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Jagiar-di-nié-ra, f., the female gardener, the gardener's wife. L' ué-mo, m., the male person, man, husband. La dén-na, f., the woman, wife lady, mistress. g Il sol di-to, m., the soldier. IZ sér-vo, m., the servant. Lo sco-ld-re, m., the pupil, learner, scholar. Lo scul-tá-re, m., the sculptor, statuary. Jo spéc-chio, m., the lookingglass, mirror. \ Jo scri-gno, m., the coffer, casket, safe, iron safe, strongbox, small money - box, drawer, portable desk. so scan-no, m., the long stool, form, bench. Lo scrit-to, m., the writing. Cór-lo, Charles. J): Cór-lo, of Charles. A Car-lo, to Charles. Da Cár-lo, from or by Charles. Ion-ri-co, Henry. D'En-rá-co, of Henry.

Ad En-ri-co, to Henry.
Pat Jon-ri-co, from
Henry.
Mi-ld-no, Milan.
JDi Mi-ld-no, of Milan.
A Mi-ld-mo, to, in or at Milan.
Da Mi-ld-no, from Milan.
Gio-van-ni, John.
Lu-á-gi, Lewis.
Pran-ce-sco, Francis.
Gu-gli-él-mo, William.
A-dál-fo, Adolphus.
Iči-dól-fo, Podolph, Ralph.
An-tá-hio, Anthony.
Sté-fa-no, Stephen.
Fer-di-nan-do, Ferdinand.
Car-li-'na, Caroline.
Lic-í-gia, Louisa.
Vo-éz-na, Vienna.
Ve-né-zia, Venice.
Pa-rá-gā, Paris.
Lóz-dra, London.
Ar-ri-vd-to, arrived.
Par-ti-to per— departed for—
Si chid-ma, is called (i. e. one
calls or names, we, they,
people call or name).
E" di-belongs to—(i.e. is of )

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ENGLISH-ITALIAN.

Our gardener is a good man. Your gardener's wife is a good woman. My friend is the uncle of this young man. ; have bought this tree from your gardener. Our (female) neighbour has a very good son and a very good daughter. Hast thou seen this poor man's child : My (male) cousin's looking-glass is very large. Thy (male) neighbour is the pupil of my

father. My book is on the form. I have given my hat to this poor child. The boek which I have received from a friend is lost. , Louisa has lost her bonnet. Have you (sing.) found

Charles's ring; Henry's father (i. e. the father of Henry) is very rich. John's garden is very small, William's friend has departed. My cousin has (i. e. is) arrived. We have received a letter from Louis ; he is at Milan. Have you seen Francis and Ferdinand? Rodolph has departed for Venice. We have written a letter to Stephen in Paris. Have you (sing.) seen th-s-tch of Louis: , Has (i. e. is] your (sing.) uncle departed for Paris? Caroline's aunt is in London. Our (male) neighbour has a son, who is called Adolphus, and a daughter who is called Louisa.

ENGLISH-IIAs.IAN.

The nephew has gone with the general's son and daughter into the park to dine there. Next week they will go together into the country. A courier has arrived with the news of the conclusion of peace. The cousin came here with the express order to buy a horse and a coach. I have never offended hina with one single word. In time, and with patience, one learns everything. Man ought to spend the first part of his fife with the dead, the second with the living, and the third with hinself. The world is filled with ungrateful persons: we live with the ungrateful, we work for the ungrateful, and we always

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L E S S O N S IN G R E E K.—No. XXII. By John R. BEARD, D.D. According to these general statements and explanations, the verb may be regarded as a total comprising a number of ideas, or representing a number of facts. This may be exemplified in Astro, I leave; and Astop6sarnv, they two are left ; thus –

Astorw. person. Number. Tense. Mood. Voice. First. Singular. |Present. Indicative. Active, Asto0strov. f -A- wo- -\ Person. Number. Tense. Mood. Voice. Third. Dual. Aorist, 1st. Optative, Passive.

From this instance you learn that the Greek verb varies, or is modified in person, in number, in tense, in mood, and in voice. Accordingly, it is the business of the learner to become familiar with the verb in all these its modifications, so as to at once recognise every form he may neet with in reading, and be ready at first sight to assign its meaning. The task is not an easy one, but will yield to persevering application. The task, being difficult, must be undertaken in detail.

Before we proceed to the general conjugation of the Greek verbs, we must present a peculiar form, namely, that of the substantive verb, or verb of existence, stvav, to be.

