No. 114.]

lian's expedition into Perfia, defcribes, with his ufual force of painting, the entire deftruction of "three stately palaces, laboriously enriched with every production that could gratify the luxury and pride of an eastern monarch." After which he makes the reflection, that these wanton ravages need not excite in our breafts any vehement emotions of pity or refentment. "A fingle naked ftatue, (fays he,) finished by the hand of a Grecian artist, is of more genuine value than all thefe rude and coftly monuments of barbaric labour."

I reperufed this paffage juft after viewing, with great delight, Mr. Daniell's Exquifite Views of the remains of ancient Edifices in Hindoftan; and it led me to confider, with some attention, the foundation of Mr. Gibbon's f-ntiment, as far as it related to the comparison of different works of art. It appeared to me, that the purposes of thofe arts, which have not mere utility for their object, might be claffed under the two heads of imitation and creation; and that the true mode of estimating the respective value of productions in the two claffes, was, to examine the nature of the ideas acquired by the mind on the view of each. Simple imitation, if execured in a perfect manner, excites, in the first place, a fenfe of admiration of the fkill of the artift, which is doubtless a pleafing emotion, and connected with enlarged ideas of the human powers. But the effect of an imitation muß firally depend upon the thing imitated; and if that be either void of intrinfic beauty or grandeur, or fuch as is rendered indifferent to us through frequent occurrence, it cannot be faid that the mind has made any confiderable acquifition by contemplating it. The Dutch fchool of painting abounds with objects of this kind. We are truck with the accuracy with which a carpet, or a piece of household-furniture, is reprefented, and wonder at the skill and labour bellowed on a head, in which every hair MONTHLY MAG. No. 114.

and wrinkle is exactly delineated; but, after all, nothing is produced except a likeness of realities which every where meet our eyes. Now, what is the naked

but, for the most part, an imitation of this kind? I know I fhall be told of Apollos and Venufes which furpafs in grace and beauty all ideas of the human form that can be derived from the observation of real nature. But, not to fuggeft that fuper-human figures are in fome fense a-kin to monfters what are the gladiators, athletes, dancers, litening-flaves, &c. which are the admired productions of Grecian art, but forms of common life transferred to marble? Exquifite skill, indeed, is difplayed in thefe imitations; but the fkill of the artift is the only impreffin which they convey to the mind above the fame figures in flesh and blood. It is a great mistake to fuppofe that the taste of Greece itfeif was fo fimple and chastised as to be content with fuch performances.— When its artists meant to elevate and astonish, they did not confine themselves to common materials and every-day models. The most celebrated works of their great fculptors, which were confecrated to religion, and intended to inspire the sublimelt emotions, were of coloffal dimenfions, and richly decorated with gold and ivory.

In the estimate of art we may therefore allow creation the procedence over imitation. Belides the novelty that always accompanies attempts to create, an unlimited fcope is afforded for all the beauty and grandeur that the mind is capable of conceiving. I prefume, that Mr. Gibbon could fcarcely have hesitated to place a Grecian temple higher in the scale than a Grecian ftatue. What the architecture of the palaces of King Sapor was, he knew as little as myfelf; and his epithet of barbaric is no more than claffical cant. But if they bore any resemblance to that ftyle of oriental building, of which Mr. Daniell has given us fpecimens of fuch remote antiquity, neither greatnefs of defign, nor fanciful variety of ornament, could be wanting to them. And, I prefume, few Το

curious

curious obfervers of ancient art, in the leaft emancipated from the prejudices of early education, would regard with indifference or contempt any fubfifting relics of an age and country which we know to have been far advanced in civilized luxury. There is fomething in magnitude of dimenfions alone which expands the mind, and aggrandifes our ideas of human power; and, in that view, the existence of the Egyptian pyramids, little as they imply of refined art, is of more value to the Speculatift than that of any fingle remain of painting or fculpture. But when magnitude is united with useful and ornamental contrivances, all confpiring to a great whole, devoted to purpofes of fplendour and magnificence, it is petty faftidiousness to regard the work with contempt, becaufe it deviates from thofe models which have obtained the exclufive admiration of local and artificial tafte. There appears to me an intrinfic beauty in the domes, fpires, and pinnacles, of an oriental ftructure, depending upon principles anterior to all architectural rules, which it requires only eyes and imagination to perceive. Thefe principles are the love of novelty, which is gratified by the creation of objects of which nature and common art afford no examples-the fenfe of fublimity, called into exertion by the vast height and extent of the edifices the perception of elegance, grace, lightnefs, and variety with uniformity, which is excited by the fine invention which many of them difplayand, finally, the reflex fentiment of human power, art, and civilization, carried back to remote periods, which they cannot fail to fuggeft to the speculative mind.

