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very, from the 4th Geo. III. 1730, to the 40th Geo. III. 1800, by Thomas Leech, Efq. Barrister at Law, the third edition, with cerrections and additions," in 2 vols.; "Reports of Cafes relative to the Duty and Office of a Juftice of the Peace, from Michaelmas Term, 1776, inclufive, to Michaelmas Term, 1785, inclufive, part III. and laft, by Thomas Caldecott, Eq. Barrister at Law;" "a Comper endious View of the Ecclefiaftical Law, being the Subftance of a Course of Lectures read in the University of Dublin, by Arthur Browne, Efq. S. F. T. C. D. &c." vol. II.; "the Spirit of Marine Law, or Compendium of the Statutes relative to the Admiralty, being a concife and perfpicuous Abridgment of all the Acts relative to Navigation, alphabetically arranged, and the Substance and References to the feveral Claufes placed in the Margin, by John Irving Maxwell, of the Honourable Society of the Inner Temple ;"

Reports of Cafes argued and determined in the High Court of Admiralty, commencing with the Judgments of the Right Hon. Sir William Scott, Michaelmas Term, 1798, by Chr. Robinson, LL. D. Advocate," vol. I. part Il; "an Argument of Dr. Croke in the High Court of Admiralty, 27th November, 1799, in the Cafe of the Hendrick and Maria, &c. upon the Queftion of the Validity of a Sentence of Condemnation, while a Veffel is lying in a neutral Port, taken in Short Hand by T. N. Mendham;"" a Report of the Cafe of Horner against Liddiard, on the Question of what Confent is necellary to the Marriage of illegitimate Minors, determined on the 24th of May, 1799, in the Confiftorial Court of London, by the

Right Hon. Sir William Scott, Chancellor of the Diocese, with an introductory Effay on the Theory and Hiftory of the Laws relating to illegitimate Children, and to the Encouragement of Marriage in general, by Alexander Croke, Eiq. LL. D. &c.;" "the modern Prac-. tice of levying Fines and fuffering Recoveries in the Court of Common Pleas at Westminster, with an Appendix of felect Precedents, by W. Hands, Gent. one of the Attor nies of the Court;"" Memoranda Legalia, or an alphabetical Digest of the Laws of England, adapted to the Ufe of the Lawyer, the Merchant, and the Trader, by Geo. Clark, Attorney at Law;" the 19th edition of the Juftice of the Peace and Parish Ŏfficer, by Richard Burn, LL. D., continued to the prefent Time by John Burn, Efq. his Son, corrected and confiderably enlarged, including the late adjudged Cafes, and the Statutes of the laft Seffion of Parliament (39 and 40 Geo. III)," in 4 vols.; "an Abridgment of the modern Determinations in the Courts of Law and Equity, being a Supplement to Viner's Abridgment, by feveral Gentlemen in the respective Branches of the Law, vol. III.— Creditor and Bankrupt-Durefs;"

"a Treatife on the Revocation and

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Republication of Wills and Teftaments, together with Tracts upon the Law concerning Baron and Feme, including Curtefy, Dowers, Jointures, Leafes, Settlements, &c., by R. S. Deniton Roper, Efq. Barrister at Law;" "the Law of Exe cutors and Adminiftrators, by Samuel Toller, Efq. Barrifter at Law;" "the Principles of the Bankrupt Law, by Archibald Cullen, Efq. Barrister at Law, and a Commiffioner of Bankrupts;" "the Principles of Conveyancing, defigned for RA

