606 effected by similar means; and as the adaptation of means to an end is as evident in the works of nature as in the works of man, the argument is as conclusive in one case as in the other, TABLE, Showing the amount of £1 at 3, 4, 5, 6, and 7 per cent. compound interest, for any number of years from 1 to 40, Thus, suppose it to be required to communicate motion to a ball on a plane, by sending an impulse through a hundred balls, the principle known to all mechanicians is, that the force necessary to give the desired motion must be communicated to the first, and from the first to the second, and so on, until it reaches the ball intended to be moved. And this principle is equally applicable to all causes which operate through a suc- LESSONS IN ARITHMETIC.-No. XXXV. cession of particulars. If at the commencement of a series, an intelligent cause operated, and then ceased, or stopped short of the last effect, no sign of intelligence could exist in this, which brings us back to the same obvious principle with which we commenced, viz. that when any effect is produced, an adequate cause must exist, and be in operation at the time of its production. The simple inquiry, then, is, had the progenitors of this dog, or horse, when the animal came into existence and became animated, the skill necessary to continue the animal frame, with all its curiously contrived parts, and power and skill to give to this individual that constitution of instincts, appetites and passions suited to its condition in the world, which it possesses? I leave the atheist to answer this question. The same course of reasoning will be equally forcible as applied to fruits and vegetables, Every one of these organised beings furnishes an irrefragable argument for the being of a God; for in any one of these is evidence of the existence of a wisdom and a power which certainly do not exist in the several particulars of which the series consists. The only modern attempt to invalidate the argument for the being of God founded on the appearance of design in the universe, is that of Mr. Hume, which is substantially this: that this argument supposes that we have seen similar works performed, from which, by analogy, we conclude that an intelligent cause is necessary to account for them; as if we find a watch we believe it to have been made by an artist, because we have before observed such works made by skilful men; but in relation to the world, it is a singular work, entirely unique. We have never seen any world produced, and, therefore, the reasoning which would hold in regard to the conclusion that the watch was made by an artist does not apply. More importance has been given to this objection, especially by Dr. Chalmers, than it deserves. The objection of Hume is a mere sophism, and can unsettle no mind which understands the nature of the argument in question. According to Mr. Hume's argument we could not infer from any work of art that it had an intelligent author, unless we had seen a work of the very same kind by an artist. Suppose a boy who has never been away from his father's farm, where he has seen nothing superior to ploughs, carts, and harrows, to be conducted to a seaport, and to see a steam-frigate. As he has never seen on the farm any thing formed like this, according to Mr. Hume, he could not infer that this stupendous work was produced by an intelligent cause. To the boy it would be a singular effect, the like of which he had never witnessed, and, therefore, he could infer nothing respecting it. Now every child knows better than this. Any boy of common sense will conclude in a moment that this steam-vessel must have been the work of a skilful artificer. In order to apply the argument from design to any effect, it is not at all necessary that we should have seen an artist engaged in producing its like. All that is necessary is, that there should immediately appear an adaptation of means to produce a certain end; and it matters not as to the argument whether we ever conceived of a similar work, or knew any thing of the artist; the certain appearance of design, or a skilful adaptation of means to an end, is always sufficient to produce the certain conclusion, that there has been a designing cause at work, The works of nature are not a singular effect, as far as the argument a posteriori is concerned. The adaptation of means to an end in these