PREFACE.

IN the name of God, clement and merciful. Praife and thanksgiving without end be rendered, worship and adoration without bounds be given, to the Supreme Being, the creator of the elementary world and celeftial fpheres, whofe pure effence has no fimilitude nor affociate; and confequently let us pray for and implore due bleffings without number on our Mafter, the founder of our holy religion, revealed and demonftrated by the infalli bility of the feal of the Prophete and chief worthies, his kinfmen, and the primitive of Apostles. Let us alfo pray for those believers: which being accomplished, be it known, that for strength of argument, fubtility of inveftigation, and ftrictness of demonftration, geometry holds a decided pre-eminence over the other established fciences. Aftronomy, the art of menfura tion, the knowledge of the latitudes and longitudes of places, called geography, are derived from and depend on this noble fcience. By means of geometry, the art of war alfo has been brought to its present ftate of grandeur and perfection; the con ftruction of forts, trenches, and other fortified works; the plans and defigns of encampments; the digging and loading of mines; the throwing of bombs; the building of bridges and fhips: in fhort, most of the neceffaries and conveniencies of this life being connected with and having a dependence on this, admirable fcience. It becomes, therefore, an indifpenfable duty to cultivate it with the greatest care and affiduity; for, independently of its other great advantages; geometry, like logic, that ftandard of human reafon, inveftigates truth, and forms the mind to restitude, by establishing a habit of clofe thinking and accurate reafoning; yet for juftnefs and precision it is far fuperior to all the fyllogifms hitherto invented. The regularity of its firft principles, the concatena ion of its parts, the fimplicity, clearnefs, and convincing certainty, of its demonstrations, the univerfality of its application, and practical utility, being in all cafes comprehenfive and obvious. Now the books compofed by the ancients on the above-mentioned fcience, owing to the dif order and confufion of the text, are very defective and obfcure. The moderns, too, have rejected what ought to have been re

tained;

tained; and, with an idea of improve ment, have introduced many exceptionable principles, whereby the subject is rendered ftill more perplext. Of the works of the ancients, therefore, the most celebrated and univerfally esteemed is that which contains the Elements of Geometry attributed to Euclid: nevertheless, in laying down and explaining the definitions, poftulates, and axioms, he is fomewhat confuted and inaccurate. The enunciations of fome of the theorems and problems are liable to profound objections. Some paffages are fo intricate, that the meaning is altogether unintelligible, and many of the demonftrations are exceedingly lax. Moreover, by confidering attentively, it will be found that fome of the premisses are falfely affumed; many of the propofitions, as they are extant in the copies, are not legally demonftrated; and in the courfe of the work he has committed feveral paralo gifms. The method of proof, alfo, which Euclid has adopted, on fome occafions is vague and unfatisfactory; as the beft judges have fhewn by irrefragable arguments, who, after having examined with due caution, have detected the fallacy of his reafoning. Nevertheless, if there be any clue or way of deducing and inferring one geometrical truth from another, in a logical manner, as a necessary confequence, the plan and method which Euclid has ftruck out is most natural and judicious. In order, therefore, to adhere as clofely as poffible to the faid plan, both in matter and form, the present truly valuable performance was undertaken in the year one thoufand feven hundred and eighty-nine from the Nativity of Jefus, (on whom be peace,) which is the year one thousand two hundred and three, according to the date of the Retreat (Hegire,) of the most perfect Apostle. At this time one of the geometers of England, named Bonnycaftle, profeffor of mathematics and philofophy, endowed with nice and fubtile difcrimination, and pre-eminent in the fciences, actuated by a laudable defire of reftoring the Elements of Euclid, and of rendering the subject more familiar and perfpicuous, by avoiding a needle's prolixity, and omitting fuch propofitions as are of no immediate utility, and by fubAituting others which have an evident connection, has abridged the most effential parts of the science, and has, at the fame time, preferved methodical precision and rigour of demonftration, and has pointed out and rectified, with fcientific candour, feveral errors which occurred in the work. The art of menfuration, and the

properties of numbers, not appertaining to pure geometry, are rejected; and thofe books, at the end of Euclid, which treat of the five Platonic bodies, not being of any very extenfive ufe in their application, are here omitted,

The above work being, as it were, melted down in the crucible of the underftanding, like pure gold freed from its base alloy, confifts of eight books of pure gecmetry, brought into a fhort compass, and rendered quite clear and familiar; and in the opinion of the learned, the work is unequalled for general utility and facility of comprehension.