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* * **** ------ e, ,

S. D. P.-That is, the singular number, the dual, the plural.

N. denotes the nominative case.

G. denotes the genitive case.

M. denotes the masculine gender.

F. denotes the feminine gender.

N. denotes the neuter gender.

The English is only given in part, it being presumed that the learner can easily supply the rest; thus, when he knows that sip, means I am, he can hardly fail to know that the plural runs we are, you are, they are. Let it be premised that the significations given in the paradigms, or examples of conjugation, are sometimes only approximately correct; for the exact meaning the student must wait until he is familiar with the details of Syntax and other details, which will follow. The verb whose forms are given above, belong, it will be seen, to the class of the verbs in ut. There is another form, distinguished in part by accents, namely, sipu, I go, (siut, I am); the conjugation of which will be given in its place under the verbs in ut. The second person of the present, et, is more used than sug. In the imperfect, the second person, mg, often becomes no 6a, by the addition of a euphonic suffix; the third person is mov, more frequently than m. Instances are found, particularly in the first person singular and the third person plural, of another imperfect, which resembles the imperfect of the middle voice.

S. mpany moo jro. P. muséa mobs myro.

A middle imperative form is also found in the second person singular, namely, too, be thou. The entire present subjunctive, namely, to pc p, &c., supplies terminations to all the verbs in o. The second and third person singular have the iota subscript, as seen above.

The optative forms, stny sung sun, lend their terminations inv, &c., to the optative of the verbs in put. For the form sumptsv, episv is used; and for sumoray, susy is much more common; elev is also found in the sense of well / very well / be ft so The future, in all its moods, is a middle form ; its termination, oroplat, is that of all the middle verbs in the future. The original forms were

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In so ea at the second a was elided, and the word became eaeat. The ea was contracted into m, the 1 was written under, and thus egg arose. This observation extends to all the second persons in y, of the middle and passive verbs. Also, in the optative, sooto stands for £ootoo sorat, a contracted form of so stat, is more common than sosrat. The participle soopswog (the Latin futurus) is declined like ayabog, aya.0m, aya.6ov. to The substantive verb lacks the perfect, the pluperfect, and the aorist ; these tenses are supplied from ytyvouai, I become. The stem of the verb is sc, as found in so usv, so opat, &c.

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SYNTAX is that part of Grammar which unfolds the relations and offices of words as arranged and combined in sentences. The essential parts of every sentence are the subject, which is that of which something is affirmed; and the predicate, which is that which contains the affirmation. The subject is either a noun or that which is the representative or equivalent of a noun; the predicate is either a verb alone, or a verb in conjunction with some other part or parts of speech. All other words entering into a sentence are to be regarded as mere adjuncts. The following sentences exhibit the subject and the predicate under several varieties of form :

Subject. Predicate.

God exists.

Man is mortal.

To be, contents his natural desire.

Throwing the stone was his crime.

In the sentence, God exists, the verb exists is the predicate: affirming, as it does, existence of the Almighty. But in the sentence, man is mortal, mortality is what is affirmed of man ; and the verb (is) is the mere link that connects the subject and the predicate together. It is thence called the copula. § 158.

Sentences are either simple, that is, contain a single assertion or proposition; or compound, that is, contain two or more assertions or propositions. Of the various parts of a sentence, waether principal or adjunct, we come now to speak more in Stetail; so as to show the relation, agreement, government, and à-rangement of words in construction.

§ 120. THE ARTICLES. RULE.

The article in German, whether definite or indefinite, is generally employed wherever the corresponding article would be used in English.

OBSERVATION.

This rule is of course founded upon the presumption that the student is familiar with the usage of the English in respect to the article. In the specification that follows, therefore, he is to look only for the points in which the German differs from the usage of our own language.

(1) The Germans insert the definite article : (a) Before words of abstract or wmiversal signification; as, be r \tensö ist sterölid), man (i. e. every man) is mortal; b a 6 (Šoso ist besitbat, gold is ductible; b a 3 octen ist furs, life is short; b ic §ugent füğrt sum (Städte, virtue leads to happiness : (b) before the names of certain divisions or periods of time: as, bet &omittag, Sunday; ber ostontag, Monday; ber 3)egentöer, December; bec Ślugust, August; ber ©ommer, Summer: (c) before certain names (feminines) of - countries; as, bic Şürfei, Turkey; bie Gómeis, Switzerland; tie $ombarbei, Lombardy: (d) before the names of authors, when used to denote their works; as, td, Iese be it £eijing, I am reading Lessing: (e) before the proper names or titles of persons, when used in a way denoting familiarity or inferiority; as, grüße bi e oatie, greet (or remember to me) Mary; sage bem outset, taff id) isom ju sessen müničje, tell Luther that I wish to see him ; also, when connected with attributive adjectives: as, bi e fleine &epsie, little Sophia: (f) before words (especiairy proper names of persons) whose cases are not made known either by a change of termination, or by the presence of a preposition; as, bas 8ebell set Śārsītis, the

