8. Reduce the equation x2-8bxh. 2+ax + = x2xhd. x2+3rd+6. ax =h. b In these, and similar instances, the root of the third term of the completed square is easily found, because this root is the same half co-efficient from which the term has just been derived. Thus, in the last example, half the co-efficient of 1 26' 1 z is and this is the root of the third term 462• Thus, ax + bx+dx=(a+b+d) × x. The square of half this compound co-efficient is to be added to both sides of the equation. 9. Reduce the equation Uniting terms And 10. Reduce the equation Therefore . '+(a+b) x x + ( ~ + 3 ) = ( " + 3) " + ". 11. Reduce the equation x2+ax-x=b. LESSONS IN GREEK.-No. LIII. BY JOHN R. BEARD, D.D. MOODS. The indicative denotes that in consequence of an apprehension of the mind, whether the object apprehended be material or intellectual, the subject is simply applied to the verb, and therefore serves to express historical events and absolute facts; its office being merely to indicate or declare a reality. In Greek the use of the indicative generally resembles its use in other languages. Some peculiarities, however, have to be set forth. The indicative, in union with the particle av (KE, Kεv), presents a condition whose realisation depends on circumstances, to which reference is made by the conjunction. This form of speech occurs partly in the historical tenses and partly in the Τίς αν ψηθη ταυτα γενεσθαι ; Who could believe that these things happened? This usage may be represented by these English formswould or could ... if; would or could have... but for, indicating that as the conditional circumstances did not (or do not) exist, so the contingency did not take place. Frequently are these forms used-sides av, you would have seen; nynow av, you would have thought; εyv av Tis, one would observe. Sometimes for the expression of this sense you find the indicative without av, when the condition which, under certain circumstances, would have taken place, is represented as actually taking place. In most verbs this mode of expression is admissible only when a subordinate hypothetical sentence is subjoined to the principal sentence; e. g. Ηισχυνόμην μεντοι, ει ὑπο πολεμιου εξηπατηθην I should be ashamed indeed, if I were deceived by an enemy. Μενειν εξην τῳ κατηγοροῦντι τῶν αλλων So wishes, which are not fulfilled or cannot be fulfilled, take the indicative without av; e.g. Ωφελε Κυρος ζῆν The general import of this idiom is the exclusion of fact. THE moods represent the circumstances under which the sub-KE, KEV), signifies that a future event is not absolutely certain, Εγω δε κε τοι δώσω The indicative is also used by the Greeks in questions which express surprise, and which are intended to show that a condition of things assumed by another has no real existence; e.g. Σωκράτης πιστευων θεοῖς πως ουκ εἶναι θεους ενόμιζεν ; As Socrates believed in the gods, how did (could) he deny their existence ? The subjunctive and the optative moods denote that the predicate is applied to the subject according to a conception; consequently the relation here is one of dependence, the dependence may exist exclusively in the mind, or it may exist in the mind as represented by a word, that is, a verb or a conjunction. The subjunctive and the optative are in their essence very much alike, differing merely in regard to time; for the subjunctive sets forth the conception as at present lying in the mind of the speaker; the optative places that conception in the past. Thus, the subjunctive present in Greek corresponds with the subjunctive present in Latin, while the optative in Greek corresponds with the imperfect subjunctive in Latin. In simple sentences the use of the subjunctive is very limited, and extends only to these instances: 1. Homer, and the Epic poets in general, put positive as well as negative propositions sometimes in the subjunctive. By this mode of expression it is intimated that the speaker has not a certain but only a doubtful idea of the matter in question; and consequently the form serves to set forth an opinion, or an undecided notion; e.g. Και ποτε τις ειπησιν And once, I suppose, some one said. In this way certainty is intimated, and a positive assurance given; thus the example may be rendered— By no means will I leave thee; or, Thou hast no need to fear I will leave thee; where the statement is exemplified, that the subjunctive depends on a state of mind. The subjunctive is the mood of conception or idea, as the indicative is the mood of