The above-mentioned book contains, indeed, the elements of geometry only; yet it is manifeft that from thence the principles of the art of war, the arrangement of military ftores, the management of artillery, the defence of the frontiers and fortified places, and the most effectual means of refifting the mifchievous attacks of an enemy, with innumerable other folid advantages, may be ultimately deduced.

The fupreme Lord and Ruler of the univerfe, whose works and decrees are begun and executed in beautiful order and fublimity, whofe effence is infinite, having in his boundless wildom thought fit to give stability to the religion of Islam, and rettore order to the ever-enduring empire, did by his divine favour raife up an Emperor with the youthful fortune of the wife Darius, Lord of the Khalifate, poffeffed of found judgment, viz. a Sultan of the race of Sultans, Sultan Selim Khan the Third, fon of Sultan Mustafa Khan the Third, fon of Sultan Ahmed Khan the Third; may God grant him long to live and gloriously to reign; and may God prelerve his empire and his fubjects, and give authority to his, and stability to his ordinances, till the end of time. This Malter of the world formed the gracious and beneficial defign of difciplining his troops, and of introducing falutary regulations into the war-department; which matters depend chiefly on geometry for their expianation: and as the above-mentioned books were compofed in the English language, this must also be known, previous to deriving from the work any advantage: in order, therefore, to extend its ufe allo to the Mufulman regions, this humble, deficient Selim, the geometrician, your fervant, having in my youth studied the mathematics under the above mentioned mas ter, as a fpecimen of what I had learnt, did purpofe to tranflate the faid book: but the Turkish not being my native language, I was obliged to have recourse to

Ttz

the

the affistance of some one of the country, fkilled in geometry, that by confulting him I might make ufe of appropriate terms, corect the folecifms, and contruct the phrafes according to the true idiom of the language, which perfon is Hufein Rifky, native of Taman, fecond fub mafter of the well appointed new mathematical academy; and in concert with him, by God's help, it was tranflated into the Turkish language; and folely by dint of the good fortune of the King of Kings, to whom all princes bow the neck, and by the encouragement and protection of his Imperial Majefty, which fertilizes and bings to maturity, the work is now brought to a happy conclufion. Thofe readers who have a just tafte, and right notions of things, will confider, that, owing to the frailty of human nature, no book but that of God alone can be perfect; therefore if they happen to meet with any faults or obfcurities, we hope they will have the goodnels to correct and amend them.

It remains to fay, that, befiles bestowing the greatest care and attention which lay in our power in the compofition and arrangement of this Tranflation, we have alto made an addition thereto of fome new and ufeful propofitions. Several objections and critical remarks, which have hitherto escaped the notice of commentators, are placed at the end of the book: there. fore those students who wish to have a true idea of the science, and of the unexceptionable principles on which it is founded, ought carefully to confult what is there written for their inftruction. So farewel.

The First Book of the Elements of Geometry. Be it known, that every science has its fubject, principles, and theorems.

The fubject of a fcience is that which treats of its effential properties; accordingly the fubject of geometry is magnitude, exifting by the effential properties of continued quantity.

The principles of a fcience are thofe things which are requifite for establishing the theorems, and thefe are of two kinds. The first kind are the ideal principles, i. e. the definitions of fuch terms as are ufed in that fcience. The fecond kind are the fyllogiftic principles, which arife from the arrangement and comparison of the propofitions themselves. Now if thofe propofitions are felf-evident, they are call. ed axioms; but if they are not self-vi dent, yet nevertheless are easily and rea fonably conceived to be poffible, then they are called poftulates and if fome

propofitions are admitted with doubt and hesitation, until demonstrated in their proper places, they are called anticipated propofitions; and from thefe anticipated propofitions, how much foever others may have made ufe of them, yet as they are not held in efleem or repute, this book is entirely free.

The theorems of a science are those propofitions, wherein, by means of the ideal and fyllogiftic principles combined, we inveftigate certain properties.

In grometry the faid propofitions are either practical or speculative: the practical requires the previous conftruction of fomething unfinished, and afterwards to demonftrate it: the fpeculative requires only the demonftration of fomething that is already constructed.