the

the Ufe of Students, with an Introduction on the Study of that Branch of Law, by Charles Watkins, Efq;" "An Enquiry into the Laws, ancient and modern, refpecting Foreftalling, Regrating, and ingroffing, together with adjudged Cafes, Copies of the original Records, and Proceedings in Parliament, relative to thofe Subje&ts, by William Illingworth, of the Inner Temple;" "the Trial at large of John Ruby, Corn-factor, for Regrating Corn at the Corn Exchange, Mark Lane, London, 8th November laft, tried before Lerd Kenyon, and a Special Jury, in the Court of King's Bench Guildhall, the 4th of July 1800, taken in Short Hand by a Barrister of the Inner Temple;" "the Proceedings of the Houfe of Lords, in the Cafe of Benjamin Flower, Printer of the Cambridge Intelligencer, for a fuppofed Libel on the Bishop of Llandaff, &c., by the Printer; to which are added the Argument in the Court of King's Beach. on a Motion for a Habeas Corpus, and a Poftfcript, containing Remarks on the Judgment of the Court, by Henry Clifford, Efq." "A Letter to a Noble man, on the propofed Repeal of the Penal Laws which now remain in Force against the Irish Roman Catholics, 1rom Charles Butler, Efq. of Lincoln's Inn;""Confiderations on the Coronation Oath to maintain the Proteftant reformed Religion, and the Settlement of the Church of England, as preferibed by Stat. 1. W. and M. Ch. 6. and Stat. 5. Anne. Ch. 8, by John Reeves, Efq;" the Queftion as to the Ada ifion of Catholics to Parliament confidered, upon the Principie of exifting Laws, with fup. plementary Obfervations on the Coronation Oath, by a Bariifter;" "A further Supplement (ocafioned

by the fecond Edition of Mr. Reeves's Confiderations, &c.) to a Pamphlet entitled the Question as to the Admiffion of Catholics,' &c." by the fame Author; "Cafe of the Catholics confidered, and an Expedient propofed for the final Settlement of it, with an Appendix, containing Remarks on Mr. Reeves's Pamphlet:" "a fhort View of the Catholic Question, in a Letter to a Counsellor at Law in Dublin, by the Hon. Auguftus Dillon, M. P.," and "the Cafe of Confcience folved, or Catholic Erancipation proved to be compatible with the Coronation Oath, in a Letter from a Cafuit in the Country to his Friend in Town, with a Supplement in Anfwer to Confiderations on the Coronation Oath by John Reeves, Efq."

Our lift of the Mathematical Pro ductions of the year commences with "Tracts on the Refolution of affected algebräic Equations, by Dr. Halley's, Mr. Raphfon's, and Sir Ifaac Newton's Methods of Approximation, publified by Francis Maferes, Efq. F. R. S. Curfitor Baron of the Exchequer." Thefe Tracts, which are ten in number, confift of a method of finding the roots of any equation generally, and that without any previous reduction, by Dr. Halley, taken from the Philofophical Tranfactions; an Appendix to the preceding, by Baron Maferes; Dr. Wallis's Solution of Colonel Titus's arithmetical Problem, with an Explanation of the difficult Pallages that occur in it, by Baron Maferes; another Solution of the fame, by Mr. Frend; Obfervations on Mr. Raphfon's Method of refolving aff-ted Equations of all Degrees by Approximation, by Baron Maferes; an Application of Simon Stevin's General Rule to extract

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impoffible quantities, and carefully refraining from the ufe of terms that appear abfurd or unintelligible in the folution of his problems. With respect to the propriety of that meafure, the mathematical world is much divided in opinion; but to our mind the arguments in favour of it appear more fatisfactory than thofe adduced to fupport the ancient fyftem. This part of the author's work is confined to the Doctrine of Equations; which are divided into four claffes, according to the number of their unknown terms, and are all fubjected to one general rule, viz., that none in any clafs can have more roots than it has unknown terms. In the forms of each clafs, however, the number of roots depends, partly upon the co efficients, which he denominates the co-parts, and partly upon the changes of the marks of addition or fubtraction. Mr. Frend's folutions of his problems are direct, accurate, and perfpicuous; and are followed by fome general obfervations, which convey to the learner much useful practical information. On the whole, we think that his work deferves to be recommended as a valuable elementary treatife to those inftructors who wish to teach, or to thofe young perfons who with to acquire a knowledge of, the principles of algebra, in the most easy and expeditious manner.