fact; as the latter implies independence, so the former implies dependence. In sentences with un ou you are to understand or supply before the un, opa, see, or σKOTEL, consider. In this way you as good as say, "You must take care that this or that does not take place." The phrase, therefore, serves to express an undecided or doubtful denial. Αλλα μη ουκ ή διδακτον αρετη That is, σκοπει μη ου χαλεποι, etc., consider whether it is not easy to avoid death. The optative, which represents a conception as lying to the speaker beyond the present, finds its proper application in the expression of a wish. Of the use of the optative in simple propositions there are two different forms, namely, the optative in and by itself (without av), the simple optative; and the optative with av. The optative without av represents the expression as the free act of the mind, and without any stands in a sentence subordinate to another, which is hyporeference to the province of reality. The optative with av thetical, and which arises from the nature of the case; consequently the conception appears to ensue from certain prevailing circumstances. But the conception assumes the form occurred, then the consequent result would take place. Inof an eventual reality, since, if the required circumstances stances of these usages are the following: 1. When to a proposition which in narrative sets forth an opinion or statement, the determining cause thereof is subjoined in narrative, the optative is used without av; as, Απεκρίναντο αυτῷ, ότι αδυνατα σφισιν ειη ποιεῖν ἁ They answered him that it was impossible for them to do what προκαλεῖται ανευ Αθηναίων· παιδες γαρ και γυναίκες he asks for, without the Athenians; for the children and women παρ' εκείνοις ειησαν. were in their hands. 2. Hesitating views and determinations, if they intimate only an inclination in the mind of the speaker, are expressed by the optative without av; if, however, it is intended to intimate that those views and determinations may, on a certain event's taking place, prove realities, then the optative with av is employed: Hesitation; opt, without av: 'Peĩa Oɛos y'ε0eλwv kai rŋdodev avèpa σαωσαι. Easily, I think, can a god, if willing, even at a distance save a man. Hesitation; opt. with av: Ovк av εyw Taνтa Önoayu, I could not, I think, affirm these things. In the refined tone of Attic conversation the optative with av was a polite form of expression, by which convictions and determinations were set forth in a hesitating or qualified manner, and by which the harshness of direct requests was softened down; e. g. Ώρα αν ειη πράττειν τα δέοντα Λέγοις αν ά δεί λέγειν Be so good as to say what ought to be said. The optative without av may denote repetition; e. g. αν παντα τον λογον. conversation to the assumed principle. EXERCISES.GREEK-ENGLISH. Ει τι έχοις, δοιης αν, if you had any you would give some, and you may have some. Ηδέως αν τοῦτο ακουσαιμι, gladly, if permitted, would I hear this. Ει τι εἶχον, εδωκα αν, if I had any, as I have not, I would have given some: which now I cannot do. Λῆλος εἶ, etc., you clearly sin in saying this. What part of the verb is διηρωτα: προςεδέξατο ? ενικων ἐχρῆν? μελήσεται ? σωφρονησαντα? σκοπῶμεν? λεξης ? αντεχειν ? ἡγοῖτο ? γεγενημένα? ὁμολογήσαιτε? ἡμαρτανες. Why is av used, and what is its force in these sentences? εδωκα αν ? δοῦναι αν? χαίροις αν? αν προςεδέξατο διηρωτα αν αποφεύγοις αν? ενικών αντ LESSONS IN SPANIS H.-No. IV. DEGREES OF COMPARISON.-Continued. prefxed, or by the ending isimo. There are a few, however, Most adjectives may have their superlatives formed by muy such as those ending with ial and antepenults (i. e. those accented on the last syllable but two) ending with co, go, 10, which form their superlative absolute always with muy, as, social, social; muy social (and not socialisimo), very social; magnífico, magnificent; muy magnifico, very magnificent; pródigo, prodigal; muy prodigo, very prodigal; garrulo, garrulous ; muy garrulo, very garrulous. As a general rule, adjectives of many syllables form the superlative absolute by muy and not with isimo. The superlative of mucho, much, is always muchisimo. Πότε μεν επ' ημαρ εἶχον, εἶτ ̓ οὐκ εἶχον αν. Αναλαμβανων ὁ Σωκρατης τα των τραγῳδῶν ποιηματα, διηρωτα αν αυτους, τι λεγοιεν. Ουκ αν φομην. Ὁ Περσων βασιλευς ασμενος αν τους Αθηναίους εις την συμμαχίαν προςεδέξατο. Εδει, ω άνδρες Αθηναίοι, τους λεγοντας άπαντας εν ύμιν μητε προς εχθραν ποιεῖσθαι λόγον, μητε προς χάριν. Ει δε τουτ' εποιει