"The normal distinction of gender in these languages is logical, or it indicates the difference between subject and object. The sexual system of gender is characteristic of the Semitic tongues. The primary idea of tense in the Japetian tongues embraces the distinction between action or condition as continuous in one class of tenses, and terminated in another class. The marks for difference of time are independent of this, and these distinctions are subordinate to the other." pp. 38, 136, 180, 225. pp. 53, 121, 137.

The influence of the Grecian mind as being the well-spring of taste, or the origin of the truly beautiful in art, will be coeval with our race. Much has perished in which they established principles of harmony, because these were developed in things not capable of permanence. Much remains in regard to things æsthetic and intellectual, which will be models to all generations. It is results only, however, which are presented to us. In regard to the successions of thought and trial and labor, which led to these results, are we left greatly in the dark. Their Geometry may be considered as one of the fine arts. The results embodied in it have eminently the Greek type. No other people could have produced abstract truths in a form so simply elegant and precise. But, as is the case with poetry, or sculpture, the lessons and the inductions which led the national mind on to create it, have vanished.

The Greek mind, however, was not so pre-eminently scientific, as it was rich and powerful in the creative faculties which awaken emotions or satisfy taste. Their earlier efforts in the severer sciences were directed in all probability, rather to ornament or to simplify, than to extend and systematize. Great effort was needed before men could reach those first steps of the ascent on which the Greek placed his science, but it may be doubted if the effort was his. Much appears in the form of truths considerably isolated, while the steps by which they were reached are by no means obvious. We may readily admit the position that geometrical truths were ascertained originally by experience or measurement, and would be known as facts, before any logical demonstration of them was sought for. Such truths, it may be, the Greek borrowed from other people, but he applied his own sharp and versatile thought to their demonstration. We may ascribe to his inventive powers the methods of proof, while the facts were gathered up anywhere.

The earlier steps of these methods or discoveries are the most interesting and the most wonderful. The famous 47th Proposition of Euclid's first book expresses one of those truths, the recognition of which, as a fact, was probably due to practical art. It comes on us in the system very abruptly, without being foreshadowed by anything preceding it. Its demonstration is a notable and characteristic example of Greek ratiocination, preferring to deal throughout with the sensible and represented. The Hindoo mode, which rests on the position, that the sum of the squares of two lines is equal to twice their rectangle added to the square of their difference, is equally characteristic of the people who framed it, among whom a mind of deeper reflection dealt more widely with the relations of abstract quantity, and reposed less on the external and visible.

The Greek geometry needs yet to reach its true ideal. This can be effected only by bringing under the dominion of two principles, its whole constituents, and the ratiocination which systematizes them. Of these principles, one relates to demonstration, and may be stated thus-that there be no proposition needing to be proved in the course of an argument, except such as are absolutely geometrical. All more general truths or propositions which are true of other modes of quantity, are algebraic. Some such propositions will be repeatedly employed in the progress of ratiocination. To include the demonstration of them in our geometrical arguments makes the reasoning to be perplexed and cumbrous. Where the same course has to be pursued in different arguments, we become involved in needless repetitions. All such general or algebraic truths as become necessary in our reasoning should be withdrawn the geometrical argument, treated as preparatory to our proceedings, and be systematized and demonstrated in their appropriate mode.

Provision is made, though only slightly and inefficiently, for simplifying arguments in this mode, by means of collections of truths called axioms. In examining the course of an argument, it will be obvious that these socalled axioms have exactly the same effect in forwarding our ratiocination as any other of those general truths have, to which allusion has now been made. They are quoted just as we might, without immediate proof, but on the assumption that it is proved and known, quote the logical position -that half the sum of two magnitudes added to half their difference will constitute the greater of them, or that in a proportion the products of alternate terms are as the squares of adjacent terms, or any such like. This leads us to a right understanding of what ought to be indicated by the word axiom. To say, as the definition of such propositions, that they "are self-evident truths," limits nothing, and is a test of nothing. Those which are generally quoted as axioms, are in truth corollaries or conclusions from definitions of terms. The mere fact that their deduction is easy, offers no ground of limitation to them as a class. They are only a subdivision of an extensive group, and should come under its definition, which may be announced thus: all truths are axiomic in respect to a given science, which are more general than the subject of that science. Hence geometrical axioms are algebraic truths. They may form two classes. 1st. Axiomic corollaries, such as, that the whole is greater than a portion, &c. 2d. Axiomic theorems, such as, that in a proportion the sums or the differences of adjacent terms are to one another as alternate terms, or such like. It cannot but be obvious how greatly elegance and compactness of argument will be promoted by the abstraction of all propositions of this character from among the details of an argument, so that attention should be confined to geometrical relations alone.

