MULTIPLICATION OF RADICAL QUANTITIES. Radical quantities may be multiplied, like other quantities, by writing the factors one after another, either with or without the sign of multiplication between them. 1. Thus the product of a into √b, is √ a X √b. 2. The product of 3 into y, is hy. But it is often expedient to bring the factors under the same radical sign. This may be done, if they are first reduced to a common index. Hence, quantities under the same radical sign or index may be multiplied together like rational quantities, the product being placed under the common radical sign or index.' 3. Multiply into 3⁄4y, that is, into y3. (23), and The quantities reduced to the same index, are (23)3, 4. Multiply 5. Multiply dx into √hy. 6. Multiply a 1 into x*. 12. Thus a1× a3=a3+š = a3+ŝ= a§. The values of the roots are not altered by reducing their indices to a common denominator. Therefore the first factor aa The product therefore is a X a® X aa × a® X a® = N.B. In all instances of this nature, the common denominator of the indices denotes a certain root; and the sum of the numerators shows how often this is to be repeated as a factor to produce the required product. Any quantities may be reduced to the form of radicals and may then be subjected to the same modes of operation. 23. And x x x =x n+1 1요 27. Multiply ab into c√d. The product of the rational parts is ae. But in cases of this nature we may save the trouble of reducing to a common index, by multiplying. 29. Thus ax1 into bd3= axbu3. Ans. 1 30. Multiply a(b+x)3 into y(b—x)*. 32. Multiply a 33. Multiply ax into b1x. into by 34. Multiply x 3/3 into y 3/9. If the rational quantities, instead of being co-efficients to the radical quantities, are connected with them by the signs + GENERAL RULE FOR MULTIPLYING RADICALS. Radicals of the same root are multiplied by adding their fractional exponents. If the quantities have the same radical sign, or` index, multiply them together as you multiply rational quantities, place the product under the common radical sign, and to this prefix the product of their co-efficients. If the radicals are compound quantities, each term in the multiplier must be multiplied into each term of the multiplicand by writing the terms one after another, either with or without the sign of multiplication between them. HORACE, Book 3, Ode 7. Austeria, why bemoan the youth Whom favouring winds and love of truth, Laden with precious things will bring Back to thy side in early spring? Thy Gyges long by tempests tossed, To catch him with her young bright eyes, Had raised the assassin's knife on high, What youth like Gyges could restrain A fiery courser on the plain? Then close thy door at night betimes, Nor heed the serenader's ryhmes; To Gyges ever constant prove, And Gyges will requite thy love.-J. T. P. THE RICH MAN'S SON AND THE POOR MANS SON. BY J. R. LOWELL. The rich man's son inherits lands, A heritage, it seems to me, The rich man's son inherits cares; One would not care to hold in fee. What does the poor man's soon inherit? Stout muscles and a sinewy heart; A hardy frame, a hardier spirit; In every useful toil and art: A heritage, it seems to me, A king might wish to hold in fee. What does the poor man's son inherit ? Wishes o'erjoyed with humble things; A heritage, it seems to me, A king might wish to hold in fee. What does the poor man's son inherit?— A patience learned by being poor, A fellow feeling that is sure To make the outcast bless his door : A king might wish to hold in fee. Oh! rich man's son, there is a toil Worth being rich to hold in fee. Oh! poor man's son, scorn not thy state;There is worse wearines than thine, In merely being rich and great; Both heirs to some six feet of sod, Both children of the same dear God; Well worth a life to hold in fee. Quand vous aurez donné à une femme le nom sacré d'épouse, vous devez vous consacrer à son bonheur, comme elle doit se consacrer au vôtre. Mais l'obligation qui pèse sur vous est d'autant plus grande que votre femme est une créature plus faible, et que vous lui devez, comme étant le plus fort, le bon exemple et toutes sortes de secours.-Silvio Pellico. Le méchant fuit sans être poursuivi de personne; mais le juste est hardi comme un lion, et ne craint rien.