is similar to the works of design among men. The difference between a telescope and the eye of an animal is not so great as between a plough and a steam-engine. If there was any difference between the inference from seeing a steamfrigate or complicated spinning-machine, which has never been seen before, and another plough or cart, it would be in favour of the contrivance not before witnessed. The argument seems to be a fortiori in this case. And as the whole argument in regard to the works of man is founded simply on observing an adaptation of means to accomplish an end, and not the adaptation to produce come particular end which we had before seen Yrs. 3 per cent. per cent. 1.040,000 8 10 11 12 1.425,761 13 1-468,534 14 1.512,590 15 1030,000 3.555,673 4.549,383 5-80,735 3.733,456 4.822,346 6.21,886 Discount is the abatement or deduction made for the payment of money before it is due. For example, if I owe a man £100, payable in one year without interest, the present worth of the sum is less than £100; for, if £100 were put out to interest for 1 year at 6 per cent., it would amount to £106; at 7 per cent., to £107, etc. In consideration, therefore, of the present payment of the sum, justice requires that my creditors should make some abatement from it. This abatement is called Discount. The present worth of a debt payable at some future time without interest, is that sum which, being put out to legal interest, will amount to the debt, at the time it becomes due. Ex. 1. What is the present worth of £756, payable in 1 year and 4 months, without interest, when money is worth 6 per cent. per annum? Analysis. The amount, we have seen, is the sum of the principal and interest. Now the amount of £1 for 1 year and 4 months, at 6 per cent., is £1.08; that is, the amount is 108 of the principal £1. The question then resolves itself into this: £756 is 188 of what principal? If £756 is 188 of a certain sum, This Th of £756; now £756 ÷ 108 — £7, and 188 £7 × 100, which is £700. 100 LESSONS IN ARITHMETIC. Or we may reason thus: Since £1.08 (amount) requires £1 principal for the given time, £756 (amount) will require as many pounds as £1.08 is contained times in £756; and £756 £1.08 £700, the same as before. - PROOF.-£700 08 £56, interest for 1 year and 4 months; and £700 56 £756, the sum whose present worth is required. Hence, To find the present worth of any sum, payable at a future time without interest. First find the amount of £1 for the time, at the given rate, as in simple interest; then divide the given sum by this amount, and the quotient will be the present worth. The present worth subtracted from the debt will give the true discount. This process is often classed among the problems of interest, in which the amount (which answers to the given sum or debt), the rate per cent., and the time are given, to find the principal, which answers to the present worth. 2. What is the present worth of £424-83, months, when money is worth 6 per cent.? true discount? payable in 4 What is the Solution.-£424·83 ÷ £1·02= £416·50= £416 10s., present worth; and £424.83 · £416-50 £8.33 £8 6s. 7 d., the true discount. 3. What is the present worth of £1,000, payable in 1 when the rate of interest is 5 per cent. ? year, year [on the given sum from the time it is discounted to the time it becomes due. Hence, in ordinary business transactions, discount is the same as simple interest paid in advance. Thus, the usual discount on a bill for £105, payable in 1 year, at 5 per cent., is £5 5s., while the true discount is only £5. The difference between ordinary discount and true discount, is the interest of the true discount for the given time. On small sums for a short period this difference is trifling, but when the sum is large, and the time for which it is discounted is long, Ordinary discount is the difference is worthy of notice. always supposed to be meant, unless the word "true" is prefixed. It is usual to charge interest for the 3 days' grace. To find the discount on a bill or promissory note. Calculate the interest of the bill or promissory note for three days more than the specified time, and the result will be the discount. The discount subtracted from the sum named in the bill or note will give the present worth required. Note.-Interest should be computed for the three days' grace in each of the following examples. 