The other principle to be noticed, as requisite to raise the Greek geometry to a higher ideal, relates to arrangement, and may be stated thus : the classification of truths propounded, ought to be absolutely in accordance with the natural relations of their subjects. In this respect, the Greek system is especially defective. Theorems relating to angles, lines, VOL. V.-9

arcs, surfaces, are thrown together in confusion throughout the various subdivisions of the subject. Even the mode of establishing relations, or of proof, is made the source of subdivision, as when theorems relating to all sorts of magnitudes, are forced together into a group, because proportions are employed in order to reach the conclusions. Logically natural classification, requires that theorems take some such order as this. 1st. Those relating to angle. 2d. Those relating to straight-line boundingfigure. 3d. Those relating to arc. 4th. Those relating to rectilineal surface-figure. 5th. Those relating to arc-bounded figure. The same principle may be carried out in subordinate divisions. Thus taking the first section, or that relating to angle, we should find groupings of this form present themselves. 1. Angles at one point. 2. Angles at two points presenting us with parallelism. 3. Angles at more points than two, comprising the relations of the angles of figures. Demonstrating any theorems comprised in these sections, never requires that we go beyond the subject matter of the section itself. If the definitions expressive of an idea, or serving as a test of the existence of a property, have the proper degree of precision and effectiveness, no difficulty should occur in deducing by means of them the properties of things defined, or of their combinations.

Such are the considerations regarding this subject, presented in the small work which we have noticed. It will be seen to be somewhat unique in its character and aim. The terminus of it is the theorem, that a line forming a eircumference contains the maximum area. Above five hundred geometrical truths are introduced, either as the arguments leading to this result, or as subsidiary deductions from them. From proceedings, such as have now been analyzed, it is evident that great advantage will be gained in giving instruction. Besides other circumstances leading to this effect, the advantages of strictly natural classification in presenting such truths as the subject matter of tuition, will be perfectly obvious. All truths of the same order being brought together, and logically connected, the whole series become easily attained; and when anything new is presented to the pupil, his first apprehension of its nature leads the mind at once to that section of the system where known truths relating to the same subject are to be found.

The Greek geometry, with its great outline thus rectified and filled up, will probably throughout all time be recognized as among the most powerful agencies for developing and disciplining the understanding. But an analysis of its rectified and fully-developed form, will render it a guide to still higher ends.

We have already noticed the view given in this treatise of axiomic truths in Logic. This is essentially connected with the position, that definitions are the only postulates admissible in argument, or the only hypotheses admissible as the foundation for a series of arguments. A glance at these principles, as developed in the treatise, brings to view the true form of constructive or inventive Logic.

It is manifest, that if we assume one definition only as the foundation

for argument, we may perhaps deduce conclusions from it; but these can only be different modes of the property, or different modes of expressing the property of an object, which serves to define it. Only very rarely can even such statements as are requisite for this purpose, be brought within the narrow range of that kind of argument which is called syllogism.

True progressive or inventive ratiocination stands in combination of ideas. Its arguments are theorems, as defined in the treatise before us. A theorem shows the relation between three truths; of which two constitute the hypothesis, and one becomes the conclusion. The argument is analyzed and presented thus: If the propositions constituting the hypothesis predicate of the same kind of object, then they may be directly combined. If otherwise, then one or both must be modified that they may predicate of the same kind of object, so as to be capable of combination. The conclusion gained by their combination may require to be modified in terms, so as to become the conclusion aimed at. An argument, therefore, may include three operations, viz., modifications of its hypotheses, their combination, and lastly modification of the result. The process of detecting sophisms consists in the examination of these operations, to see that they are legitimately conducted. The origin of such fallacies will be found almost universally in the first of them, consisting in an illicit degradation of the hypothesis through the omission or introduction of a characteristic of some sort, not provided for in the definitions. Hence the conclusion may be true, and legitimate as a combination of truths; but it is not a combination of the truths offered in the hypothesis, and is of necessity a fallacy.

