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however, when applied to fx or 0x, &c. generally represents thë second term of the series that arises from expanding fx or o x, when for *,*+ 1 is substituted: that second term can always be known, since all the expressions which f (x+1), or Q(x+1) is inade generally to represent have been previously expanded, ibus Dru=mom-' P.42,
This leads us to the doctrine of fluxions; and the natura of vanishing fractions is treated with great propriety,
These vanishing fractions have caused many discussions amongst mathematicians; they have caused many false reasonings. It was not perceived that, to assign the value of (r=a), there was an
Xtrant " absolute necessity of some definition, convention, or extension. The notion of an inherent signitication, and of an essential value, belonging to such an expression, as , bewildered men who valued themgelyes on the clearness of their apprehension, and the justness of their inferences.
• The method of limits, or of prime and ultimate ratios, Landen's method, the method of finding the value of ** (fr, Fx = 0) are related methods: they all demand the same arbitrary assumption, which has never been expressly made; they are all equally subject to an objection, which has never been satisfactorily removed.' P.71.
The contact of curves is then examined, and the mode of drawing tangents, and finding the radii of curvature, explained. On the latter subject, the following remark occurs, which will scarcely be thought satisfactory.
• It is needless to give examples, since, in these cases, examples do not illustrate the theory : if given, they ought to be considered only as exercises by which the dexterity of the student is to be improved : they merely require the value of an analytical expression to be found, for which purpose rules have been previously laid down.' P. 181.
Phis may be true: but experience informs us, that gene. ral truths are fixed in our minds by examples; and that, if they be left to their own naked energy, their influence will be found, comparatively speaking, very small. The work before us is an instance in point: it will exercise the talents of the higher mathematicians, and will be neglected by all, even at Cambridge, who have not found a place among the first six on the first tripos.
Yet, though we apprehend the work doomed to have but few readers, we do not the less recommend it to those whose duty it is to give instruction on these subjects. They may þence discover the insufficiency of many modes of reasoning in which they have placed implicit confidence: their views will be enlarged; and they may be profitably employed in bringing Mr. Woodhouse's calculations down to the level of the humbler class of mathematicians. When they are disembarrassed from the novelty of their terms, and the terrors of their scries-when a few simple instances are added, by which a learner may catch the spirit of the general demonstrationwhen the whole is simplified and stated, so as to create a greater interest-the merit of this acute writer will be more generally acknowledged, and he will be deemed highly worthy of the patronage of the university by which the work has been printed.
Art. VII. – An Enquiry into the Necessity, Nature, and
Evidences, of revealed Religion; by Thomas Robinson, A.M. &c. 8vo. 6s. Boards. Baldwin. 1803.
THE intent of this work is to show the necessity, nature, and evidences, of revelation, in a plain and popular manner, and to point out the incompetency of reason as a religious instructor. There are two ways of discovering the will of God--by reason apd by revelation; and the state of the heathen nations, unenlightened by revelation, is brought before us, to show how inadequate a guide is the former in subjects of religion; while the confession of their philosophers teaches us that a divine revelation was even by themselves thought possible, probable, and even necessary. Such a revelation we have in the Bible, of which an account is given in the work before us, beginning with the five books of Moses, whose genuineness and authenticity are proved; while many very judicious observations are advanced on the three branches of the Mosaic law, the moral, ceremonial, and political. If the arguments be demonstrative on the genuine. ness and authenticity of these books, of which, notwithstanding some late cavils, we entertain no doubt, their divine authority is proved, as the author justly observes, by ' so strong and decisive a body of evidence, as cannot fail to remove every reasonable doubt, and satisfy every candid and unprejudiced inquirer.' Having brought those arguments before the reader, which are derived from the character, the miracles, and the prophecies, of Moses, which evidence his divine mission, the author next takes a summary view of the ensuing books, written by the prophets and other holy men, applying to them the same mode of proof which he has so successfully employed with respect to the Pentateuch; and con, cluding his discussion on the Old Testament with an inquiry into its canon, and pointing out the alterations which have been made, and explanations gireu of certain passages by Ezra, hereby bringing his history of it down to the time when the division into chapters and verses was adopted by both Jews and Christians.
The great division of the Bible is into two parts, the old and the new covenant; the old being the groundwork of the new, and creating an expectation of that teacher by whom the whole system was to be consummated.
This person, distinguished by the name of Jesus of Nazareth, is represented by his followers, 'as endowed with such great and supernatural powers, as to justify his claims to be regarded as a teacher sent from God; and is describerl, as corresponding, with such wonderful exactness, with the types and prophecies which the Jews applied to their expected Messiah, that no reasonable doubt can remain on a candid and unprejudiced mind, but that he was in reality that illustrious prophet. Such is the language of the advocates for Christianity. Before we accede to, or reject a proposition of such magnitude, it will be necessary to enter on a serious and particular investigation of its nature, and examine the grounds on which such high and extraordinary pretensions are supported. This inquiry will naturally be directed
o the book that professes to give us an account of the life and doctrines of this new teacher. If the statements of the writers appear. on examination, impartial and consistent; if the internal evidence of the narrative itself be credible and unsuspicious; and if it be elucidated and confirmed by such external testimony, as we have no suiiicient reason for calling in question, and which would be readily admitted on similar occasions; we cannot be justified in withholding our assent from that which carries with it such strong and distinguishing characteristics of truth. But should it, on the other hand, be found incapable of withstanding so severe a scrutiny; should it appear to have been erected on the basis of deception ; and for no better purpose, than the advancement of private interest or ambition; we may then, and then only, reject it with safety, as fabulous and unfounded: P. 140,
The inquiry into these points is conducted, as before, by examining the history given of our Saviour, and his doctrine in the New Testament, under its separate heads of Gospels, Acts, Epistles, and the book of Revelation. To each of the Gospels, as also to the Acts, is allotted an appropriate chapter, in which the author offers a concise account of the writer, and the nature of his work. A similar chapter is given to each writer of the epistles, and one of far too much brerity, to the very important but neglected book of the Revelations. The canou of the New Testament is then investigated, and the genuineness and authenticity of the whole established. We bave thus an authentic history of the sacred writings: that they are credible, the author proves from the knowledge and character of the writers, and the sacred influence by which they were guided. The divine inspiration is asserted, but with a modification which does credit to our author's judgement,
who does not run into the extreme of regarding every tittle in every book as possessed of equal authority.
