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و في الحي احوي ينغض الهرا شادن ضظاهر سطي لولؤ وزبرجد
which, in classical prosody, would run thus:
Wáfi'l hai | iš wāyān 1 fõdho'lmērol | ăshadinon
There played; and plucked the berry's purple spray.' All these different branches of superabundant metre were nevertheless disapproved, as equally inelegant, unfortunate, and even monstrous; and Claudio Tolomei contrived a new order of versification, and one which, in the language of Ruscelli, was to have listed poetry out of the hands of artisans, women, and children, and effectually discriminated the liarned from the unlearned. This consisted in a re-introduction of the old Latin harmony and cadence, and especially in the use of the hexameter and pentameter verse. The plan of Tolomei was adopted and followed, for some time, by many of the literati of his age: but this also gradually fell into dis-use, as inconsistent with the genius of the l'uscan tongue.
Mr. Crescembini now proceeds to a description of the different orders of versification admitted in the present, or rather in his own day. These he divides into the two grand classes of blank verse (versi sciolti) and rliyme; respecting which, we unite with him, in believing the latter to have been the elder of the two. The former he subdivides into three species—that of hendecameter, or of cleven syllables, which, notwithstanding the rival claims of Giovanni Rucellai, Sannazzaro, or even Luigi Alamanni, was, in all probability, the invention of Trissino, towards the beginning of the sixteenth century; hendecameter; with a redundant syllable, or the surucciolo, which our author attributes to Ludovico Ariosto, who was contemporary with Trissino; and that in which the hendecameter and heptameter, or verses of eleven and seven syllables, are intermixed, which was also introduced about the same period, but by a disputed inventor. Rhyme-poetry, among the Italians, both is at present, and always has been, more common than blank verse. Mr. Crescembini divides it into regular and irregular, both being of nearly equal standing, and almost as old as the very commencement of vulgar Italian poetry of any kind. The tide of opinion, however, ran so much in favour of regular rhyme, in the earlier æras from their common birth, that, towards the close of the fifteenth century, it had almost supplanted its rival upon every occasion: the Canace of Speroni at this period, nevertheless, tecalled it into notice; and Alessandro Guidi has given it a fashion which it will not readily lose. Regular rhyme has; nevertheless, been at all times more common, and conceived to possess a higher degree of perfection. Mr. Crescembini divides it into two classes: the one with invariable, the other with variable, harmony; meaning, by the former, those compositions in which verse corresponds with verse, rhyme with rhyme, and even pause with pause; and, by the latter, those in which the correspondence of pause with pause is dispensed with. It is the first which constitutes the true perfection of Tuscan poetry, and which, under the form of terzets, quartets, quintets, sestines, and octaves, has been, with but few variations, applied to all Italian canzoni and canzonetti, sonnets, simple and duplicate ballads, and madrigals.
Our author closes his first book with a brief account of the different styles of writing which were progressively adopted by the bards of his own country, from the earliest origin of vulgar poetry, to the æra in which he wrote himself. He observes, that, after the rude and unadorned diction of the earliest poets of Italy, the language acquired its first appearance of dignity under the plastic hands of Guido Guinizelli, by the introduce tion into his rhymes of the sentiments of the Platonic school; and, immediately afterwards, by the exertions of Dante, who made it a language of philosophy; but that its prime reputation and glory were derived from the labours of Cino da Pistoia and Pe. trarch, and especially of the latter, who gave it its finest and most laboured polish. This polish, however, from the depraved taste of subsequent ages, it has frequently been in danger of losing: it continued to lose it, till the age of Lorenzo de' Medici, who, in conjunction with Agnolo Poliziani, restored it to all its splendour. It shortly afterwards, however, sustained a still deeper decline, by the barbarous intermixture of the Lombard with the Tuscan dialect, and the absurd and affected orthography of Tia baldeo, Cornazanno, and many others of the same school; and seldom recovered much of its essential glory, till the age of Bembo, Guidiccioni, Sannazzaro, Casa, and their illustrious coevals of the sixteenth century. Finally, it received its utmost purity and exquisite appropriation to heroic subjects, from the immortal genius of Ariosto, and of Torquato Tasso
The remaining books, which treat of the different erders, together with their respective regulations, of the compositions which have been derived from the Provençals, of those invented by the Italians themselves, and the laws to which they are subject, are so truly vernacular, that we could scarcely hope to render an epitome of them acceptablc to the English reader. They are, in every instance, however, most exquisitely diversified by examples, selected with equal erudition, precision, and taste, and offer to the student of the Italian tongue a CRIT. Rey. Vol. 38, August, 1803.
frivolities, absurdities, and defects, have uniformly attached to it.
• There is reason, however, to think that the author would have rendered it much more interesting, and have carried it to a higher de. gree of perfection, had he lived in an age more enlightened and better informed in regard to the mathematics and natural philosophy. Since the death of that mathematician, indeed, the arts and sciences have been so much improved, that what in his time might have been entitled to the character of mediocrity, would not at present be supportable. How many new discoveries in every part of philosophy? How many new phænomena observed, some of which have even given birth to the most fertile branches of the sciences? We shall mention only electricity, an inexhaustible source of profound reflection, and of experiments highly amusing. Chemistry also is a science, the most common and slightest principles of which were quite unknown to Ozanam. In short, we need not hesitate to pronounce that Ozanam's work contains a multitude of subjects treated of with an air of credulity, and so much prolixity, that it appears as if the author, or rather his continuators, had no other object in view than that of multiplying the volumes.
• To render this work, then, more worthy of the enlightened age in which we live, it was necessary to make numerous corrections and considerable additions. A task which we have endeavoured to discharge with all diligence.' Vol. i. p. vi.