13. What is the discount on a bill for £465, payable in 6 months, at 6 per cent.? 14. What is the discount on a bill for £972, payable in 4 months, at 5 per cent. ? 15. What is the discount on a bill for £1,492, payable in 3 months, at 7 per cent. ? 16. What is the discount on a bill for £628, 1 ayable at 60 4. What is the present worth of £1,645, payable in 1 and 6 months, when the rate of interest is 5 per cent. ? 5. What is the true discount on a bill for £2,300, payable in days' sight, at 5 per cent.? 6 months, when the rate of interest is 5 per cent.? 6. What is the true discount, at 6 per cent., on £4,260, payable in 4 months? 7. What is the present worth of a bill for £4,800, due in 3 months, when the rate of interest is 6 per cent. ? 8. What is the present worth of a bill for £6240, payable in 1 month, when the rate of interest is 4 per cent.? 9. A man sold his farm for £3,915, payable in 23 years: what is the present worth of the debt, at 6 per cent. discount? 10. What is the present worth of a bill for £10,000, payable at 30 days' sight, when interest is 5 per cent. per annum? 11. What is the difference between the true discount of £8,000 for 1 year, and the interest of £8,000 for 1 year, at 5 per cent.? It is customary for banks and bil-brokers, in discounting a bill or promissory note, to deduct in advance the legal interest 17. What is the present worth of £2,135, payable in 8 months, at 7 per cent. ? 18. What is the present worth of a bill for £2,790, payable in 1 month, discounted at 6 per cent. at a bank? 19. What is the discount, at 5 per cent., on a bill for £1,747, payable at 90 days' sight? 20. What is the discount, at 44 per cent., on a bill for £3,143, payable in 4 months? 8 21. What is the discount on £5,126, payable in 30 days, at per cent. 22. What is the discount on £3,841, payable in 60 days, at 64 per cent.? 23. What is the present worth of a bill for £6,721, payable in 10 months, discounted at 6 per cent. at a bank? 24. What is the present worth of a bill for £1,500, payable in 12 days, at 7 per cent. discount? 25. What is the discount on £10,000, payable in 45 days, at 6 per cent. ? 26. What is the discount on £25,260, payable in 90 days, at 7 per cent. ? 27. What is the difference between the true discount and ordinary discount on £5,000 for 10 years, at 6 per cent.? CASE II. 28. A man wishes to make a bill payable in 1 year, at 6 per cent., the present worth of which, if discounted at a bank, shall be just £200 for what sum must the note be made? Analysis. The present worth of £1, payable in 1 year, at 6 · £τόσ = £; that is, the present per cent. discount, is £1 worth is of the principal or sum discounted. The question then resolves itself into this: £200 (present worth) is of what sum? Now, if £200 is of a certain sum, Too is of £2.12766 X 100, £200; and £200 94 £2-12766, and 188 which is £212-766 £212 15s. 3 d. Ans. Or we may reason thus: Since £ present worth requires £1 principal or sum to be discounted for the given time, £200 present worth will require as many pounds as £ is contained times in £200; and £200 £94 £212-766, or £212 15s. 3d. 100 94 PROOF £212.766 ×·06 = £12·7659, the discount for 1 £12.7659 £200, the given sum. year; and £212-766 Hence, To find what sum, payable in a specified time, will produce a given amount, when discounted at a bank, at a given per cent.? Divide the given amount to be raised by the present worth of £1, for the time, at the given rate of bank discount, and the quotient will be the sum required to be discounted. 29. How large must I make a bill, payable in 6 months, to raise £400, when discounted at 7 per cent. discount? 30. What sum, payable in 4 months, must be discounted at a bank, at 5 per cent., to produce £950? 31. What sum, payable in 60 days, will produce £1,236, if discounted at a bank, at 8 per cent.? 32. For what sum must a bill be drawn, payable in 34 days, the proceeds of which, at 6 per cent. bank discount, will be £2,500? 33. For what sum must a bill be drawn, payable in 90 days, so that the proceeds, at 7 per cent. bank discount, may be £3,755? 34. A man bought a farm for £4,268 cash: how large a bill, payable in 4 months, must he take to a bank to raise the money at 6 per cent. discount? 35. A man wishes to obtain £6,324 from a bank at 6 per cent, discount: how large must he make his note, payable in 1 month and 15 days? 36. What sum, payable in 8 months, if discounted at a bank, at 6 per cent., will produce £1,000? 