• A divine influence was not only claimed, but readily admitted, in the earliest ages of the Christian church. In regard, however, to its nature and extent, it is suthicient to observe, that we must be careful to confine it to the ministerial writings and discourses of the apostles. It is not to be supposed, that it affected their personal conduct as men, or their ordinary concerns as private individuals. Paul, we are informed, “ withstood Peter to the face, because he was blamed ;” and whenever he spoke of private business, prudential advice, or the circumstances of his travels, he makes use of terms which plainly indi. cate, that he did not apprehend that he was, in all instances, under an infallible direction. These particular exceptions form, indeed, an argument highly in favour of the general rule; for if he never had been inspired, there could have been no propriety in such exceptions. We may, therefore, conclude, that the apostles were under the infallible guidance of the spirit of truth, as to every religious sentiment which they taught; every sentiment that constitutes a part of Christian doctrine or Christian duty; and that the New Testament contains a true and perfect account of the whole will of God; of every thing that is necessary for us to know, believe, or practise, “ in working out our salvation.” P. 226.
It having been proved that the writings of the New Testament contain a divine revelation, a consideration of the intrinsic excellence of its matter necessarily follows; but the author evinces also its divine origin, from the superiority of its doctrines, precepts, and motives, as well as from the prophecies, miracles, virtues, and particularly the resurrection of the founder of our religion. The wonderful propagation of this religion, with its beneficial consequences to society, and the dispersion and preservation of the Jews, are introduced as additional arguments; and the Scriptures are shown to have been transmitted to us without any material corruption or alteration, But, if the books of the Scriptures be thus excellent and important, whence is it that they are so much neglected, and in what manner are they to be most profitably studied? Upon the latter point the author recommends and we join strenuously in the recommendation-diligence and humility: both are necessary, and, with both, the meanest capacity cannot fail of acquiring the truest wisdom. : • No quality is of greater use, or more indispensably necessary in any study, than that of diligence; nor can any one hope to make a proficiency in scriptural knowledge, without some degree of labour and exertion. The surest method of interpreting any thing obscure or difficult in the sacred writings, is to compare one passage or expression with another. To do this with the greatest effect, we must be able to refer to different places, for terms of similar import and expression; a facility which can be attained by diligent application only. As the sense of Scripture cannot be understood but by understanding the force of scriptural language, we must carefully distinguish figurative ex. pressions from those which are literal. We must consider that the eastern figures of speech are uncommonly bold ; and essentially different from those in use amongst ourselves. We must take every sentence as it stands in connection with the rest of the discourse; and carefully attend to the occasion, scope, and coberence of the whole. We should be previously acquainted with the several articles, which are absolutely necessary for understanding and explaining the sacred writers. We should have a general knowledge of the times and countries in which they lived; of their language and character; and of the religion, manners, customs, and history of those whom they addressed. We must go back, as it were, to the times and countries ia which they wrote. These things, and many more, are necessary for reading the Scriptures with the greatest effect; and these things re. quire a considerable degree of assiduity and attention. But in this, as in every other duty, the variety of human circumstances and conditions must be duly regarded. To whom much hath been given, of them will much be required. They who have been exempted by the bounty of Providence from the necessity of constant labour and exertion in other occupations, have the more leisure to bestow upon this. But even the most engaged may find time sufficient for this important study. One day in seven has been appointed for a season of general rest; on that day, the lowest and most necessitous have a respite from their labours, and may easily attain the whole of the knowledge for which they can have occasion. The character of diligence cannot, therefore, be determined by any general rule. He only deserves it, who carefully embraces every opportunity, which his life and education afford him, of attending to and learning his duty. Every man, on this point, must decide for himself; as his own conscience will not fail to inform him, whether he is justly to be classed amongst the remiss or diligent. Serious reflexion willl shew him the necessity of repeated application to those writings, which are the rule and measure of human actions; he will think no time too long, no labour too great, to make himself acquainted with these unerring guides to eternal life. Like the psalmist, « The law of the Lord will be his delight, and all the day long his study will be in it.” P. 292.
The work concludes with a judicious recapitulation, and may be made a useful companion to the Bible by those who have not an opportunity of consulting more voluminous publications on the same subject.
Art. VIII.—Poemis. By John Lowe, Jun. of Manchester,
12mo, Boards. No Publisher's Name. 1803. MR. John Lowe, junior, is a bold man. He rejects the astronomical system of Newton; and he has written an epic poem. As a philosopher, we are not now called upon to ex