this part of the work the Editor has made ample ufe of the Dif
quifitiones Pliniana of Count Rezzonico, a Venetian nobleman,
who published, not long ago, an excellent Italian translation of
Pliny. The whole will be concluded by three tables. The
firft will contain the names which Pliny has given to the dif-
ferent productions of nature, and, in a parallel column, the
names that are appropriated to the fame productions in the sys-
tem of Linnæus: and the second and third will exhibit a lift
of the ancient authors which have been illuftrated in the notes,
or quoted by Pliny.

M.

MONTHLY CATALOGUE,
For MAY, 1778.

MATHEMATICS and PHILOSOPHY.

Art. 15. Mathematical Principles of Natural Philofophy. By Sir
Ifaac Newton, Knight. Tranflated into English, and illuftrated
with a Commentary. By Robert Thorp, A. M. Vol. I. 4to.
11. I S. Cadell. 1777.

HIS firft volume of Mr. Thorp's tranflation of the Principia T comprehends the first book of that immortal work. The commentary with which he has enriched this verfion, part of which I is extracted from the works of Maclaurin, Saunderson, Keil, and fome other writers, is added with a view to fupply those demonftrations which the Author had omitted, on the fuppofition that they were previously known; to point out the extent and limits of problems; and to fhew their practical ufe and application to the fyftem of the world.'

That the Reader may receive benefit from this commentary, the
Editor requires only that he should be perfectly well acquainted with
the geometry of Euclid, the elementary parts of algebra, and a few
view to elu-
of the primary properties of the conic fections. With
cidate the ufe and tendency of the most abstract propofitions, feveral
corollaries and philofophical Scholia are added: and as the Synthetic
form of demonftration is best suited to those for whofe ufe the com-
mentary is intended, Mr. Thorp has, in his notes, adopted the geo-
metrical ftyle of the Author. He has, however, occafionally made
ufe of the Author's method of fluxions, which he has employed in

a few analytical demonstrations of fome of the principal propofitions. B.y
Art. 16. The Elementary Parts of Dr. Smith's Complete Syftem of

Optics, felected and arranged for the Ufe of Students at the Uni-
verfities. To which are added, in the Form of Notes, fome Ex-
planatory Propofitions from other Authors, 4to. 10s. 6d. fewed.
Nourfe, &c. 1778.

The fcarcity of Dr. Smith's Complete Syftem of Optics having been
long a fubject of complaint, particularly at the univerfities; and
there being no appearance of a speedy republication of the whole of
that excellent treatife: the prefent Editor, who dates his preface
from St. John's College, Cambridge, was induced to abridge and
digeft the elementary parts of that work into a regular fyftem; and

tq

to

1

arrange them in fuch order as should beft correfpond with the plan
of lectures given by the tutors in that univerfity; not without a
view, at the fame time, of adapting his performance to the ufe of
others who may wish to be inftructed in the first principles of optics.
The Editor appears to have executed this talk with judgment; and
his demonstrations are fufficiently perfpicuous to be understood by
those who are acquainted with the mere rudiments of geometry.
Art. 17. Defcription of an Engine for dividing Mathematical In-
fruments. By Mr. John Ramfden, Mathematical Inftrument-
Maker. Published by Order of the Commiffioners of Longitude.
410. 5 s. Nourfe. 1777.

The Commiffioners of Longitude having, on certain conditions,
paid Mr. Ramfden the fum of 6151. as a reward for the improve-
ments made by him in the art of dividing mathematical inftruments,
by means of a particular engine, and for affigning over to them the
right and property of the faid engine, for the ufe of the Public: Mr.
Ramfden has, in this pamphlet, given a full defcription of the ma-
chine, and of the manner of using it; together with a description of
another engine, by which the endless screw, which is a principal part
of the dividing engine, is made. These descriptions are illuftrated
by four plates, in which the different parts of the apparatus are.
delineated on a very large scale.
Art. 18. A Difcourfe on the Invention and Improvements of the
Reflecting Telescope, delivered before the Royal Society, Nov. 30,
1777. By Sir John Pringle, Baronet, Prefident. 4to. I s. 6 d.
1778.

Boy.

Sir Godfrey Copley's prize medal having been adjudged to Mr.
Mudge for his excellent paper containing directions for making the
beft compofition for the metals of reflecting telescopes, and for grind-
ing and polishing the great Speculum, and giving it the true para-
bolic form; the Prefident gives a concife hiftory of the invention of
that noble inftrument; and fails not to beftow on Mr. Mudge thofe
praises to which he feems fo juftly intitled, for the improvements he
has made in the different proceffes that relate to it, and for his dif-
interefed and liberal communication of them to the Public.
Art. 19. A Treatise concerning Porifms. By Robert Simfon,
M. D. In which the Author hopes that the Doctrine of Parisms is
fufficiently explained, and, for the future, will be safe from Ob-
livion. Tranflated from the Latin' by John Lawson, B. D. 4to.
2s. 6d. Printed at Canterbury, and fold in London by Nourse.
3777.