Now as every book whatsoever refts neceffarily on its ideal and fyllogiftic principles, therefore this book alfo muit reit on the definitions, axioms, and poftulates ; which being the things requinte in gea. metry, we have above explained; and fo God help us through,

By the affiftance of the Lord of the Univerfe, the work which we had undertaken, draws near to a conclufion; and it is evident, from the preceding remarks, how much the Elements of Euclid have been vitiated and spoilt by unskilful editors. Whoever attentively confiders and reflects on the above blemishes, will be furprised and difgufted at the indecent behaviour of thofe people, who, without any capacity or requifite abilities, pretend to teach others; and who, not knowing even the principles of the Icience, and unable to comprehend even the fimpleft the orem in geometry, pick up here and there a few practical rules, and, throwing them together in a loose disorderly manner, arrogate to themselves the title of fçavans. Such men, inftead of affuming unbecoming airs of importance, fhould first learn the moral duties of modesty and decorum. — Now in order to form a true and decided judgment whether a propofition is or is not legally and fcientifically demonftrated, the rules of logic fhould be known previously to commencing the ftudy of geometry. The greater part of those who begin to learn the Elements, content themselves generally with barely knowing fomne of the properties of the figures, without Y y troubling

troubling themselves to investigate in what manner thofe properties have been demonAtrated to exist, for which reason they remain always in ignorance, and confequently liable to error. But as this Work has corrected the faults, and removed the blemishes, which were in Euclid, and as it was undertaken in order to ferve as an introduction for those who wish to know the reason of things, and who earnestly defire to make a progrefs in the mathematics and natural philofophy, as they are now taught, by means of demon@ration and experiment, we hope for their fakes that the trouble we have had in tranflating it will not prove altogether ufelefs, and that it will prove acceptable to all thofe capable of diftinguishing a ftri&t and legitimate demonftration.

It remains to fay, that a more comprehenfive and fcientific form might have been given to this book; but as it was particularly defigned for the ufe of beginhers, the advantage of the prefent method appeared fuperior to every other confideration.

While preparing and arranging this Tranflation, we examined and collated with it the Elements of Euclid, by Nafired-din Touly; when it appeared that the foregoing remarks and objections were equally applicable to that Work also.

To the Editor of the Monthly Magazine.

A

SIR,

Confiderable time ago, I read a letter from one of your Correspondents, complaining of the fufferings endured in a journey, from the difproportionate fize of a frage-coach to the paffengers it carried. It might have been expected that the nofice of fo frequent an evil would have been followed by fome propofals for redress; but, in fact, fupineness in matters of public concern is one of the characte riftics of this country; and almost every one calculates whether it is not better for himself to fubmit to an inconvenience, than to take any trouble in preventing its recurrence to himself and others. For my own part, I confefs that it is only the ftimulus of pain not yet forgotten, that has induced me to take up the subject.

A fhort time fince, I entered the fifth into a stage coach, (I shall openly name it-the Luton and Ampthill.) One fide was fo completely filled by two tolerably bulky perfons, that no doubt was left which I was to take. With difficulty I fqueezed in the midft of the other two,

and was thrown fo forwards, that I not only fat very ill at eafe, but touched the oppofite feat with my knees. It was agreed by all, that to have placed a fixth would have been impoffible; yet we were under continual alarms left our coachman fhould force another upon us. I need say little of the cramps and aches endured in riding thirty or forty miles under fuch circumitances. They completely deftroyed the pleafore I fhould otherwife have derived from an agreeable fet of compa nions. Now, I think it cannot be denied, that to take an adequate price for conveying paffengers from place to place, and not to provide the means for doing this with a reasonable degree of comfort and conve nience, is downright impofition. The perfon who takes his place, can know no. thing of his accommodations beforehand, and has a right to expect that the space provided fhould bear a proportion to the number carried, and that fix are not, by dint of cramming, to be compressed into the room of four. It is furely no trifling confideration, that not a day in the year paffes in which numbers of public vehicles go out from, and arrive at, London, with companies of paffengers, the comfort of whofe journey is entirely des troyed by fuch unjuit treatment.

I am not much of a projector, but I am tempted, Sir, on the prefent occafion, to abler Correlpondents may confider and offer a remedial plan, which fome of your improve. Let all the ftage-coaches going from London be placed under the inspec tion of the commiffioners of hackney coaches, for the purpose of enforcing a certain dimenfion of infide length and breadth, accommodated (according to fome fair and reasonable calculation,) to the propofed number of paffengers. Let every fuch coach be obliged, under a hea vy penalty, to have on the outfide, in a confpicuous place, a fmall plate, (ftamped by the office,) indicating the number it is to carry, and let all paffengers be entitled to refilt any attempt on the part of the coachman to introduce more. A fmall fee for the admeasurement and plate would be a fufficient recompence for the trouble incurred by the office: indeed, confidering the heavy taxes already levied on every mode of travelling, it would not be much for Government to confer fuch a benefit on the public gratis.

I flatter myself fome attention will be paid to this propofal. In the meantime you may depend upon it, Mr. Editor, that whenever I again meet with a fimilar im

pofition,