37. What sum, payable in 4 months, will produce £5,000, if discounted at 7 per cent. at a bank? 38. A man received £4,625 as the proceeds of a bill, payable in 60 days, discounted at a bank at 5 per cent.: what was the amount of the note? 39. A merchant wished to pay a debt of £8,246 at a bank, by getting a bill payable in 30 days discounted, at 8 per cent. : how large must he make the bill? INSURANCE. Insurance is security against loss or damage of property by fire, storms at sea, and other casualties. This security is usually effected by contract with insurance companies, who, for a stipulated sum, agree to restore to the owners the amount insured on their houses, ships, and other property, if destroyed or injured during the specified time of insurance. Insurance on ships and other property at sea is sometimes effected by contract with individuals. The insurers, whether an incorporated company or individuals, are often termed underwriters. The written instrument or contract is called the policy. The sum paid for insurance is called the premium. The premium paid is a certain percentage on the amount of property insured for 1 year, or during a voyage at sea, or other specified time of risk. Rates of insurance on dwelling-houses and furniture, stores and goods, shops, manufactories, etc., vary from to 2 per cent. per annum on the sum insured, according to the exposure of the property and the difficulty of moving the goods in case of casualty. It is a rule with most insurance companies not to insure more than two-thirds of the value of a building or goods on land. Coasting vessels are commonly insured by the season or year. In time of peace, the rate varies from 4 to 7 per cent. per annum; in time of war it is much higher. Whale ships are generally insured for the voyage, at a rate varying from 5 to 8 per cent. on the sum insured. When the general average of loss is less than 5 per cent., the underwriters are not liable for its payment. CASE I. To compute insurance for 1 year, or a specified time. Multiply the sum insured by the given rate per cent., as in interest. Ex. 1. A man effected an insurance on his house for £1,500, at 11 per cent. per annum : how much premium did he pay? Solution.-£1500 X 0125 (the rate) £18.75. Ans. 2. What is the premium for insuring a store to the amount of £2,760, at per cent. ? 3. What premium must I pay for insuring a quantity of goods, worth £6,280, from Liverpool to New York, at 1 per cent.? 4. What is the annual premium for insuring a stock of goods, worth £10,200, at per cent.? 5. What is the annual premium for insuring a coasting vessel, worth £1,600, at 6 per cent.? 6. A bookseller shipped a quantity of books, valued at £4,700, from London to Dublin, at 1 per cent. insurance: what amount of premium did he pay? 7. A merchant shipped a cargo of flour, worth £4,500, from Liverpool to New York, at 2 per cent.: how much premium did he pay? 8. What is the insurance on a cargo of teas, worth £7,500, from Canton to London, at 24 per cent.? 9. What is the annual insurance on a factory, worth £6,500, at per cent. ? 10. A powder mill was insured for £1,945, at 12 per cent.: what was the annual premium? 11. A ship embarking on an exploring expedition was insured for £4,536, at 8 per cent. per annum: what did the insurance amount to in 5 years? 12. A policy of insurance for £1,500 was obtained on a whale ship, at 7 per cent. for the voyage: what was the amount paid for insurance? CASE II. 13. If a man pays £16 annually for insuring £800 on his shop, what per cent, does he pay? Analysis. If £800, the amount insured, costs £16 premium, £1 will cost bo of £16; and £16 £800 = •02, which is 2 per cent. PROOF.-£800 X 02 £16, the premium paid. Hence, To find the rate per cent., when the sum insured and the annual premium are given. Divide the given premium by the sum insured, and the quotient will be the rate per cent. required. Note. This case is similar in principle to Problem II. in Interest. 14. If a man pays £60 annnally for insuring £2,400 on his house and shop, what per cent. does it cost him? 15. A merchant pays £200 per annum for insuring £8,000 on his goods: what per cent. does he pay? 16. A merchant paid £122 10s. premium on a cargo of flour, worth £12,250, from Charleston to Portland: how much per cent. did he pay? 17. An importer paid £35 insurance on a quantity of cloth, worth £2,800, from London to New York: what per cent, did he pay? CASE III. 18. A man pays £45 annually for insuring his library, which is 3 per cent. on the amount of his policy: what is the sum insured? 