tract one Root out of any poffible Equation in Numbers, either exactly or very nearly true, taken from Mr. Kerfey's Elements of Algebra; a Remark on an Error in the Reafoning of Clairaut, in that Part of his Elements of Algebra, in which he endeavours to prove the Rules of Multiplication laid down by Writers on Algebra concerning negative Quantities, by the Baron; a general Method of inveftigating the two, or three, first Figures of the leaft Root of an Equation, that has more than one real and affirmative Root, by the fame, and reprinted from the third Volume of the "Scriptores Logarithmici" a Specimen of Vieta's Method of refolving Algebräic Equations of any Order, or Degree, by Approximation, by the fame; and Remarks on the Number of negative and impoffible Roots in Algebraic Equations, by Mr. Frend. From tris fummary of the contents of the Tracts before us, and the well known character of the editor, the mathematical reader will be fufficiently apprifed of their value and importance. In Baron Maferes's Remark on the Error of Clairaut, he furnishes new fupport to Mr. Frend's doctrine refpecting negative numbers, in addition to what he advanced in his "Appendix to the Principles of Algebra," announced in our Regifter for the year 1798.

In our Regifter for the year 1796, we introduced to our readers the first part of "the Principles of Algebra, by William Frend." We have now to announce a fecond part of that work, entitled, "the Prin. ciples of Algebra, or the true Theory of Equations established by Mathematical Demonftration." In this continuation of his plan, the author perfeveres in fimplifying the cience by rejecting negative and

The "Analyfis Fluxionum, Auctore Guil. Hales, D. D. Rectore de Killeffandra, et nuper Trin. Col. Dublin. Socio, ac Linguarum Orientalium Profeffore," is divided into two parts. The first part treats of the Hiftory of Fluxions; in which the author neither awards the merit of their prior difcoyery to Newton, nor Leibnitz, but fuppofes that both thofe great men were led to the invention of the

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the fame principle, although differ-
ing in their conception, and ufing
different characters in their defcrip-
tion of it, about the fame time.
The bafis of the whole he makes
to be the law of prime and ultimate
ratios. The fecond part is em-
ployed in illuftrating the Method
of Fluxions. Subjoined to the work
are two appendixes. In the first
appendix we are prefented with an
investigation of the analysis of the
ancient geometricians; and, in the
fecond, with a vindication of fir
Ifaac Newton from the infinuations
of profeffor Robifon, refpecting
his doctrine of a vibrating æther,

By Alexander Ingram, Philomath."
Precluded as we are by the nature
of our work from entering into a
detail of the particulars of Mr. In-
gram's corrections and amend-
ments of the labours of preceding
editors of Euclid, we can only ob-
ferve in general, that they fhow
him to be poffeffed of that degree
of fcientific learning, acutenefs, and
accuracy, which abundantly qua-
lified him for engaging in fuch a
work, and that they cannot fail of
proving ufeful to ftudents in ge-
ometry. The Treatife which the
author has added on Plane and
Spherical Trigonometry, is judi-

and with other matter, critical, cioufly executed; as is, likewife, the tract which follows it, on Practical Geometry, illuftrated with plates, containing diagrams, &c.

In our Register for the year 1798, we noticed the appearance of the first volume of a complete Syftem of Aftronomy, by the Rev. S. Vince, M. A. F.R.S. Piumian Profeffor of Aftronomy and Experimental Philofophy in the University of Cambridge." That truly valuable and ufeful work is now completed by the publication of a fecond volume, and entitles the author to the warm acknowledgements and commendation of every English lover of the science which it teaches. For it contains the fullest, most perfect and fatisfactory information, not only refpecting plane, but alfo phyfical aftronomy, that has yet appeared in our language. And with respect to the manner in which it is executed, the teftimony which we formerly gave to the author's merits as difplayed in the first volume, is ftrictly applicable to the proofs of them in the volume before us. The body of the work is divided into eleven chapters, in which the author fucceffively treats of the general doctrine of centripetal forces; the theory

theological, and political. The
whole difplays much profound
fcience, folid learning, and a com-
mendable zeal in the interefts of
genuine philofophy, religion, and
morals. But the author has written
only for the learned; and their pa-
tience will often be put to the trial,
by the want of judgment in the
arrangement of his materials, and
the ftrange mixture of languages,
ancient and modern, in which they
are exhibited.