έκαστος, ενικών αν. Οὐκ ἐχρῆν ποτε των πραγματων την γλώσσαν ισχύειν πλεον. Εμοι δε κε ταῦτα μελήσεται. Εξημαρτε τις ακων συγγνωμη αντι τιμωρίας τούτῳ. Τί δ' ουκ οιδα; Τί ἐχρῆν με ποιεῖν ; Τί ου μελλει γελοιον εἶναι; Πῶς οὐκ ενδέχεται σωφρονήσαντα προσθεν αὖθις μη σωφρονεῖν ; Ου γαρ πω τοιους ιδον ανερας (ανδρας) ούτε ίδωμαι. Ιωμέν. Αγε σκοπῶμεν καθ' ἐν ἕκαστον. Φερε δη πειραθῶ προς ύμας απολογήσασθαι. "Α μη κατέθου μη ανελη. Καν μονος ᾖς, φαυλον μητε λεξης μητε εργασῃ μηδεν. Ου μη σου (ου φοβος εστι μη σοι) δύνωνται αντἔχειν οἱ πολέμιοι. Μη ου τοῦτ ̓ ᾖ χαλεπον, θανατον εκφυγείν, αλλα πολυ χαλεπωτερον (εκφυγείν) πονηρίαν. Ου μη εκπλαγής, ουδε μη αισχυνθῇς. Ισως αν τινες επιτιμήσειαν τοις ειρημένοις. Χειρίσοφος ἡγοῖτο. Οἱ κακοὶ ουποτ' ευ πράξειαν αν. Τα ηδη γεγενημένα ουκ αν δυνηθείημεν κωλῦσαι. Απελθοις αν. Our αν αποφεύγοις την νόσον. Παντες αν όμολογήσαιτε ὁμονοιαν μέγιστον αγαθον εἶναι πολει. Ει τοῦτο ελεγες, ήμαρτανες αν. Εἰ τοῦτο ελέξας, ἡμαρτες αν. Εχαρης αν. Ειθε τοῦτο εγιγνετο, Ευτυχης αν ην. Ει τοῦτο λεγοις, ἁμαρτάνοις αν. Ει τι έχοις, δοιης αν. Χαίροις αν. Ηδέως αν τοῦτο ακουσαιμι. Γενοιτ' αν πᾶν εν τῳ μακρῳ χρονῳ. Ειθε τοῦτο γιγνοιτο. Ει τι είχεν, Μis hijas son las ménos doctas de todas las doneellas, my daugh. ἔφη, δοῦναι αν. Ει τι εἶχον, εδωκα αν. Ει τι εχοι, εφη, δοῦναι αν. Ει τι εχοιμι, δοιην αν. Δῆλος εἶ ἁμαρτανων αν, ει τοῦτο λεγοις. ENGLISH-GREEK. They would rejoice. They would have rejoiced, had their parents come. He would be glad to hear those songs. If I have any, I will give some. If I had any, I would give some. If I had any, I would have given some. Would that these things could be! May that come to pass! If they said that, they sinned, but they did not say it. May they be happy! Suppose that they advisedly sinned Well! they left the house. Not know? How could I help it? Men once wise must be wise a second time. I never yet saw such women, nor do I expect to see such. Come let us draw up the soldiers. My children, though you are alone, neither do nor say anything bad. Thy son cannot oppose thee. Thy son may oppose thee. Thy son might oppose thee. Thy son might have opposed thee. Xenophon may lead the way. I wish they were gone. They would all confess, that friendship and wisdom are the greatest good of life. VOCABULARY, QUESTIONS, ETC. Ποτε μεν, now I had enough for the day, and novo frequently I had not (I would not have.) Ουκ αν φομην, I could not have thought it. Προς εχθραν, etc., under the influence of hatred. Τί δ' ουκ οιδα ; how can I avoid knowing this? The superlative relative is formed by placing the definite article before mas (more) or menos (less), and putting these before the adjective; as, El Judio es el mas rico de todos, the Jew is the most rich (the richest) of all, La madre del Frances es la mas rica de todas las mugeres, the mother of the Frenchman is the richest of all the women. ters are the least learned of all the maidens. Remark.-Some of the adjectives have, besides the regular superlative absolute, also an irregular one, derived from some ancient form of the adjective; as, fidelisimo, very faithful; bonisimo, very good. The regular superlative of these adjectives is fielisimo and buenisimo, from fiel, faithful, and bueno, good. The irregular forms in general use are few, and are all to be found in Spanish dictionaries; therefore they offer no impediment to the student. La muger es muy amable. El juez es muy viejo. La Francesa es muy vieja. El criado es muy culpable. La Χειρίσοφος ἡγοῖτο, Cheirisophus may lead the way; hence by an lengua españolar es bella y muy armoniosa. La luna es muy easy inversion, may Cheirisophus lead the way. brillante. Las estrellas son muy brilliantes. Las torres son altísimas. Las Españoles son muy sobérbias. El juez es muy escrupuloso. La casa es altisima. El buey es tan fuerto como el caballo. El caballo es tan viejo como el buey. El pintor es mas robusto que el impresor. Las criadas de la i Española son mas garrulas que los criados del Aleman. El sol es mas brilliante que la luna. La luna es ménos brilliante que el sol. La hija del médico es ménos hermosa que la hija del juez. Las casas no son tan altas como las torres. ENGLISH-SPANISH, The mountain is very high. The male-servant is very old. The Spanish language1 is elegant and very harmonious. The sun is most brilliant. The stars are very brilliant. The painter is as proud as the judge. The horse is as strong as the ox. The carpenter is as rich as the printer. The daughters of the