-Salomon. The Prepositions. The prepositions require careful study, as on them, as well as on other invariable verbs, the sense very much depends, and you will be ignorant of some of the most delicate shades of meaning, and unaware of many an elegance, if you do not familiarise your mind with the import and the usage of the prepositions and the conjunctions particularly. Prepositions have a relation to place, and denote the direction of an action in regard to place. Thus, I say "you go from home;" "you go to home;" "you go round the house;" "you go over the wall." In order, therefore, to your possessing an exact knowledge of the prepositions, of which there are in Greek eighteen, you must study them in their relation to place. In the ensuing table, they are arranged as they stand in regard to place. The Prepositions arranged in their Relations to Place. secundum, apud along Greek. Latin. English. 1. εν in in 2, εις οι ες in into 2. Place whither you go 3. προς ad to 4. Ex or ε ex, e 5. απο ab, a up In this general view it is only the general meanings that I have been able to give. It is the office of Syntax to set forth details, especially as the import of the prepositions is modified by the case which they govern, for, as you already know, most of them take more cases than one. A little close attention will show you that the Latin prepositions are intimately connected with the Greek in origin as well as signification: thus, & and in are the same; so are εK and ex; so, also, vπep and super, and iπo and sub. The following six words may also be considered as prepositions, namely: with over, above on against instead of παρα τον ποταμον, to walk along the river.. μεтa тоυ жатρos, to be with your father. σvν τ σтрary, to follow the army. ύπερ των επόμενων, to be above those who follow. oi vo Tivi, those who are under some one. πро тшν πνλшv, before the gates. φᾶρος βαλεῖν αμφι τινα, to throw a cloak around a person. Tа TEρi Tivos, the things around a person, circumstances. εφ' ίππων είναι, to be on horseback. αντι βασιλεως ( to make one who was a king δοῦλον ποιειν αναβαινω αναλαμβάνω καταβαίνω παραγω παραβαίνω μεταμορφόω μεταλαμβάνω συλλαμβάνω ὑπερβαίνω ὑποβαλλω ὑπογελαω προβαίνω αμφιβαίνω περιβαίνω { επιβαλλω αντιβαίνω αντιδιδωμι a slave. I go up, mount, ascend. I resume, take up. I go down, I descend. I lead beside, aside. I go beyond, transgress. I change the form of, metamorphose. I take part with, partake. I put under, I subject. I laugh a little, I smile. I surround. I throw on, I add. I go against. 1 give instead, in exchange for: More than one preposition may combine with a verb; e.g. εayw, I lead out (an army from its camp). TaρεEαуw, I lead out (an army against the enemy). avтiжаρežaуw, I lead out (an army and march it to assail the enemy). Adverbs. Acc. diкny (Kara), in the form or manner of. χαριν (προς), in favour of. προίκα (κατα), gratuitously. Sometimes the preposition is expressed and united to the noun, as: παραχρῆμα (παρα, at; χρῆμα, the thing), at the moment. πроνρуоν (πро, for; epyov, the deed), usefully, beforehand. EKTOдWV (EK, from; move, the foot), at a distance, far from. Adverbs formed from adjectives imply a substantive :Dat. ίδια (εν ιδια χωρα), in particular ; πεζῇ εν πεζῇ ὁδῳ), on foot. Acc. μακραν (εις μακραν οδον), a long way, at a distance. The neuter of the adjective is often employed as an adverb; as the dat. Toλq, much, by much; ov, agreeably; devov and deva, terribly; TOTEрa, whether? Emirηces, on purpose. ρα, TOL, in, then, certainly, assuredly. Hev denotes a contrast, and strengthens, indeed, quidem. ye asserts something in addition, and gives emphasis to its word, at least. vai (Lat. næ, English, nay), yes, truly. είτε ει μη ει και ότι ἵνα μη επει διοτι sive nisi, si non et si, etiam si et si quod ut ut ne, ut non quia quia itaque cum or quum postquam quum dum quomodo sicut Of these conjunctions some are simple, as κat, TE, ws; others are compound, as ούτε (ου and τε), μεντοι μεν and τοι), και τοι (και and τοι), τοινυν (του and νυν), ώςτε (ὡς and τε), διοτι (δια ότι, neuter of όςτις), γοῦν (γε and οὖν), επειδη (επει and δη), επειδαν (επει, δε, and ar), όταν (ότε and αν); and others are two separate words, as ει μη, ίνα μη. There are other conjunctions, whether a single word, as ἡνικα, when, or several words united, as τοιγαρτοι (τοι, γαρ, τοι), now then, τοιγαροῦν (τοι, γαρ, οῦν), wherefore, on that account; or, again, several words in a separate state, ov μnv aλa, however; λŋv ε μŋ, if only. One or two others deserve notice, as ȧre, seeing that, as being, e.g. ȧre ayabos, as being good (Latin, utpote bonus); wep, although, e.g. ayabos rep, although good. There are certain words employed as adverbs, in the composition of which there is a conjunction, e.g. dnλovori, evidently; that is, dnλov eσTI Or, it is evident that; Eviore, sometimes, made up of evi, for ear, and ore (in Latin, est quando). The Greek is rich in conjunctions. Some of its conjunction express shades of meaning which can scarcely, if at all, |