00 Analysis. Since £y will insure £1 at the given rate for a year, £45 will insure as many pounds as Too are contained £1,500. Ans. times in £45; and £4503 PROOF.-£1500 X 03 £45, the given premium. Hence, To find the sum insured, when the premium and the rate per cent. are given. Divide the given premium by the rate per cent., expressed in decimals, and the quotient will be the sum insured. Note.-This case is similar in principle to Problem III. in Interest. 19. An importer paid £650 premium on goods from London to New York, which was 14 per cent. on the amount insured: how much did he insure? 20. A merchant paid £1,640 premium on goods from London to Constantinople, which was 2 per cent. on the worth of the goods insured: how much did he insure? 21. A premium of £487 10s. was paid on a cargo of cotton from Liverpool to New Orleans, which was per cent, on its value: what amount was insured on the cargo? 22. When the rate of insurance is 1 per cent., what sum can you get insured for £860 premium? 23. At per cent. per annum, what amount can a man get insured on his house and furniture for £20 10s. per annum? CASE IV. To find what sum must be insured on any given property, so that, if destroyed, its value and the premium may both be recovered. 24. If a man owns a vessel worth £1,920, what sum must he get insured on it, at 4 per cent., so that, if wrecked, he may recover both the value of the vessel and the premium? Analysis. It is plain, when the rate of insurance is 4 per cent. on a policy of £1, the owner would receive but £ towards his loss; for he has paid £yo for insurance. Since, therefore, the recovery of £ requires £1 to be insured, the recovery of £1,920 will require as many pounds to be insured as £ is contained times in £1,920; and £192096 Ans. £2000. PROOF.-£2000 X 04 £80, the premium paid, and £2000 £80 £1920, the value of the vessel. Hence, to find what sum must be insured on a given amount of property, so that, if destroyed, both the value of the property and the premium may be recovered. Subtract the rate per cent. from £1, then divide the value of the property insured by the remainder, and the quotient will be the sum to be insured. 25. What sum must be insured on property worth £8,240, at 1 per cent., so that the owner may suffer no loss if the property is destroyed? 26. What sum must be insured on £13,460, at 3 per cent., in order to cover both the premium and property insured? 27. If I send a cargo to the Sandwich Islands worth £25,000, what sum must I get insured, at 7 per cent., that I may sustain no loss in case of a total wreck? If an attribute is of such a kind that it belongs either exclusively or preferably to a single object, or if out of the contents of the proposition there undoubtedly or easily arises the idea of the object to which the attribute is ascribed, in such cases the substantive is often omitted in Greek, and the attribute only is employed to denote the object together with its quality. In this way the Greeks use the genitive of possession in union with the article, to designate persons, things, and circumstances which are severally to be regarded as belonging to the idea or person contained in the genitive. Thus the masculine article with the genitive denotes the son cf, and in the plural, the relatives of, the subjects of; in general, him, or those persons or things which belong to the object: e.g. Aλežavôpos ó PITTоv, Alexander the (son) of Philip; oi euavrou, the of me, that is, my (friends, children, etc.), mine; oi IIepurλeovs, the (family) of Pericles. The feminine article with the genitive, after a similar manner, signifies the wife or the daughter of: e.g. Maia Arλavтos, Maia the (daughter) of Atlas; Expaтovs avoirη, Xantippe, the (wife) of Socrates. The neuter article with the genitive indicates in the most general manner that which belongs to a person-his possessions, his condition, his circumstances: e.g. TO TOU DEμLOтOKλεOVS, the (relations, condition) of Themistocles; ra Tov Kuvog, the (nature) of the dog; ra piλwv, the (interests) of friends; Ta ENLARGE-TS TONews, the (affairs) of the city. Sometimes this form of expression is employed merely to designate the object itself contained in the genitive, as, тα τNS TUXNs, fate, fate particularly considered in its workings; τα της αρετης, virtue in its most comprehensive form. As intimated in the last lesson, adverbial attributes in connexion with the article, are often employed to denote the relations of time, place, and things indicated in the adverbs severally; thus, oi tw, those (who are) without; oi porepov, those (who were) aforetime. In a similar manner with prepositions may the article be used: e.g. ò ET TIVI, the (person who is) over something, the superintendant; oi Tо Tivi, those (who are) under some one, his subjects, το επ' εμοι, so far as I am concerned; τα προς τινα, the relations to some one; οἱ απο τινος, his descendants, οἱ εν Toe, the indwellers of the city; oi ev ry nλikig, those who Oi apoi riva, and oi Tepi Tiva, originally meant some great are of age ; οἱ κατα τινα, and οἱ επι τινος, the contemporaries. person and his attendants; but as the eye was always directed chiefly to the great person himself, so in time it fixed exclusively on him, and the phrase came to denote the principal personage alone. LESSONS IN GREEK.-No. LVI. ATTRIBUTIVE WORDS WITH SUBSTANTIVE IMPORT; Attributives employed as Nouns. AN adjective acquires a substantive import when an object, whether a person or a thing, is set forth as the material image of a quality, or when the abstract idea of the quality is designated as a substance in and for itself. Thus, uelav, in the neuter gender, is black; that is, blackness. In the same way we use the concrete black for the abstract blackness. Thus Shakspeare "If in black my lady's brows be deckt." Sο σκληρον, hard; καλον, beautiful; ταχυ, swift, are used by the Greeks as nouns. The former member of the statement given above, is illustrated by the fact that some noun of general import is understood with the adjective; as, pov, a living (thing); VEKpov, a dead (body), a corpse; xonarov, a useful (thing); deov, what is needful, duty. With each of these adjectives, xpnua or payua is said to be understood. The simple fact, however, is, that these adjectives in the neuter gender are used as nouns. The adjective in the neuter gender approaches most nearly to the abstract quality, the denoting of which is the office of the substantive. Thus, when we say, "Do you prefer green or yellow?" we use the adjectives as abstractives, meaning the colour green and the colour yellow. Indeed, the noun and the adjective are intimately connected in sense, so that the one may, in many cases, be used for the other in other languages besides the Greek, especially in the Hebrew and the English. The article is prefixed to these adjectives with substantive meaning, as it is prefixed to appellatives. A participle with the article acquires the form of a noun, and may often be best rendered by a relative clause, e.g. ò paowv, the scholar, or he who has learnt; & Bovλouevos, the willing man, he who is willing; o xpnooμevos, he who will use; o Tuxwv, he who chances, any one, a common-place person. This use of the participle with the article gives rise to some of the nicest shades of meaning, and affords great flexibility to the language; these varieties of meaning may be expressed in Greek by means of this form, and by means of the infinitive with the article already noticed, for which other languages have no equivalent except in circumlocutions. For example, the participle of TurTw, with the article, undergoes many modifications. With adjectival attributes, nouns were omitted which suggest themselves from the nature of the attribute itself. Thus, Xep is omitted with dia, the right (hand), apiorepa, the left (hand); μepic with ǹ dekarn, the tenth (part), ELKOOTH, the twentieth (part), etc.; μoîpa, a portion, an allotment, with ειμαρμένη, ή πεπρωμένη, fate, fortune; γῆ or χωρα with ή pia, and roleμia, a friendly (country), a hostile (country); and so with the adjectives denoting names of countries, as, ATTIEN (scil. Yn); also, i woλλŋ (yn), the greatest part, the most part; odos with neveia, the straight, direct (way); and nμepa, with the cardinal numbers, to indicate the days of the month, as, voтepaιa, ǹ εñiοvσa, aupiov, the next day, the coming day, the morrow; and pоrepaia, the day before. Texvn is understood with adjectives ending in kn, denoting skill in a certain art or profession, e.g. iarpin, the healing (art), pnropun, the speaking (art), whence the word (and the form of the word) rhetoric. 