We might have written down the process thus: 35)9298 (200 7000 35) 2298 (60 2100 35) 198(5 175 23 The quotient is therefore 200+ 60+5, or 265, and the remainder 23. 9. The above explanations will sufficiently elucidate the following- Rules for Division: (1.) When the divisor contains only one figure, write the divisor on the left of the dividend, with a curved line between them. Beginning at the left hand, divide successively each figure of the dividend by the divisor, and place each quotient figure directly under the figure divided. If there be a remainder after dividing any figure, prefix it to the next figure of the dividend, and divide the number so formed as before. If there occur any figure which does not contain the divisor, place a cipher in the quotient, and prefix this figure to the next one of the dividend, as if it were a remainder, and proceed in the same manner to the last figure. (2.) When the divisor contains more than one figure, beginning on the left of the dividend, find how many times the divisor is contained in the first fewest figures of the dividend which will contain it, and place the quotient figure on the right hand of the dividend, with a curved line between them; then multiply the divisor by this figure, and subtract the product from the figures divided. To the right of the remainder bring down the next figure of the dividend, and divide the number so formed as before. If this number be less than the divisor, annex a cipher to the quotient, and bring down the next figure continuing this process until the number thus obtained be equal to or greater than the divisor. Proceed in this manner until all the figures of the dividend are exhausted. 10. Tests of Correctness of Division : (1.) Multiply the divisor by the quotient, and add the remainder to the product. This should, as already explained, give the dividend. (2.) Subtract the remainder, if any, from the dividend, and divide the difference so obtained by the quotient. The result should be equal to the divisor, if the working be correct. EXERCISE 9. (1.) Divide 47839 by 42; 75043 by 52; and 93840 by 63. (2.) Divide 325000 by 85; 421645 by 74; and 999999 by 47. (3.) Divide 145260 by 1345; and 1912500 by 425. (4.) Divide 8893810 by 37846; and 9302688 by 14356. (5.) Divide 9749320 by 365; 65358547823 by 2789; and 908070605040 by 654321. (6.) Divide 10000000000000000 by 111; 100000000000 by 333; and 10000000000000000 by 11111. (7.) Divide the product of 12345 multiplied by 67890 by 97, 213, 4351, 59, 847, and 6939. 1. Thou fearest and art frightened. 2. If I am silent I am blamed. 3. He rejoices. 4. We rejoice. 5. They rejoice. 6. He tries to bite. 7. We try to educate. 8. Thou obeyest and art praised. 9. We bite. 10. If we bite we are blamed. 11. They exercise. 12. You are moved. 13. He dances. 14. They are delighted. 15. You are adorned. N.B. In this exercise, and in those which follow, words and forms previously given are repeated for the sake of practice. EXERCISE 8.-ENGLISH-LATIN. 1. I obey. 2. If I obey I am loved. 3. He is loved much. 4. He writes well. 5. They paint ill. 6. They dance well. 7. I rejoice if he reads much. 8. Thou paintest. 9. They obey and are praised. 10. If you rule well you are loved. 11. They defend. 12. You are defended. 13. He is deceived. 14. They are pricked. Singular. Plural. Singular. Plural. Singular. I thou Plural. -entur, they. -it, he -itis, -iunt, they. -itur, he iris, thou -imini, ye -tuntur, they. EXAMPLE.-Monere. to remind: stem, mon. EXAMPLE.-Audire, to hear: stem, aud. 1. Custódis. 2. Fulcítur. 3. Venit. 4. Cur dormis ? 5. Bene dormit. 6. Eruditur. 7. Pungis. 8. Occídit. 9. Valde fallis. 10. Auditur. 11. Si valde dormis puníris. 12. Reperit. 13. Si bene erudis laudáris. 14. Vincitur. 15. Cur taces? 16. Tacet et punítur. 17. Reperiuntur. 18. Vestíris. 19. Bene vestiuntur. 20. Si bene vestimini delectamini. 21. Male erudiuntur. 22. Si vinceris vincíris. EXERCISE 10.-ENGLISH-LATIN. 1. Why do you slay? 2. He is guarded. 3. They guard. 4. If you are guarded you are conquered. 5. He blames and punishes. 6. He hears and is instructed. 7. You are well educated. 8. Thou sleepest much. 9. They read. 10. If you dance you are delighted. 11. He is supported. 12. Why are they punished? 13. They are beard. 14. I am clothed ill. 15. They are struck and reminded. RECAPITULATION-TERMINATIONS OR PERSON-ENDINGS OF EXERCISE 11.-LATIN-ENGLISH. 1. Cedo. 2. Legis. 3. Movémus. 4. Exercéris. 5. Mordent. 6. Florent et gaudent. 7. Legĕre tentat. 8. Cur male legis? 9. Dormit male. 10. Valde diligĕris. 11. Vincimini. 12. Bene scribunt. 13. Si bene pingitis laudámini. 14. Defendimur. 15. Ferímus. 16. Cur fanitis? 17. Vestímur. 18. Vincímus. 19. Vincimur. 20. Vincímur. 21. Vincitis. 22. Custodiris. 23. Ornátur. 24. Laudantur. 25. Timémur. 26. Valde times. 27. Mordémini. 28. Educámus. 29. Male saltant. EXERCISE 12.-ENGLISH-LATIN. 1. They yield. 2. If you yield you are conquered. 3. If you are conquered you are bound. 4. I am supported. 5. They sleep. 6. Why do they punish? 7. Why are they punished? 8. You are clothed ill. 9. Thou conquerest. 10. Thou art conquered. 11. Thou Lindest. 12. Thou art bound. 13. They prick. 14. They are pricked. 