With such a determination, and with such means to execute it as M. Montucla possessed, it was impossible that such a work should pass through his hands without obtaining considerable improvement. He threw the whole into a new form, correcting the absurdities, and rejecting the frivolities, which Ozanam, or his editors, had introduced; and not only arranged, in a more judicious order, the materials which lay before him, but, from his own capacious stores, supplied others of equal value and importance. In this state of the work, it was deemed worthy of an introduction to the British public; and, accordingly, the translation was undertaken by the present editor, who has both improved the work by his own emendations, and increased its utility by the addition of a variety of interesting articles. An early edition of the • Récréations' was, indeed, translated into the English language many years since; and we have also seen a little volume under this title, published at least a century ago, which, though in itself curious and amusing, is, in comparison with the volumes now before us, triAing and contemptible.
We now proceed to the contents of the present work. The first volume is occupied by arithmetic and geometry. Of arithmetic, the different kinds and systems are explained ; aná accounts are giver of the most singular properties of numbers, short and curious modes of computing by arithmetical machines, and Napier's rods. The principles of combinations and progressions are laid down with clearness and precision, and exemplified in a great variety of curious problems resulting from the subjects, with a selection of examples for exercise. These are followed by political arithmetic, including whatever is most interesting with regard to population, the duration of human life, &c. In geometry, we meet with the various properties, constructions, transformations, and measures, of geometrical figures; the quadrature and rectification of the circle; a number of remarkable problems respecting the lunules of Hippocrates, &c. The volume terminates with a collection of very curious problems, without demonstrations, for the purpose of exercise. M. Montucla observes, very justly, that they are rather simple and elegant, than difficult; although some of them are not unworthy the attention of the experienced geometrician or analyst.
From this volume we select the following extract, by way of showing the manner in which the work is executed. The author, after treating of the different kinds of arithmetic, thus remarks on the duodenary system, or that formed upon a series of twelves, as the system now in use is founded upon a series of tens.
. It is nct improbable that the duodenary system would have been preferred had philosophy presided at the invention; for it would have been readily seen that twelte, of all the numbers from 1 to 20, is that which possesses the advantage of being small, and of having the greatest number of divisois; for there are no less than four divisors by which it can be divided without a fraction, 2, 3, 4 and 6. The number 18 indeed has four divisors also ; but being larger than 12, the latter deserves to be preferred for measuring the periods of numeration. The first of these periods, from 1 to twelve, would have had the advantage of being divisible by 2, 3, 4, 6; and the second from one to 141, by 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 49, 72 ; whereas, in our system, the first period, from 1 to 10, has only two divisors, 2 and 5 ; and the second, from one to a hundred, has only 2, 4, 5, 10, 20, 25, 50. It is evident, therefore, that fractions would less frequently have occurred in the designation of numbers in that way, namely by twelves.
But what would have been most convenient in this mode of numeration, is that in the divisions and sub-divisions of measures, it would have introduced a duodecimal progression. Thus, as the foot has by chance been divided into twelve inches, the inch into twelve lines, and the line into twelve points; the pound would have been divided into twelve ounces, the ounce into twelve drams, and the dram into twelve grains, or parts of any other denominations; the day would have been divided into twelve equal portions called hours, the hour into twelve other parts, each equal to ten minutes, each of these parts into twelve others; and so on successively. The case would have been the same in regard to measures of capacity.
Should it be asked, what would be the advantage of such a division ? we might reply as follows. It is well known by daily experience, that when it is necessary to divide any measure into three, four, or six parts, an integer number in the measures of a lower denomination cannot be found, or at least only by chance. Thus the third or the sixth of a pound averdupois does not give an exact number of ounces, and the third of a pound sterling does not give an integer number of shillings. The case is the same in regard to the bushel, and the greater part of the other measures of capacity. These inconveniences, which render calculations exceedingly complex, would not take place if the duodecimal progression were every-where followed.
"There is still another advantage which would result from a combination of duodenary arithmetic, with this duodecimal progression. Any number of pounds, shillings, and pence; of feet, inches, and lines ; or of pounds, ounces, &c. being given, they would be expressed as whole numbers of the same kind usually are in common arithmetic. Thus, for example, supposing the fathom to consist of twelve feet, as must necessarily be the case in this system of numeration, if we had to express 9 fathoms, 5 feet, 3 inches, and s lines, we should have no occasion to write yf. 5f. 3in. 8li. but merely 9538; and whenever we had a similar number expressing any dimensions in fathoms, feet, inches, &c. the first figure on the right hand would express lines, the second inches, the third feet, the fourth fathoms, and the fifth dozens of fathoms, which might be expressed by a simple denomination, for example a perch, &c. In the last place, when it might be necessary to add, or subtract, or multiply, or divide similar quantities, we might operate as with whole numbers, and the result would in like manner express, according to the order of the figures, lines, inches, feet, &c. It may easily be conceived how convenient this would be in practice.' Vol. i. P.. 5.
Notwithstanding all these advantages, and though philosophy might, if at first appealed to, have established such a system as this, we conceive it not very likely that the deep-rooted customs and prejudices of mankind will ever be so far removed, as that they will be persuaded to adopt the duodenary arithmetic in the place of those methods which time has conses crated, and practice made familiar.
The subjects of the second volume are mechanics, optics, acoustics, and music. On the first of these we meet with a great number of well-selected and interesting problems, with the general principles of the science, and accounts of the most celebrated machines. A valuable history is also given of the attempts which have been made to produce a perpetual motion, in the course of which many curious facts relating to the subject are developed, Water-wheels, steam-engines, celebrated clocks, &c. as the next objects of consideration, are described with ability, and explained with clearness.-In optics, the most material discoveries are detailed, and applied to many curious purposes. Under the heads acoustics and music are included the principles of the formation and propagation of sound, the