'Tepa, rites, is to to be supplied with the names of festivals, as, ra εTIVIKIα, the victor's (festival); ra Atovvota, the (feast) of Bacchus, the Bacchanalia. So yvwun goes with vikwσa, the conquering (opinion), the prevailing view. In the same way are used several technical terms, as, in the military art, To detov (scil. Kepas, wing), the right; ro Evwvvμov, the left (wing); also the grammatical word Trois, case, e.g. Yevikη, genitive, dorin, dative, etc. way συλλάβη, syllable, is understood with ληγουσα, the terminating syllable; rapaλnyovaa, the penult, that is the last syllable but one; and προσῴδια, accent with βαρεῖα, οξεία, the acute and the grave; βιβλος and βιβλιον, also συγγραμμα, book, writing, with parts and titles of books; finally, the musical term xopon, string, is implied with rarn, the highest, vnrn, the lowest (on the lyre), and appovia, concord, with n These modifications may be extended through the middle δια πασῶν, ἡ δια τεττάρων, etc. and passive voices. In the same Other omissions of substantives are permitted only when Terms of general import which are added to the predicate of the negative proposition in a substantive or adverbial form, and which are added to the object in the form of adjectives, are generally each accompanied by a negative. Instances are given in the exercise, besides the following: οὐκ ἔστιν οὔτε τεῖχος ουτε χρηματα ουτ' αλλο δυςφυλακτον ουδεν ὡς ἡ γυνη they may be readily learnt from the verbs, which, if expressed, they would accompany. Thus, with verbs signifying to go, etc., όδος is omitted, e.g. πορεύεσθαι μακραν (όδον), to go a long way (far); so with λειαν, an easy road, τραχείαν, τ rough road; ιεναι τὴν παρα τεῖχος, to go along the road by the wall; τρέπεσθαι την επί Μεγαρα, to enter on the road to Megara ; ἡγεῖσθαι την συντομωτάτην, to lead on the shortest road; αγειν την επί θανατῳ, to conduet to death. On the same principle are explained ellipses (omissions) like την εναν. nothing is so difficult to guard as a woman-neither a fort, nor τιαν (ψῆφον) θεσθαι, to vote in opposition ; ερήμην (δικην) κατά ηγορεῖν, to bring a deserted charge, that is, to accuse a person in his absence ; ίσην (δικήν) τινειν, to undergo equal justice, to pay the penalty, to atone for; κοιμᾶσθαι βαθυν (ύπνον), το sleep a deep sleep; and the like. εις With the prepositions ev and ag, you often find the genitive of a personal noun to signify the residence of the person, which is left out, as being easily supplied by the mind. Thus the Greeks commonly said, φοιτᾶν εις διδασκαλου, to go to school; φιλου, to a friend's ; that is, to the house of a teacher, the house of a friend, εις εμαυτοῦ, to my house ; εις το των σεμνων θεων, to the temple of the Furies; εν Ασκληπιού, in the temple of Esculapius; 60, εν κιθαριστοῦ μαθειν, to learn in a harper's house, in an academy of music. Very common, and for the most part without variation, are the phrases ev Aidov, in Hades (hell), εις Αίδου, to Hades (scil. δομον and δομῳ). Enlargement of the Predicate. The enlargemen of the predicate is partly external, partly internal. The external enlargement of the predicate consists in this, that several predicated qualities are ascribed to a common subject. Several predicate terms which have a common subject are united to each other by copulative participles, και, τε και, τε - τέ, και Ka; or by the disjunctive particles, η, η - η; or, again, by the adversative (opposing) particles, μεν - δε, αλλα. The internal enlargement of the predicate is two-fold; it is either attributive or objective. If attributive, it more closely defines the nature and the circumstances of what is declared in the predicate. If it is objective (or transitive), it indicates the object to which what is said in the predicate is directed. Enlargement of the Predicate by an Attribute. The attribute added to the predicate contains either an essential idea which individualises and determines (determinative attribute) the idea conveyed in the predicate, and then connects itself in an adverbial form with the predicate, or a merely accidental idea which joins (appositive attribute) or arises out of (explanatory attribute) the predicate, and appears either in an adverbial