15. Why dost thou move ? As in the exercises which are immediately to follow, we shall have occasion for parts of the verb, esse, to be, I shall here lay before you so much of that verb as may be necessary for my purpose. do not commonly say good am I. But in Latin we may say either sum bonus, I am good or bonus sum, good am I, This change in the relative position of the words of a sentence, is called inversion. The Latin language has great capability of inversion. The inversions which it employs are neither unnatural nor arbitrary. The inversions depend on the sense. If we wish to throw emphasis on the epithet good, then we must place bonus first. For example, suppose you wish to say that I am good but not safe, you do so by putting bonus before sum. But if you wish to say I am good, in opposition to some one who says you are not good, then, you say, sum bonus, and not bonus sum. As then these inversions were a means by which the Romans gave expression to their own feelings and opinions, they were with them perfectly natural; and if they have the appearance of being unnatural to us, it is merely because we express emphasis differently; that is, we express by certain tones of the voice the emphasis which they expressed by the position of words. In saying this, however, I do not mean to assert that the Romans never gave emphasis by intonation. The beginning of a sentence is the place of chief emphasis; next to this stands the end; an intermediate position has least emphasis. EXERCISE 13.-LATIN-ENGLISH. 1. Boni sumus. 2. Bonus est. 3. Bonus es. 4. Non sum bonus. 5. Cæcus est. 6. Non est cæcus. 7. Valde docti sunt. 8. Salvi estis. 9. Non estis salvi. 10. Indoctus sum. 11. Indocti estis. 12. Non est indoctus. 13. Valde doctus es. 14. Cur malus es? 15. Non sum malus. 16. Sumus boni. 17. Est indoctus. 18. Cur es indoctus ? 19. Non sum indoctus. 20. Sumus salvi. 21. Salvi sumus. 22. Doctus et salvus es. EXERCISE 14.-ENGLISH-LATIN. 16. 1. I am learned. 2. I am not learned. 3. He is learned. 4. They are learned. 5. You are bad. 6. You are not bad. 7. Thou art good. 8. They are good. 9. They are not good. 10. Why are they not good? 11. He is blind. 12. He is not blind. 13. Why is he blind? 14. Thou art not unlearned. 15. Thou art blind and not safe. They are blind. 17. You are good and safe. 18. He is very unlearned. KEY TO EXERCISES IN LESSONS IN LATIN II. EXERCISE 3.-LATIN-ENGLISH. 1. I praise. 2. Thou blamest. 3. He adorns. 4. We educate. 5. You grieve. 6. They wound. 7. He tries. 8. He tries to dance. 9. Thou art wounded. 10. He is grieved. 11. We are praised. 12. Thou adornest. 13. They are educated. 14. Thou art grieved. 15. You are wounded. 16. I delight. 17. Thou delightest. 18. He delights. 19. We delight. 20. You delight. 21. They delight. 22. I am delighted. 23. Thou art delighted. 24. He is delighted. 25. We are delighted. 26. You are delighted. 27. They are delighted. EXERCISE 4.-ENGLISH-LATIN. 1. Laudo. 6. Laudant. 7. Laudor. 8. Laudaris. 11. Laudamini. 12. Laudantur. 13. Vexamini. 16. Educantur. 17. Saltat. 20. Tentamini. 21. Vulneratur. tamus. 2. Laudas. 3. Laudat. 4. Laudamus. 5. Laudatis. 9. Laudatur. 10. Laudamur. Delectant. 14. Ornas. 15. 18. Vituperamini. 19. Ten22. Educor. LESSONS IN DRAWING.-III. BEFORE commencing our remarks upon the methods of drawing rules with regard to retiring lines and retiring planes; these solid objects, we must lay before the pupil some very important rules belong to Perspective. As we are now getting into deeper water, we must ask for the patient attention of the pupil in a branch of the subject which would be much easier to explain in his presence, with the help of a piece of chalk and the blackboard, than to express in writing. First, then, retiring lines are lines which go away from us. For instance, suppose we are standing at the end of a street and looking down its length; the lines of the eaves, and spouts, tops and bottoms of windows, and doors, etc., are retiring lines. And secondly, the fronts of the houses are retiring planes, or surfaces. Again, sit at the end of a table; the lines or edges on the right side and on the left are retiring lines, and the surface or top of the table is a retiring plane; so that retiring planes, like retiring lines, may be horizontal (parallel with the earth), perpendicular (upright), or inclined. We also direct the attention of the pupil to Figs. 28, 29, etc. In Fig. 28, fb, g d, h e, and i c are horizontal retiring lines, and the whole surface of the pavement is a retiring horizontal plane. In Fig. 29 the wall to the left is a retiring perpendicular plane. In Fig. 30 the fronts of the steps are parallel perpendicular retiring planes. The tops of the steps are horizontal retiring planes. In Fig. 31 the lid of the box from its position is an inclined retiring plane. We advise the pupil now to make himself familiar with the following fixed principles relating to retiring lines and planes:1. The Line of Sight, or, as it is sometimes called, the horizontal line, represents the height of the eye in the picture, which, when we come to the explanation of these terms, we will mark in the illustrations H L (see Figs. 28 and 29). 