From the ample title of the next work which we have to notice, our readers will receive fufficient information respecting the nature of the task which the author has undertaken. It is "the Elements of Euclid, viz. the first Six Books, with the Eleventh and Twelfth. In which the Corrections of Dr. Simplon are generally adopted, but the Errors overlooked by him are corrected, and the Obfcurities of his and other Editions explained. Alfo, fome of Euclid's Demonftrations are restored, others made fhorter and more general, and feveral useful Propofitions are added: together with Elements of Plane and Spherical Trigonometry, and a Treatife on Practical Geometry,

theory of the moon; the figure of the earth; the preceffion of the equinoxes, and the nutation of the earth's axis; the denfities, quantities of matter, light and heat of the planets; the motions of the planes of the orbits of the planets, from their mutual attractions; the effects produced on the motions of the planets in the planes of their orbits, from their mutual attractions; the tides; the principles of projection, and the conftruction of geographical maps; the ufe of interpolations in aftronomy; and the hiftory of aftronomy. Thefe chapters are followed by a forcible, perfpicuous, and fatisfactory argument in favour of the existence of an intelligent, omnipotent, and infinitely good First Caufe, deduced from the fimplicity and regularity obfervable in the conftruction and procedure of the universe. To the whole the author has added numerous valuable tables, for facilitating aftronomical calculations, with precepts and examples to each; Dr. Bradley's Catalogue of 389 fixed Stars; M. de la Caille's Catalogue of 515 Zodiacal Stars, and his Catalogue of 307 principal Stars; Zach's Catalogue of 301 principal Stars, and his Catalogue of the Declination of 162 principal Stars; and Mayer's Catalogue of 992 principal Stars.

To military men the following work will prove acceptable and ufeful, from the fullnefs and excellence of the inftructions contained in it, and the judicious intelligible manner in which they are conveyed. It is entitled "the firft Principles of Field Fortification: containing concife and familiar Precepts for the Conftruction, Attack, and Defence of Field Works; with preliminary Introduction to the Science of Fortification in general. By

Charles Auguftus Struenfee. Translated from the German by William Nicolay, Captain-Lieutenant in the Corps of Royal Engineers." It is illuftrated with thirteen correct and well executed plates.

The fecond and third parts of "a Collection of Papers on Naval Architecture, &c.," complete the fecond volume of a very useful and interefting work, which increafes in value and importance as it fwells in magnitude. The publication of the preceding divifions of this Collection was announced in our Regifters for the years 1791 and 1795.

The Effavs on Gothic Architecture, by the Rev. T. Warton, Rev. J. Bentham, Captain Grofe, and the Rev. J. Milner, &c." conftitute a judicious and pleafing compilation, which furnishes the reader, at an eafy expence, with fome of the best treatifes on Gothic architecture, extracted from voluminous or coftly works, and forming together an ufeful manual on that interefting fubject. They confift of an Effay on Saxon and Norman Architecture, from Bentham's elaborate Hiftory of Ely Cathedral; Captain Grofe's Preface to his Antiquities of England; Profeflor Warton's concife Hiftory, in his Notes on Spenfer's Fairy Queen; and the Hiftory of the Origin and Progrefs of the pointed Arch, fromMr. Milner's Hiftory and Antiquities of Winchefter. They are preceded by a preface from the pen of Mr. Taylor, the editor, which displays a confiderable acquaintance with the fubjects difcuffed; and "Obfervations on the Means neceffary for further illuftrating the ecclefiaftical Architecture of the middle Ages," by the Rev. Mr. Milner. And they are illuftrated

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