life of princes; bie Śrau t e 8 &efrates, the wife of Socrates; ber gag ber 9tadt, the day of (the) vengeance : (g) before the names of ranks, bodies, or systems of doctrine: as, bağ garlament, Parliament; bie Regierung, government bie ostomardjie, monarchy; bag ($9ttitentium, Christianity ; also in such phrases as, in b et &tact, in town; in b c : &lrdjo, at church; bie meistem oenföen, most men : (h) before the words (signifying) half and both as, bie jusée (not ja(6ebie) 3a5(, half the number; b it beibeu (not beinen bie) 3riber, both £he brothers: (i) before words denoting the limit within which certain specified numbers or amounts are confined, wherein in English, the indefinite article would be used: as, 3m)cimal bie goodje, twice as week: (2) Note, further, that the German differs from the English in omitting the definite article, (a) before certain law appellatives: as, Bettagter, (the) defendant; otăget, (the) plaintiff; Qīpeessant, (the) appellant; ©upplicant, (the) petitioner : ) before certain common expressions; such as, in Šester Submnig, in (the) best order; tieberbringer biesco, (the) bearer of this; and certain adjectives and participles treated as nouns; as, etstetet, (the) former; setterer, (the) latter; beingter, (the) beforesaid (person): (c) before certain proper names and places: as, C#intien, (tie) East Indies: Şeflinbich, (the) West Indies; and betore the names of the cardinal points: as, Qsten, (the) East; qBeiten, (the) West; Güven, (the) South ; 9terton, (the) North : (d) before a past participle joined with a noun, which, in English, precedes the participle : as, bağ betterelic Baratics, (literally, the lost Paradise) Paradise Lost. (3) Note, again, that the Germans, in using certain collective terms preceded by adjectives, employ the indefinite article where the English would use the definite: as, ein (oductset oats, the (lit, a) most learned Senate; cine obside limiversität, the (a) honourable University. (4) In German, also, the indefinite article stands before (not after, as in English) the words, such, half: thus, ein so(dyer oam, (not soldiet ein outn), such a man; eit flatbc& Sast, (not asses cin Şāşr), half a year. In questions, direct or indirect, like the following: (Suen mie sangen &psigietvitt sat et gemgöt, how long 2 ride has he taken; it must be noticed that the article stan,s before mic: thus, cimen mie sangen (a how long) and not, as it, English, how long a, , (5) The German differs again from the English in not using an article at all in the phrases answering to the English; a few ; a thousand ; a hundred. § 121. THE NOUN. RULE, A noun or pronoun which is the subject of a sentence must be in the nominative case : as,

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Cicero was called the father of his country : (or is alscrantet go, tutift porten, he has been christened Alexander. From this remark, however, must be excepted the verb ses)tem, since it has no passive.

§ 123. RULE.

A noun used to limit the application of another noun signifying a different thing, is put in the genitive; as, £er £auf bet &onne, the course of the sun. 9er on mcilité Öreuttes, the son of my friend. 9ic Groicoung ect Stiùbet, the education of the children. Øic QBasil eineš Šreunted, the choice of a friend.

How this limitation is made, is easily seen : thus, ber gauf ber $onne, the course of the sun. Here we speak not of any course indefinitely, but of the sun's eourse definitely: the word ber &ome, is the genitive, limiting ter Qaus, which is the governing word. OBSERVATIONs.