2. The Point of Sight, marked PS, is the point opposite the eye in the picture, and is consequently upon the line of sight. 3. The Station Point is the place where the spectator is supposed to stand when viewing the object represented; marked s P. 4. A Ground Plan is the horizontal extent of the object when drawn upon the ground. 5. The Vanishing Point is that point in the plane or surface of the picture, where retiring lines if produced or continued, would meet or terminate; marked v P. 6. All retiring lines have vanishing points. 7. All horizontal retiring lines have their vanishing points upon the line of sight. 8. All parallel retiring lines have the same vanishing point. each way within a greater angle, he would have to turn his head, and consequently he would require two or more points of sight; this is only allowable in panoramas (viz., long pictures generally placed upon upright rollers, and so drawn out as a ribbon would be from a reel), when the view of a country for any number of miles in extent is exhibited; the proper or more convenient distance from the object is, when it is placed within an angle of from 20° to 25°. Let a b, Fig. 25, be two objects to be drawn in the same picture; the distance from them at c would be the nearest approach we could make; then the angle a cb would be an angle of 60°. If we removed our position to d, then the angle would be much less, and more suitable for our picture. We beg it may be understood that hereafter when we say drawing from Nature, we allude to all objects, trees, buildings, etc. Although buildings are not natural objects, yet they are included under this expression. 4th. Ground Plan. The best illustration of a ground plan is a map; it has nothing to do with heights or depths. Suppose the walls of a house were removed, and only the foundations left, we should then see the plan of the house. 5th. Vanishing Point (v P). If a line be drawn from the eye parallel to any original straight line of the object the point PS & VP b C 9. All horizontal lines which are parallel with the picture plane, are drawn parallel with each other, and the line of sight. 10. All horizontal retiring lines forming right angles with be picture plane, or with our position, have the point of sight for their vanishing point. 11. All lines inclined with the horizon, and with the picture plane, have their vanishing points above or below the line of sight, according to the angle they form with the horizon, their vanishing points being always on a line perpendicular to the vanishing point upon the line of sight, to which they would have retired had they been horizontal. Before going any further we will endeavour to explain the above fixed principles or definitions, taking them in their order. 1st. The Line of Sight, H L (horizontal line), is drawn parallel with the base of the picture, according to the height of the eye from the ground. If we are drawing a house from a higher point of view than when standing or seated on the ground, the line of sight will be higher in the former than in the latter case. 2nd. The Point of Sight (P S) is subject to the same conditions as to its height from the ground as the line of sight. 3rd. The Station Point (s P) may be at almost any distance from the object that is most convenient; but observe, if too near, we get a distorted view of the object when drawing from Nature. Let the reader for a moment place himself in an upright position, keep his head perfectly still, and turn his eyes to the right and to the left; all that he can possibly see whilst so doing is included in an angle of 60° (sixty degrees), considerably too near the objects he is looking at to make a pleasing picture, though it would not be wrong. But if he included more objects where that line cuts the picture plane (or surface of the picture) is the vanishing point of that original line. When the pupil has read this, let him rise from his chair, and stand about eight or nine feet from the window, and look out upon the objects beyond. Suppose that a house is in sight, having one of its cor ners towards him. If he stood without moving from the position he has chosen, and took a long stick having a piece of charcoal, or something that will make a mark on glass, fastened to the end, he might trace the form of the house upon the glass in the same way as tracing a drawing through a piece of thin paper; he would then have made a true perspective drawing of that house upon the glass. This glass is the picture plane; the place where he stands when making the tracing is the station point. Now, supposing the retiring side of the building he is tracing is on the left as he looks at it, let him raise his left arm and hold it parallel to that retiring face or plane of the building, he will then be pointing to the vanishing point of the retiring face or plane, and all horizontal lines upon that plane would be retiring also, and consequently meet at the same vanishing point. He might, for the sake of experiment, actually make a tracing on the window of one or more of the parallel retiring lines of the building, and at the same time make a mark upon the wall for the vanishing point. Then if he continue the traced lines on the glass he would eventually find that they will meet the mark