The porifms of Euclid, contained in three books, were a curious
collection of many things which related to the analysis of the more
difficult and general problems, and were distinguished, according to
Pappus's account of their nature, from theorems in which fomething
was propofed to be demonftrated, and from problems in which
fomething was proposed to be constructed, as in these something was
proposed to be inveftigated. Nothing remains in the works of the
ancient geometers concerning this fubject befides what Pappus has
preserved in his mathematical collections. The celebrated D. Gre-
gory, in the last page of his preface to Euclid's works, expreffes his
opinion," that it would not be difficult in fome measure to restore
the porifms, when the Greek text of Pappus fhould fee the light;"

but

B.Y.

but Dr. Halley, after having published this Greek text in as correct
a ftate as poflible, defpairs of applying the information it contains
to any important and ufeful purpose. Pappus's general propofition
is very imperfectly and obfcurely flated; the first porifm of the first
book is the only one which he has preferved entire; and on this ac-
count mathematicians were difcouraged from purfuing an inquiry
into a fubject, of which there were only fome few confufed traces re-
maining. However Dr. R. Simfon undertook the difficult and labo-
rious investigation, and fucceeded beyond his own expectations. The
firft fpecimen of his labour in this way was published in the Phil.
Tranf. for 1723, No. 377. See Abridg. vol. vi. part 1, p. 76, &c.
Fle afterwards purfued the inquiry, and in a pofthumous work which,
among other pieces, was printed at the private expence of the Earl
Stanhope, premifed fome eafy porifms to the explication given of
them by Pappus, and fubjoined fuch of Euclid's porifms as he could
distinguish to be his; to which he added feveral other propofitions
of a milar nature. The publication before us is a translation of
part of this work, which Mr. Lawfon has undertaken with a view of
making it more generally known: and he propofes to compleat his
defign in three other numbers of the fame kind, if he meets with
fufficient encouragement merely to defray the neceffary expence at-
tending the publication.

GEOGRAPHY.

Art. 20. Geographical Exercifes, calculated to facilitate the Study of Geography, and by an expeditious Method to imprint a Knowledge of the Science on the Minds of Youth. With a concife Introduction, explaining the Principles of Geography. By William Faden. Folio. 15 s. Printed for the Proprietor, Succeffor to the late Mr. Jeffries, near Charing-Crofs.

Thefe Exercifes confit of nine maps, judiciously felected and neatly engraved; and of as many correfponding theets, with the fcales of longitude and latitude, together with the meridians and latitudes upon them; which are to be filled up by the fcholar with the coals, boundaries, rivers, provinces, &c. of the oppofite map. The utility of exerciting young perfons in drawing maps is fufficiently evident and this performance may contribute much to facilitate the acquifition of a science which it is thameful to be ignorant of POLITICAL.

R.S.

B.n.

Art. 21. Two Letters from Mr. Burke to Gentlemen in the City of
Bristol on the Bills now depending in Parliament, relative to the
Trade of Ireland. 8vo. 13. Dodfley. 1778.

Mr. Burke having concurred with adminiftration, in favour of the bills above alluded to, on general [perhaps too general] principles of fair, open, national commerce, (confidering the Irish as a part of ourfelves) and regardless of the particular objections made to those bills by the merchants of Bristol, Liverpool, Glafgow, &c.-Murmurs were, confequently excited amongit his constituents, of the firit mentioned

•

What those objections are, does not particularly appear in these Letters; but they may be feen in every news-paper; and they feem to have weight fufficient to merit Mr. B.'s utmost attention.

city,

city, who complained that they could not have him for their advocate. On this occafion, Mr. B. deemed it neceffary, not only to affert the independency of his opinion, and to evince the rectitude of the vote he had given, but to endeavour, alfo, to convince the gentlemen of Bristol, that the natural tendency of the Bills in queftion, would be for their benefit, on the whole, as well as that of Ireland: Since Bristol, from its peculiarly advantageous fituation for commerce with Ireland, must ever find its best account in the profperity of that Ifland,-in proportion as it is better to trade with a rich and flourishing country than with a poor one.-Mr. B. has thrown out a variety of remarks drawn from more general confiderations; efpecially from the prefent critical fituation of government, &c. for which we refer to the letters, at length.

