by Constantine. Cathedral has a linsey-woolsey alio Bramante, in the sublimity of his pearance.” He now passes along genius, so projected St. Peter's, the still and retired regions of Balo that the most perfect of the ansena and Montipascone, without a cient temples, the pantheon, could single remark, though the poet be sustained by this solid super

here recommended so strongly, structure of christian faith. That . this pleasant and sweet retreat from is, that the dimensions of this ca

the cookshops, and noise, and dust thedral should be proportionable of the city.

to the dimensions of the pantheon ** Si te grata quies, et primam somnus in horam, for its dome. Delectat, si te pulvis, strepitusque rotarum, But the lines of Bramante, beSi lædit caupona, Ferentinum* ire jubebo."

ing reduced by the succeeding ar

tichects of St. Peter's, the dome We are now in the ancient capital of the world, and seem forever feet in diameter, and in 1588 Do

was consequently reduced a few to have lost our guide among ru- menico Fontana hung this bright ined temples and falling monuments. We sometimes see hiin hemisphere over that world of arleaning against a tottering column, nade, which was alterwards added,

chitectural beauties. The colonand sometimes catch him gliding (and which our author calls a through the broken arches of huge sweeping forest of 300 columns,"? aqueducts ; and so do we the lean and cold-blooded priesi, or the fat

is the splendid work of Bernini. and sweltering capuchin.

We must now confess, that we Here

have no sympathy in a single de This was an ancient town, situated between scription of Mr. S. at Rome, and Montefioscone and Viterbo.

we can remain with him there na Vol. III. No. 2. M

Horat.

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