(1) If, however, the limiting moun (unless restricted itself by an adjective or some other qualifying word) signify measure, *umber, weight, or quantity, it is then put in the same case with that which it limits; as, Smti (Staš ĀBein, (not goeines), two glasses (of) wine; ités Biulio SWee (not offee8), six pound (of) tea: but (with a restrictive term), fed,8 %fumb ticité £6ees; moci (533 tiescă 98eimeå. * *

(2) It should be observed that the two nouns under this rule must be of different signification; for two nouns standing for the same thing would be in the same case, forming an instance of apposition. See § 133. (1). #

(3) The noun in the genitive, that is, the limiting noun, is commonly said to be governed by the other one. This genitive is either subjective or objective; subjective, when it denotes that which does something or has something : objective, when it denotes that which suffers something, or which is the object of what is expressed by the governing word. To illustrate this, , we have only to take the examples given above: bet Squí tet ocume, the course of the sun; bit (§rsicoung bet Stater, the education of the children; where, in the first exat ple, the sun is represented as performing or having a course,

and is consequently subjective; and, in the second example, the

Coldren are represented as being the objects of education, and the word is consequentiy objective. This objective genitive, it should be added, occurs only after verbal nouns, and chiefly those ending in the suffixes ct, which marks the doer, and ung. which marks the doing of an action. (4) It seems hardly necessary to observe that under this rule come all words which perform the office of nouns; as, pronouns, adjectives used substantively, &c.; thus, bic (jnabe bet Großen, the favour of the great. (5) We say often in English, He is a friend to, or an enemy to, or a nephew to any one; where, were these phrases put into German, we might expect the dative to be used. But, in such cases, the Germans always employ the genitive: thus, et is: ein §tino icine3 Saterlanocé, he is an enemy of his native country. (6) We say in English, the month of August, the city of London, and the like: where the common and the proper name on the same thing are connected by the preposition of The Germans put the two nouns in apposition. See § 133. (2). (7) So, too, in English we say, the fifth of August; but in German, the numeral is put in direct agreement with the name of the month: as, tet fünfte 21ugust, the fifth (of) August, or August fifth. * (8) In place of the genitive, the preposition won, followed by the dative, is, in the following instances, generally used: «. When succeeded by nouns signifying quality, rank, measure, weight, age, distance, and the like; as, cin oann won goşem ,&timbe, a man of high standing; ein &diff won 3 oci jumbert Sonnen, a ship of two hundred tons; ein &emicot won fünf £fumb, a weight of five pounds; ein Qiquit oon adjtjig Saffren, a man of eighty years ; cine Reise won brei Qicisen, a journey of three miles; cin (śngtimber oon (9eburt, an Englishman by birth, &c. b. When followed by nouns denoting the material or substance of which any thing is made : as, ein 3rd)ct won eißet, a

| cup of silver, i. e. a silver cup ; cine list oon (Sotte, a gold watch

** ***

c. When followed by nouns whose cases are not indicated by the terminations of declension nor by the presence of the article: as, bet &otim oom Štebsidyfeit, the appearance of honesty; eim 8ater port fed)6 timbern, a father of six children; bie Rönigin oon Qongsamb, the queen of England; bie Grenzen won &ramtreid), the boundaries of France; bet bisof won tonstang, the bishop of Constance.

d. When followed by a word indicating the whole, of which the word preceding expresses but a part : as, einer won meinen ...; one of my acquaintances; mesdjet won beiten? which of

© to WO

LESSONS IN GEOMETRY. —No. XXVII. LECTURES ON EUCLID. PROPOSITION xxviii.--THEOREM. (Continued from page 298.)

16. A fallacy, somewhat more subtle than , Franceschini's, though akin to it, may be framed on the consideration of the angle of intersection. Let A B, CD be two straight lines in the same plane making with a third straight line Ac the angles c A B, A C D, of which A G D is a right angle and c A B less than a right angle. And to improve the appearance (though this is not indispensable) draw a straight line A E on the other side of A c and in the same plane, making an angle C A K equal to c A B. And

from A let a straight line of unlimited length as w x travel along the straight lines A B and A E, cutting A Galways at right angles in some point G between A and C. This line will represent Franceschini’s succession of perpendiculars. But instead of arguing from its continually cutting off greater and greater portions AG, let it be argued that because it at any time makes with A B an angle A H G or B H x, it may always be removed to a F. tion further from A without ceasing to cut A B and A. E. From which it at first sight might appear to be a reasonable conclusion, that the straight line wox may be carried forward without the possibility of failing to cut A B and A E, till it arrives at g. And the fallacy will perhaps be still more taking, if A B and A E are made to begin by being placed at C, and so are moved from C towards A, as represented by a b and a e : under which circum: stances the allegation that there must always be an angle of some kind at h, has a very inviting appearance as a reason why a b and c D, being continually prolonged, cannot quit one another or fail to meet and make an angle of some magnitude or other, the consequence of which would be that ab and a emight be moved ; a coincides with A and a b with A B, without the possibility of parting company with C D by the way. • The answer to this is by inquiring, whether there are no lines in which the same facts may be determinable on the subject of the angle, but where it is certain that a straight line as W X Gamnot be carried on to an unlimited extent as proposed. And here it is easy to show that there may. Take, for example, any hyperbola; and from the vertex draw a perpendicular to each of the asymptotes; and let the two halves of the linear hyperbola,