German-woman (Alemana) are less culpable than the daughters of the Spanish-woman (Española). The stars are less brilliant than the moon. The moon is less brilliant than the sun. The carpenter is more ignorant than the painter. The lion is stronger than the horse. The judge is wiser than the physician. The personal pronouns are-yo, I; tú, thou; usted, you; él, ella, ello, he, she, it; nosotros (masc.), nosotras (fem.), we; vosotros (masc.), vosotras (fem.), ye; ustedes, you; ellos (masc.), ellas (fem.), they; se, himself. Nos is sometimes used in the nominative for nosotros, but only when a nation or body of men issue some proclamation or law; as, we (nos) the representatives of Mexico." 66 Vos was anciently used in the nominative for vosotros, but is is now used only in addressing the Deity and celestial beings, or persons of very superior rank. Usted is the only word with which persons address and are addressed in ordinary conversation in Spanish. It is a contraction of vuestra merced (your worship); and though it is always to be translated by the second person (you) in English, it is of course of the third person, and requires its corresponding possessive pronoun and the verb to which it may be the nominative, to be in the third person. In writing, usted is nearly always abreviated into v., vm., vmd., vd., V., I'm., VM., Vtra, or Md.; and the plural (ustedes) into rs., rms., vmds., VV., Vms., Vmds.; as, ¿Como está vmd.? ¿Como va su salud? literally, How is your worship? how goes his health? or as we should render it in English, How are you? how is your health? The personal pronouns have two forms of the objective case, the direct and the indirect; the first governed by the verb or the preposition to, understood, and the second always governed by a preposition before it, expressed; as, 1st. Juan me dió un libro, John (to) me gave a book. 2nd. Juan vino por mí, John came for me. The personal pronouns are declined as follows:-t Nomin. [Wanting in the plural.] d' ello, to it. 1st Obj. se, himself, herself, itself; themselves. 2nd Obi, á si, to himself, to herself, to itself; to themselves. A pronoun of the first-objective case is placed before the verb which governs it, except with infinitives, imperatives, and gerunds; as, El hombre me dijo, the man said to me. La muger le halló, the woman found him. Los perros los siguieron, the dogs followed them. El médico les dijo, the doctor said to them. If the sentence begin with a verb, the pronoun is allowed to come after it; in other words, a pronoun of the first-objective case may or may not begin a sentence. When the pronoun comes after the verb, it is joined to it, and both form one word; as, Negoles el cielo este gozo, denied-them heaven this pleasure.* The first-objective case is employed in Spanish, when in English either the verb or the preposition to, cxpressed or understood, governs the personal pronouns; as, Pablo me mandó, Paul com- Juan te dió un libro, John manded me. gave (to) thee a book. criada me trajo un pañuelo, | El sastre nos cio, the tailor the maid-servant brought (to) me a handkerchief. La saw us. Los pastores nos hablaron, the shepherds spoke to us. When in English the personal pronouns of the third person are governed by the verb, in Spanish le and los, for the mas culine, and la, las, for the feminine, are used; as, La muger le vio, the woman El viajante los hallo, the tra saw him. veller found them, When in English the personal pronouns of the third person are governed by the preposition to, expressed or understood, in Spanish le and les are used for both genders; as, El juez le dijo, the judge said | Los libreros les dieron libros, the to-him (or to-her). booksellers gave (to) them books. A personal pronoun of the second-objective case is placed after a preposition; as, Cayó temor sobre él, fear fell | El pintor lo hizo upon him. para mi, the painter made it for me. Vino temor sobre todos los veci-Yo acceptaré el favor de vmd., nos de ellos, fear came upon all the neighbours of them. I will accept the favour of your worship.† That is, as it would be properly expressed in English, “heaven denied them this pleasure." ↑ That is, "I will accept your favour." 