Art. 22. A Letter to the Worshipful the Dean of Guild, and the
Merchants and Manufacturers of the City of Glafgow, upon their
Oppofition to the Irish Bills. 8vo. 6d. Fielding and Walker.
A tharp invective against the "Men of Glafgow," for their oppofi-
tion to the Irish Bills. The writer takes the liberty to remind them
of,-what he fuppofes them to have forgotten,-the former poverty
of Scotland, till that country experienced the benefit of thofe lauda-
ble principles of free, unreftrained trade, to which the merchants, &c.
of Glasgow now feem to have fo many objections, when it is propofed
that other parts of his majetty's dominions fhould, in their turn, re-
ceive the like advantages-There is more of fatire than of argu-
ment in this little piece; the author of which has contrived to intro-
duce the following itory, of a proclamation made, in former times, by
the Town-Cryer of Innerkeithing, viz.

"Awe ye gude fowk o' the toun of Innerkeithen; this is to let ye wat that there is cum to this toun the day, a beaft called a lamb: the laird o' the manor is to ha' the first quarter, the provoft is to ha' the fecond quarter, and the minifter is to ha' the third quarter: the heed and the harigals.gaes to the baillie. I Johnny Bell is to ha' twa fma' puddings for cawing; but if nae body ipiers for the lave o' the beaft, it will no' be kill'd the day."

The author fays he was furnished with the foregoing notable oration, by refpectable authority ;'-but he modeftly adds, I vouch not for its truth.'-How many good jefts are fpoilt by that ugly word fact !

Art. 23. A Letter to the Hon. Mr. Chs F-x, upon his proceeding in P. -t, on that memorable Day, Feb. 17, 1778. 8vo. Is. Fielding and Walker.

Arraigns the conduct, and questions the abilities of Mr. Fox; grounding his impeachment principally on what the Letter Writer terms the miferable' fpeech of this celebrated young orator, in reply to the minifter, when the latter publicly made that full and memora ble recantation of his political errors, in the unhallowed chapel of St. Stephen.'-Good heaven! fays he, what materials were there bere [you fee, reader, it is but an here and there kind of flyle in

•

It is for you, and for your intereft, as a dear, cherithed, and refpected part of a valuable whole, that i have taken my flare in this quellion.

which

which this gentleman writes] for one of the most masterly Philipptes that ever touched or acted upon the heads and hearts, of men! And the ground, throughout fo ftrong and obvious, it seems to have needed but small ability or art to feize it. Real patriotic feelings could not poffibly have refifted taking it. Your private line of interested purfuit, one cannot but think, of course, would dictate it and your perfonal animofity to the man could leave no room to doubt, how much you wished him down: and yet you let this great occasion flip. To what can we ascribe this?-How poffibly account for the ftrange congratulating ftrain, for acquiefcing language and promised suppart in the very moment of all others that called for your most powerful invigorated exertions, that demanded the most animated, violent, redoubled efforts of oppofition. Inftead of this, it is remarked, Mr. F. actually, himself, most unaccountably aided the very minifter, whofe removal had been the fingle object of his (Mr. F.'s) political life, and concurred in fuffering OPPOSITION to be the dupe of minifterial jockeyship, to a degree beyond all power of belief.-The author concludes, your letting go bye fo palpable an opening, [to push the minifter from his ftation] can only be imputed to the want of neceffary, quick, political, difcernment, to your incapacity, your unfitness for that character and part which your puny, ill-fupported ambition led you vainly to affume.'

On this point, and on the politics of the times, particularly the American revolt, the author enlarges, through forty pages, in which we meet with fome notable obfervations, expreffed in a manner fingularly uncouth and unpleafing. In principle, he is anti-minifterial, but not violent. He condemns the conduct of administration, as unhappily founded on one or both of the following capital deficiencies-the want of information, with refpect to the state of America, or, what is ftill worse, an ignorance of human nature: which he endeavours to evince by arguments drawn from notorious facts.-With refpect, however, to the gentleman to whom these observations are immediately addreffed, he takes leave of him in the following terms:

•Abilities, Sir, undoubtedly you poffefs-but I cannot fay that you have convinced me you have to that degree, or to that general extent, which your friends would feem to give you credit for. Appearing earlier than most characters, and the education you had received having been directed principally to the line of parliament, and under the immediate controul of one who felt not only a warm intereft in directing it, but who was fully competent to the task of giving it, being himself both an able politician, and a fuccefsful fpeaker in parliament-men were well and favourably difpofed to receive you upon the mere credit of your mafter, and you came forth with uncommon expectations and eclat-with every advantage too, for many of the old refpectable fpeakers were gone off-the remainder few retiring faft-and the diffipated manners and idle turn of the times furnished no fupply to thefe;-and thus ftanding in a manner alone and fingle-you appeared with unufual luftre-was regarded as a prodigy of parts. Your ftyle of fpeaking marked evidently the school in which you ftudied-and proved the wonderous pains and care with which you had been taught. But circumftances, partly of your own producing, partly in the courfe of nature, foon left you to yourself;

and