upon the wall, that mark being the vanishing point; and he would also find that the mark upon the wall is on a level with his eye, on the line of sight. He would find also that if there were any other lines parallel with the window, those lines when traced would be parallel with the line of sight, and be drawn horizontally on the glass. This explains all that is meant in the definitions numbered 5, 6, 7, 8, 9. If there be any other lines of walls or buildings to be seen through the window which are at right angles with it, these lines have the point of sight for their vanishing point; just as the retiring lines of the covers of the books at A and B in Fig. 26, which are at right angles to the edge of the table on which they are lying have their vanishing point in the point of sight, while those that are not at right angles to the edge of the table, as at E HL and F, have their vanishing points to the right and left of the point of sight. This observation will explain Definition 10. Definition 11 will come under our notice hereafter, when we will go more into the consideration of the above fixed principles with the help of diagrams. An object can be placed in two positions, to which the rules of perspective are applicable parallel and angular. Parallel perspective is a ни same way with the other lines d ge h and c i. Now observe, if all these lines were produced towards the line of sight, HL, they would meet at the P s. The other parallel lines, k, l, m, etc., must be carefully arranged according to the principles we have already laid down in our introductory lessons. The pupil may naturally inquire if there are not some perspective rules for regulating the retiring horizontal distances of objects, as well as their heights. We answer, there are. We do not intend to avoid this question, but put PS and VP it off for the present, lest the pupil should become too early involved in technicalities that belong especially to geometrical perspective— a branch of drawing to be considered hereafter. With reference to the retiring lines of the pavement (Fig. 28), we have a fitting illustration in a railroad; probably the pupil has observed when standing on a railway bridge and looking down the line, that the rails as they retired seemingly converged to a point in the distance; that point would be the vanishing P.S. b d k 6 a m Fig.28 HL h HL term used in reference to objects of & rectangular form, such as the interior of a room, a cube, etc., when these objects are so placed that their retiring sides are at a right angle with the picture plane, P P, and the remaining sides are parallel to the same, as in Fig. 27 (a). Angular perspective alludes to objects of the same form so placed that all the sides retire, as in Fig. 27 (b), which is the plan of a room in angular perspective, having one of its angles towards the picture plane P P, and its four sides retiring. PS' Parallel perspective is the more simple of the two, and easier to be understood, we therefore commence with that. The first example is a pavement (Fig. 28). Draw the horizontal line, H L, and place upon it a point marked P s and v P (point of sight and vanishing point). The reason that it is both the point of sight and the vanishing point has been explained in Definition 10. Then mark the distance of a from P 8, through a draw the line b c, and divide it in the points d and e; place the pencil on P S, and draw it over the paper through b to f, mark f, join bf, proceed precisely in the point; therefore, in drawing ness. the pupil in going along with us through these lessons have made some failures, and found some difficulties, there is no doubt that most of them may be attributed to one great neglect which all beginners so readily fall into, that is, the not "marking in the distances" before they attempt to draw the lines. It is the common failing with the majority of beginners, that they attempt to draw the lines without first arranging their positions. We have said quite enough of the practical way of proceeding with the arrangement of lines, but once more, let the attention of the pupil be ever directed to the "whereabouts" of the lines of his drawing. LESSONS IN ENGLISH.—III. SIMPLE PROPOSITIONS. THE PARTS OF SPEECH. As, in English nouns, there are at the most only two cases, so are we without an objective or accusative case. Yet sentences in English, as in Latin, have their object. That object must be recognised. Let it be called the object of the proposition, for so it is; in any given instance let it be termed the object of the verb, for it is the object of the verb. Here you must carefully distinguish between a case and a relation. A case denotes a change in a noun corresponding to the change in its relation. This you will see in these two propositions: Now, without knowing Latin you may clearly understand what case means, and learn that in English we have no objective case. The Deus of number 1 becomes Deo in number 2; but in both, the English word God remains the same, though in the former, is in what is commonly called the nominative, and in the latter in what is commonly called the ablative case. Look also at mundus and mundum; you see that the nominative mundus is, in the