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puted to be 200,000; besides these, about one-fourth as may are, in Gfequence of these fisheries, employed on shore, in the building of Mips, making ners, curing the fish, &c. &c.
* Therefore, fuppofing os only to come-in for one-half of what the Dutch ensøy, we thail gain, besides emyloyment to upwards of 12,000 arificers, an acceffion of 100,000 seamen, two-thirds of whicky would be always on our coaits, ready to man aur ficets on every emer. gency. A noit noble resource !
This thews, in the strongeit manner, the absolute necolinty there is for the free import and export of grain and provifions; becaule, from this Orly, can pr:rifions and wages become lower, and upon the lownefs of these depends the accession of the riches and power attendant on ex fenfive fisheries.
* The fame causes will produce the fame effects in the Englifh and Irish fisheries, so as to enable them to contribue their tharo to the gran. deur and increase of the British maritime power."
The other objects of doinestic improvement here infifted ott, are the methods of manning the navy, the execution of the laws in Scotland, and a revition of the laws in England rc fpc&ing the poor; an object of the firft magnitude, refpe&ting the internal police of this kingdom.
The tenth and last section contains confiderations on Eat India affairs'; but, for the particulars of this, and also of the author's appendix, relative to the emancipation of flaves, we muft-refer the inquisitive reader to the performance it felf.
Treatise concerning Porisms. By Robert Simfon, M. D. Time which the Author hopes that the Doeti ine of Porisms is jufficio i ently explained, and
for the future will be safe from Oblivion. Tranfated from the Latin by John Lawson, B. D. 4to. 28. 16d. Nourse, &c.
Mr. Lawson has here only given five 'sheets of Dr. Simson's treatise; sensible of the confined sale of publications on lo abAracted a subject, though not without hopes that the lovers of geometry will encourage the translation of the whole, for the following reasons:
ift, On account of the great curiosity of the subje&t, which has lain in total obscurity and oblivion ever fince the time of Pappus Alexandrinus, as will be feen in the Preface.
2d, On account of the great abilities of the author, the late Dr. Simfon, who has always been esteemed the first geometer
of the age
Laftly, On account of the peculiar circumstance of this and the Doctor's other Posthumous Pieces, viz. that they are not to be purchased for inoney, they having been printed at the expence of that noble Patron of mathematical learning, the Right Honourable the Earl Stanhope, only to be disposed of in Prefents. • It is out of regard to the science of geometry, and to pro. duce the necessary encouragement for continuing the tranflation of this valuable work, that we shall quote the author's preface entire; well persuaded that our geometrical readers will think themselves not a little obliged to us, for some elucidation of a subject, to which many, if not moft, of them are strangers. *** There is nothing to be found among the antient geometers con. cerning Porisms, except what Pappus bas preserved. And Fermat, in his Var. Oper. Math. page 116, afferts that the Moderos did not so such as know them by name, or only guessed at what they were. Yes I find that before Fermat Albertus Girardus thought of explaining and restoring them, who, in his Trigonometry written in French and pubkished at the Hague 1629, after enumerating the forms of rectilineal figures, which have four, five, or fix fides, add this, " Le tout, quand *tn'y a que deux lignes qui passent par un point, comme jadis eftoyent jes Poriimes d'Euclid, qui iont perdus, lesquelles j'espere de mettre bien-toft en lumiere, les ayant reltituez il y a quelques années en casa Add again in the Mathematical Works of Simon Stevin, which Girardus published, amended and augmented at Leyden 1634, after he had Faid in page 459 that Euclid very seldom used compound rario, he fubjoins, “ Mais il est à estimer qu'il en a plus escrit en ces trois livres de Porisines qui font perdus, lesquelles, Dieu aidant, j'espere de mettre en lumiere, les ayant inventez de nouveau.” From which it appears thac Girardus a man uncommonly skilled in mathematics, thought that he had restored the Porifins; but what he had written concerning them was never published, and unless perhaps it lies concealed in fome library in Holiand, it is to be esteemed as loft. But from the first of "thetè quotations it seems that he took fome propositions concerning quadrilateral figures and others and their affections for: Porisins, and that therefore he did not understand their nature.