IV. The Heathen Religion in its popular and symbolical Development. By Rev. Joseph B. Gross. Boston: Jewett & Co. Philadelphia Lindsay & Blackiston. 1856. pp. 372.

A very odd book. Its object appears to be to show, that the heathen religions-Eygptian, Persic, Greek, Roman, Scandinavian-were a great deal better, and more sensible than is generally thought; and that while multitudes of the common people worshipped wood and stone, that grand mysteries and noble ideas are contained in the mythologies.

The book proceeds upon the foolish idea, that nations began in a savage state, and worked their way up to civilization and refinement. This French infidel notion ought to be exploded by this time. Men degenerated from a high condition, originally conferred upon them by the Almighty. The genius of some of these nations, as the Greeks, glorified everything; but the Pagan religions, as religions, were just what the Bible represents them to have been-"Even as they did not like to retain God in their knowledge, God gave them over to a reprobate mind, being filled with all unrighteousness." Men amuse them now with Bacchus and Venus. Let the reader only imagine what it must have been seriously

to worship them. Let him pause long enough to bring that idea into his mind. Only consider, instead of worshipping our pure and blessed Saviour, that men should believe Venus or Bacchus to be divine, and bow down in adoration of them. What strange moral confusion! What an amazing degradation of heart, intellect, and conscience! All of our high spiritual worship can hardly keep us out of filth and vanity-what if we wor shipped, fervently and sincerely, the gods of Phoenicia or Egypt! What the Reverend Mr. Gross expects to accomplish by eulogizing Paganism, it is difficult to see; for there is certainly quite disposition enough to find wisdom everywhere, except in Revelation.

V. An Earnest Plea of Laymen of the New School Presbyterian and Congregational Churches in New York and Brooklyn, for the continued Fraternal Union and Co-operation of these Denominations in Home Missions.

We notice this pamphlet especially, to call the attention of our readers to the very remarkable comments upon it, of the New Englander. This is the ecclesiastical Quarterly of New England; its words are well-weighed. We quote a considerable part of the notice, without note or comment, only taking the liberty to put some parts of it into italics.

"The unexpected length of some of the articles in our present number, has compelled us to relinquish, at least for the present, our purpose of discussing in detail the subject which is commended to attention in this well-meaning pamphlet. Probably the subject will undergo a new discussion in the now impending session of the New School General Assembly; and a few weeks hence the agitation about Home Missions may come up again, in connection with new questions and projects. Meanwhile we take the liberty of suggesting, in connection with the title of the 'Laymen's' pamphlet, some considerations, which our friends on both sides of the question, will do well to think of.

"1. Within the last twenty-five years there has been growing up in the Congregational churches, a more intelligent and settled conviction of the superiority of their own ecclesiastical order, as compared with Presbyterianism. There was a time-not long before the revolutionary war— when the danger that an Episcopal hierarchy might be imposed on the colonies, by the authority of the British Parliament, not only had the effect of re-uniting the Presbyterian church, which had been, as now, divided in twain, but also brought the Congregationalists of New England, and the Presbyterians of the middle and southern colonies, into a close correspondence and sympathy. Thus originated those formal connections between the Congregational clergy of New England and the General Assembly of the Presbyterian church, which, soon after the revolution, ripened into a kind of federation, including a yearly exchange of delegates, and the Plan of Union,' for the temporary government of mixed churches in the new settlements. Thus there came to be among Congregationalists, and especially among the clergy, the habit of feeling that inasmuch as they and the Presbyterians were alike in rejecting prelacy, there could be no great difference between their two systems of church order. A natural consequence was, that though the New England emigrants moving westward, generally constituted Congregational churches, the New England missionaries and emigrating clergymen, almost as gen