objective or accusative case, changed into mundum. Here you clearly have two cases, but the English word world represents both. Consequently, if world is in the nominative it is not also in the objective case, for there is no alteration of form whatever. Yet in the latter case there is a change of relation; for while in number 1 world is the object, in number 2 it is the subject of the proposition. The English, then, does not conform to the Latin custom of expressing diversity of relations in nouns by diversity of form, or does so only in a limited degree. In fact, the tendency of the English language has long been to drop the terminations and inflexions which it borrowed from its Anglo-Saxon parent. The tendency has for ages continued to become more and more strong. It is a tendency which deserves encouragement, for in proportion as it is effectual, it gives freedom and power to the language, and makes the acquisition of it easy, and the diffusion of it rapid. I have intimated that propositions have each an object as well as a subject. Such is generally the case, and such is the case more widely than may at first appear. In our standard phrase Alfred reads, no object is expressed. And the statement may be made without any clear reference to an object. Verbs in which there is no reference, or no clear and obvious reference to an object, are called intransitive verbs-that is, verbs the action of which does not (intransitive-in, not; trans, across; eo, I go) pass over to an object. Alfred sleeps, Alfred runs, Alfred rides, supply other instances of intransitive verbs; because in each case the action remains with the subject. But these and most other intransitive verbs may become transitive by having an object placed after them; e.g.— INTRANSITIVE. Object. Object. Alfred sleeps. called the indefinite article, inasmuch as it leaves it indefinite what object is meant, merely intimating that it is not many objects but only one object that is intended. A, indeed, is only a variety of our word one, ane. Being so, its original form was an. The n is now dropped before a consonant for the sake of euphony (Greek, eu, well, and phoné, a sound; meaning agreeable sound). Contrasted with the indefinite article a, is another form, which bears the name of the definite article; that is, the. The is a reduced form of these. Consequently the refers to an object previously mentioned or known; as Alfred soon reads TO ME the obscure writing and manuscript. Me is a pronoun, as we found he to be. Me, you see, holds the place of a noun. Me is the objective case corresponding to the nominative case I. Our pronouns, as you here see, have some diversities of case, for in them you find varying forms corre sponding to varieties of meaning. The other word just addednamely, to, is called a preposition. The word preposition signifies, according to its Latin element, that which is put before; a preposition, then, is a word put before a noun; and it is put before a noun in order to modify its signification, or mark the relation in which the noun stands to another word, or to other words; e.g.— PARTICIPLE. The sun shining disperses the clouds. ADJECTIVE. The shining sun dazzles the eyes. The right of the participle to be accounted a separate part of speech has been contested not without reason. Perhaps less valid is the claim of the interjection. An interjection (inter, If, however, propositions in general have an object, then we must between, and jacio, I cast) is a sound of surprise, or sorrow, add an object to our grammatical formula; thus: SUBJECT. Alfred Alfred rides a fine horse. The grammatical formula is thus made complete. The verb reads is, as we have seen, equivalent in grammar (or logic) to the form is good; where the former is the copula, and the latter the attribute; so that an attribute with its copula is equivalent to the verb and its object, in forming the predicate of a proposition. The proposition which, as it stands, has all the essential parts of a proposition, may receive additions in order to express modifications of the meaning. Introduce and, then it runs, Alfred reads writing and manuscript. This particle and is termed a conjunction. Conjunctions (Latin, cum, with, and jungo, I join) join together words and sentences. Before thrown out under the impulse of strong and sudden emotion, as O! Oh! Ah! and is with little propriety placed among the forms of articulate speech. Let us introduce a participle intc our model The form is thus seen to comprise nine parts of speech. If the interjection, or exclamation, is to be reckoned a part of speech, it densed view of all the parts of speech, and in the remarks by may be prefixed in the shape of Yes! Here, then, we find a conwhich the view has been prefaced and prepared, lies the kernel of the entire English Grammar. If you have gone with me understandingly thus far, you will have no difficulty in following me to the end, for having developed these general facts and ▲ is called an article (properly in Latin a little joint). A is principles, I have now only to take up each part of speech in And, in this case, unites manuscript with writing. writing insert a; then the proposition stands thus: Alfred reads a writing. |