1 Pedro les la llevó, Peter (to) If in English two objective cases of personal pronouns are in the same sentence, one of them governed by the preposition to, understood, and the other by a verb, the one governed by the preposition is placed first; as, Maria me lo dió, Mary (to) me it gave (or, Mary gave it to me). If the pronoun be reflective, that is, if the nominative and objective cases refer to the same person, the reflective pronoun must come before the other, if another be used in the same sentence; as, SPANISH-ENGLISH. [The personal pronouns are in Italics.] Pedro me escribió dos cartas. Ella le dió un libro. El los halló. Ella les escribió algunas cartas. El médico les habló. Yo soy pobre y viejo. Tú eres muy sábio. El es ignorante. Nosostros somos fuertes y ricos. El pintor te dió una cuchara de plata. La muger nos vió. El carpintero nos habló. Los Españoles le hablaron. [In forming a negative sentence, the adverb no must come not only before the verb, but even before personal pronouns of the first-objective case; as, Juan no me lo dijo, John not to-me it El cura se me dirigió, the rector addressed himself to me. said, i. e. John said it not to-me; or as it would be commonly expressed in English, John did not say it to me. When, in the second-objective case, any one of the pronouns mi, ti, si, is preceded by the preposition con (with), this pre-versation, and though of the third person, is equivalent to the Vmd. (pronounced usted) is generally used in common conposition is prefixed to the pronoun, and the syllable go affixed, English word you: thus the sentence, 'you are rich," if the whole forming one word; as, addressed to one person, would be, vmd. es rico (your worship is rich); if addressed to more than one person, vms. son ricos Juan vino conmigo, John came Ella vino contigo, she came (your-worships are rich). When females are referred to, the with-me. with-thee. feminine form of the adjective must be used.] Vid. es muy sábio. Vmd, tiene hambre. Vd. me dió un libro. Vm. tiene una casa. Vms, tienen sed. Vms. aman la verdad. Vms. no son sobérbios. El juez tiene mucha confianza en vd. Pedro le dió el libro. El Aleman no le dió dinero. La Alemana no le habló. La muger no me habló. El pintor no te vió. El carpintero no los halló. Yo voy a darle un libro. V. es rico. VV. son pobres. Vds, son sobérbios. ENGLISH-SPANISH. Peter wrote me two letters. The painter gave him a book. She found them. He wrote to-them some letters. I am old and poor. The judge spoke to-them. Thou art very rich. painter gave thee a silver spoon. The woman saw us. He is wise. We are ignorant. They are strong and rich. The The carpenter spoke to us. The Spanish-woman spoke to him. The physician saw him. The French-woman saw them (masc.) The German-woman saw them (fem.) The carpenter made it (lo) for him. The painter has confidence in her. The printers ve much confidence in him. The Englishman made it for me. The physician has much confidence in them (masc). The mother of the painter has much confidence in us. The Spaniard saw her. The Frenchman saw them. Peter saw him. They spoke to-me. Ello, and its objective case to, are properly used for a noun to which we cannot assign any gender; thus, if we should tell a man "I am ill," and he should reply, "I am sorry for it," we perceive that the word it cannot be considered mascu- [The remaining exercises in this lesson are to be rendered by line or feminine, and in such a case in Spanish lo (not le nor la) d. and its objective cases, when the second person you occurs would be used. Though not strictly correct, the practice is in English. Instead of vmd., any of the other abbreviations, allowed of using to for the masculine le, if this pronoun be, T., V., (all pronounced usted), may be used; and indirectly governed by a verb. stead of vmdes., the other abbreviations in the plural, VV., Vs., Vis., Vds., may be used.] Personal pronouns must always agree with the nouns for which they are substituted, in gender, person, and number. Thus, if it is said, "John lost his pen (pluma) and Peter found it," the pronoun it must be rendered, in Spanish, by la, bebecause pluma is feminine. You gave me a book. You are very wise. You are hungry. You have a house. You (plur.) are thirsty. You (plur.) are not proud. You (plur.) love the truth. The physician has much confidence in you. The judge gave you the book. The Englishman did not give you (le) money. The painter did not speak to-you (le). The woman did not speak to-you (plur.). She did not speak to-me. The painter did not see thee. The carpenter did not find them. I am-going to give you (le) a book. Peter saw you (le). FRENCH READING S.-No. XXVII. SECTION II. Quand sur ces touffes d'immortelles Au point du jour, Son œil se ranime; il se dresse1 A son retour. |