“ After Girardus Ishmael Bullialdus, in his third geometrical exercitation, which with the two former was published at Paris 1667 endeavoured to explain the Porisms; but although he received fome things concerning them from Fermat, for 'he cites Fermat's words which were afterwards printed in his renovated doctrine of Porifms among his various mathematical works at Tholofe 1679; yet Bullialdus could by no means clear up the matter. Now in this book of Fermat's which was published after his death, there are found a few things, but
it feems they are all that he had committed to writing concerning Po... rifms. From which it appears, that to this most fagacious man alone any thing was known concerning their nature from the time that Papa pus lived. But fince he confeftes that he penetrated into the fecrets of
tas matter almost without any other affistance than what he stas. fura Bigged with from that corrupt definition which Pappus juftly blames the junior geoincters for giving of a Porisin, viz. thai a Porism is that which is deficient in hypothesis from a local theorem; it is certain that he did not sufficiently understand what Porisins were. For Fermat is by no means right in affirming that this definition specifically disoo vers the nature of a Porifin, since there are innumerable Porilms whick by no means depend upon a local theorem, and have nothing common with loci. - Fermat indeed promises in the same writing that he will fome time or other restore the whole three books of Porilms, and bring to light (these are his words) other wonderful and unknown matters; but this was too rafhly spoken, for there are many of Euclid's Porisms of which there is not any step or vestige extant; and Fermat has not enucleated the first of the first book, wbich alone Pappus has preferved entire. - -* There is no occafion to relate here what Charles Renaldine has on this subject in his book De Resolutione et Compositione Mathema tica, for it is by no means subservient to the knowledge of Porisms. And these are the only authors, as far as I know, who have made any mention of Porisins, at least who have in any manner attempted to ex plain them. And though the celebrated David Gregory, in his preface
pretixed to Euclid's works, fuppoled “That it would not be difficult in fome fort to restore the Porilms, when the Greek text of Pappus hould see the light,” yet his colleague, the learned Halley, not lefs couverfant in the geometry of the ancients than Gregory, after having published the Greek text as much corrected as he could, ingenuoutling fabjoins the foilowing words to Pappus's descrip:ion ot Porisms: * Thus much for the description of Porisms, which can neither be useful.coʻme nor the reader, nor can it otherwise: both on account of the want of the scheme of which mention is made; from whence many rigt lines here treated of without any alphabetical marks, or any other characteriftic distinction, arc confounded one with another, and also because of some things omitted and transposed, or otherwise vitiated, in the exposition of the general propofition; from whence I am not able to gueis what Pappus meant. Add moreover a mode of expression too Coccife, and which ought never to be used on a difficult subject, such 13 this is.
" But after I had read in Pappus that the Porisms of Euclid were a most curious collection of many things which related to the analysis of the more difficult and general problems, I was earnestly desirous of - knowing something about them; wherefore often and by various ways * I endeavoured to understand and to restore as well Pappus's general
propofition, lame and imperfect as it was, as also the first Porifin of the first book, which, as was faid before, is the only one out of the three books which remains entire ; but my labour was in vain, for I < made no proficiency. And when these thoughts had consumed much
of my time, and at length had become very iroublesome, I firmly refolyed never to make any further enquiry for the future, especially as that best of geometers Halley had given up all hopes of understanding
them. Therefore as often as they occurred to my inind I endeavoured to put them by. Yet 'afterivards'it happened that they seized me yn
awares, forgetful of my resolution, and detained me so long till fome light broke in which gave me hopes of at least finding out Pappus's general propofition, which indeed not without much investigation 1 at length restored. Now this soon after, together with the first Porism of Book I. was printed in the Plailosophical Transactions for 1723; No. 177.
“ But because at that tiine I did not fufficiently understand the na ture of a Porism, I think proper now to deliver it more explicitly, that this kind of propofitions, and the way by which they are investigated, which geometers from the time that Pappus lived have been ignorant 'of, may be restored to geometry, and may bring no contemptible in ereale thereto. And because Pappus's defcription of Porilins is not easily to be underttood without a specimen of thein, therefore I have thought proper to premise some ealy Porisms to the explication whichi Pappus offers of them; and then to Pappus's description of them to fubjain some of Euclid's Porisms, namely, such as I could distinguish to be such, either from Pappus's general propofition, or his defcription of Porilms; or lastly, by help of his lemmas for the Porisms. After thele follow four of Fernat's propositions changed into the form of Porifins, for the remaining one of his
five is concerning the parabola; and I have demonitrated it in my Conic Sections, Prop. 19. B. V. ad Ed. There are some other things added, the chief of which were proposed to me, and the conttruction of fome of them given, by that excellent geometer, Matthew Stewart, Professor of Mathematics in the University of Edinburgh, by whom this matter has already been well, And I hope for the future will be much, cultivated."
In hopes that the learned and ingenious translator will meet with proper encouragement to coinpleat an English version of Dr. Siinlon's treatise, we reserve our opinion of its execution and importance to a future article.
Thoughts on General Gravitation, and Views thence arising as ta
the State of the Universe. 15. Cadell.
It is the general error of speculative minds to be more attentive to what passes within themselves than to the observations and discoveries of others, even on subjects of their immediate contemplation. Hence it is that these profound thinkers, after a world of reflection, make wonderful discoveries of things known to every body but themselves. Not that the present writer has made any other discovery, in the present pamphlet, than that he knows very little of the professed subject of it. The late facetious author of Tom Jones foinevhere ludicrously obferves, that cvery writer will probably treat his futject the better for knowing something about it. With this. lage remark, therefore, we take leave of this thinker of general gravitation; recommending him the next time he fits down to write on any subject, to read what has already been written is
Mount Pleafant : a Descriptive Poem.' To which is added an
Ode. 4to. 25. Johnson.
To this poem is prefixed the following inodest and pertinent preface.
“ The following Poem was written fome years ago, at a very early period of life, without the leait intention of publication. It is not however by way of an apology, that this circumstance is mentioned; the author being fully covinced, that an excuse for obtruding a new publication on the world is always superfluous ; a good one being in no need of it, and an indifferent one receiving no addition to its value, from any circumitance that can be alledged in its favour.”
Mount Pleasant is an agreeable eminence near Liverpool, which commands the prospect described in this poem. A specimen of the writer's talent for poetical description is given in the following lines.
" Far as the eye can trace the prospect round,
But leek ere night the friendly port again."
“ Far to the right, where Mersey duteous pours
And on the weaken'd fight, the long, long profpcétends."
“ Yer lovelier scenes the varied prospect cheer,
Where Ceftria's plains in long extent appear;