form or in the form of a noun agreeing with the subject. The adverb, as being indeclinable, requires no special grammatical rules for its application. However, one kind of adverbs, namely, the negative-that is, those which separate a predicate from the subject-have in their application as well as their position, much that is peculiar. In simple and direct propositions the negative adverb is ου, which becomes our before a vowel, and ovy before an aspirated vowel Negative propositions which deny the predicate of a whole species of subjects, become negative by a negative adjective added to the subject; and if the predicate goes | before the subject, the negative adverb or may also be employed: thus, ουδείς αντιλέγει, but ουκ αντιλεγει ουδεις, no one contradicts. Our usage, in which we connect the negative with the noun of the predicate, is not customary in Greek, except when the object is of general acceptation; thus, οἱ των Αθηναίων νομοι ουδεν ωμον προςταττουσιν which may appear also in this form οἱ των Αθηναίων νομοι ου προςταττουσιν ωμον ουδεν. | property, nor anything else Θεος ουδαμή ουδαμως αδικος God is in no way at all unjust. In regard to the position of the negative, the following remarks have to be observed. Since the negative destroys the connection between the subject and the predicate, it belongs to that word in the sentence which denotes that connection, that is, to the verb, before which it ordinarily stands; but if a special reference to any other word is intended, then it comes before that word, having thus the effect of our emphatic accent : 1. ταυτ' ουκ εστι καλα (or) 2. ου ταυτ' εστι καλα (or again) 3. ταυτ' εστιν ου καλά these things are not honourable; where the first sentence denies in a general way, separating the predicate from the subject; the second sentence throws the emphasis on ταυτα, the subject, and the third on καλα, the attribute. In English, the form of the first proposition is given by the translation as it stands above; if you wish to give the force of the second sentence, you must emphasise these things; and for the effect in the third sentence, you must throw the accent on honourable. Thus, these things (whatever may be said of other things) are not honourable; and, these things are not honourable (whatever else they may be). If the sentence is positive in itself, but contains a negative accessory which is set in opposition to the positive idea, then the negative is subjoined to the accessory, e.g. ὑπερφρονοῦσι μεν ἡμας, ὑπομένουσι δ' ου they despise us, indeed, but do not endure us. When, however, the negation is merely in the form which occurs when the opposed positive is merely in the thought, then the negation precedes the accessory: ξύμμαχοι εγενόμεθα τοις Αθηναίοις ουκ επι καταδουλώσει τῶν ̔Ελληνων we became allies to the Athenians not for the enslavement of the Greeks. EXERCISES.-GREEK-ENGLISH. Θεος ουδαμή ουδαμως αδικος, και ουκ εστιν αυτῷ ὁμοιότερον ουδεν η ός αν ήμων γενοιτο δικαιοτατος. Το μονοειδες ουδέποτε ουδαμῇ ουδαμως αλλοίωσιν ουδεμιαν ενδέχεται. Ην ὁ ποταμος δασος δενδρεσι παχέσι μεν ου, πυκνοις δε. Συμμαχοι εγενόμεθα τοις Αθηναίοις ουκ επι καταδουλώσει των Ελληνων, αλλ' επ' ελευθερώσει. Σωκρατης επιμελεῖσθαι θεους ενόμιζεν ανθρώπων, ουχ όν τρόπον οι αλλοι νομίζουσιν. Οἱ ̔Ελληνες το παλαι ετράποντο προς ληστειαν, ἡγουμένων ἀνδρῶν ου των αδυνατωτα των. Η πολις ουχ ίκανη εστιν. Κάλος μεν εστι μέγας δ' ου. Οι δη που και συ εἰ των τοιούτων ανθρώπων. Παντες μεν ουκ ηλθον, Αριαῖος δε. Τούτο γε ουκ οίομαι. δεύτερος, οιομαι δε ουδε χιλιοστος, ίσως δε ουδε μυριοστός εστι. Η αστρονομια αναγκάζει την ψυχήν εἰς τὸ ἄνω ὁρᾶν, και απο τῶν ἐνθεν δε εκεῖσε άγει. Εν τη γη αρχουσι Λακεδαιμονιοι και εν τη θαλαττη τον νυν χρόνον. Τα πλείστα των περι τον βιον ου δι' αυτά τα πράγματα ποιοῦμεν, αλλα των αποβαίνοντων ἕνεκεν διαπονοῦμεν. Γυμνασαι πρώτον, α Ούτε πρώτος, ούτε If, however, you speak of individual objects, the negative | μακαριε, και μαθε ὰ δει μαθόντα ἶέναι επί τα της πόλεως. goes with the verb, and the object is without a negative, e.g. ουκ εχω ίππον I have not a horse ουκ έστι μοι οικια I have not a house, for I have no horse, I have no house. Ο Κυρος τους ὑφ ̓ ἑαυτῷ ώσπερ ἑαυτοῦ παιδας εθερα πευεν. Εικότως τα των Ελληνων ἣν τῳ βαρβαρῳ φοβέρα, οὐχ ὁ βαρβάρος τους Έλλησι. Ἱππικόν ουκ εἶχεν ὁ Αγησίλαος στρατευόμενος ἐπι Καρίαν. Δικαία μεν λεγοντες πολλοί αδικα |