together with the perpendiculars and the portions of the asymptosses cut off by them ou the side remote from the intersection of

the asymptotes, be placed so that the perpendiculars shal; coincide and the asymptotes in consequence be in one straight line, as S T in the figure below. Upon which it is clear, that however it may be pleaded that there may always be an angle smaller than A H G or B H x between wa and A B, w x cannot be carried beyond the line of the asymptotes S T without ceasing to meet A B ; and consequently cannot be carried till it meets CD, if G D lies on the other side of S T as represented in the figure. It follows therefore, that to say there will always be the possibility of a further diminution of the angle, is not enough. It may be (as it is in the case of the hyperbolic angle above) the sophism of Achilles and the tortoise; which argues, that because after running a mile, half a mile, a quarter of a mile, &c., Achilles would always be behind by the last-mentioned fraction of a mile, he would never overtake or pass the tortoise. The solution resolving itself into the fact, that these quantities, though endless in number, are limited and surpassable in amount. To establish the union of the lines to any particular extent that: may be desired, it is consequently. Inecessary to prove, not only that the angle at the intersection is capable of diminution, but that the, angle on each side of the travelling line (that is to say, both the angle A H G and the angle G 3 o' will never be red to less than some given angle. Which is wisat has been attended to accordingly, in the case of the intersections with a travelling line in Proposition XXVIII. C. of the “Geometry without Axioms.” 17. Another course taken has been to define a straight line to be one “of which every successive portion has the same direction,” and parallel straight lines to be “straight lines having the same direction with each other.” Froil; "-":ich it is purported to be collected, that a straight line cutting two parallel straight lines makes the interior angle equal to the exterior and opposite on the same side of the line. For, it is argued, the direction of the cutting line is at the two points cf intersection the same : and the directions of the two parallel straight lines cut, are at those points the same with each other's ; whence the differences of direction, which are the angles, will be equal. To which reply may be made by asking, what definite idea is attached to two lines having the same direction. It does not mean that they tend to the same point, for they do not. It means, then, that they never run against each other; or are parallel. , And a lime every successive portion of which has the same direction, means 2 ope of which the parts all lie in the straight line leading to a pariigalar point or object. The argument therefore resolves itself into the proposition, that if a straight line falls upon two parallel straight lines, it makes the exterior angle equal to the interior and opposite on the same side of the line; propounded in other terms, without the intervention of any new or explanatory idea. 18. In a tract entitled “The Theory of Parallel Lines perfected; or the Twelfth Axiom of Euclid's Elements demonstrated. By Thomas Exley, A.M.–London. Hatchard 1818 ° —the proof rests on taking for granted (in the Second Proposition) that if four equal straight lines in the same plane, making right angles with one another successively towards the same hand, do not meet and enclose a space, a fifth if prolonged both ways must inevitably accomplish it. A conclusion which may be resolved into taking for granted that the three angles of a rectilinear triangle are greater than a right angle and a half; for if they were equal to this, the angles of an equilateral and equiangular octagon would be right angles, and the fifth straight line in the series proposed would never meet the first; still more if they were less. And in the same manner. if it was urged that a sixth, seventh, &c. perpendicular must meet the first straight line, it would only resolve itself into a demand for admitting, without proof, that the three angles of a triangle are greater than some other amount capable of being specified. There is no obscurity about the fact that four such straight lines, and still more five, are found on experiment to meet; but the object was to discover why they necessarily meet. And between the observed fact and the explained fact there is a difference of the same kind as between Kepler’s observation of the proportion between the periodic times and distances of the planets, and Newton’s expla– nation of the cause. 19. In “A Treatise on Geometry, by D. Cresswell, M. A. Cambridge, 1819, the principle proposed to be taken for granted is, that through any point within an angle less than the sum of two right angles, “a straight line may be supposed to pass, which shall cut the two straight lines that contain the angle.” The grounds for such admission, being stated to be, that “if it be granted that among the infinite number of points outside the angle, there are two, on contrary sides of the angle, which are in the same straight line with the point within; or if it be granted, that, inasmueh, as the sides that make the angle are: unlimited in length in the directions removed from the angular point, two points in those sides may be taken, one in each, so that every point in the straight line which joins them shall be fartier

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