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Là, cette jeune plante en vase, disposée,

Dans sa coupe élégante accueille la rasée. (THE SAME.)

Ces honneurs que le vulgaire admire, Réveillent-ils les morts au sein de monuments? SOUIEL.

There that young plant prepared as a A KEY TO THE EXERCISES IN THE rase, receives the dew in its elegant

сир.

Do these honours admired by the
vulgar awake the dead from their
sepulchres?

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LATIN LESSONS.
(Continued from page 299, Vol. II.)

By JOHN R. BEARD, D.D.

Page 38, col. 1, vol. II.-LATIN-ENGLISH.

tion; the citizens, having made a treaty with the enemies, enjoyed The safety of men depends not only on truth, but also on repatapeace; by reflection, we comprehend God and the divine mind; we live on milk, flesh, and many other things; take care that you do not avenge yourselves on your enemies; the Romans promised this to the Numidians; the Numidians continued to harass the Carthaginians by war; the Romans are about to strive; the Romans say that they will strive; the Romans returned the favour

(1.) The possessive adjectives, which are always joined to a with increase; the Romans promised the Numidians, if they would noun, relate to possession or property; they are:

Singular.

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Plural.

Both genders.

mes,

tea,

ses,

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our.

VOS,

leurs,

his, her, ils.

your. their.

(2.) In French these adjectives take the gender and number of the object possessed, and not, as in English, those of the

possessor:

Masc. sing,

Fem. sing.

mon frère, my brother, ma soeur, my sister, ton livre, thy book, ta plume. thy pen, son papier, his or her poper.

notre cheval, our horse votre lit, your bed, leur foin, their hay,

Pl. both genders.

mes cousins, my cousins. tes maisons, thy houses.

sa table, his or her ta- ses habits, his or her ble, clothes. notre vache, our cow, nos prairies, our meadows votre chaise, your chair vos crayons, your pencils. leur paille, their straw, leurs fermes, their farms. Sobriety in all things, is, my friend, the true enjoyment.

Sobriété dans toute chose,
Mon ami, c'est l'art de jouir.
DU TREMBLAY.
Ma main de quelque fleur es.
quisse la peinture. CASTEL.
Mes sens sont glacés d'effroi.
J. B. ROUSSEAU.
De son propre artifice on est sou-
vent victime.

COLIN D'HARLEVILLE.
A sa vocation chaque être doit
répondre. FR. DE NEUFCHATEAU.
Il faut de ses amis endurer quel-
que chose.
MOLIERE.
Notre vie est une maison,
Y mettre le feu c'est folie.

NIVERNAIS.

Vos mailles se rompront sous la charge pesante. CASTEL.

Leurs fleurs suivront mes pas, en récréant ma vue. (THE SAME).

My hand sketches the picture of some flower.

My senses are frozen with fear. One is often the victim of his own artifice.

Every being should fulfil his vocation.

We must bear something from our friends.

Our life is a house; to set it on fire is folly.

Your meshes will break under the heavy burden.

Their flowers will follow my steps, and please my sight.

(3.) The adjectives mon, my; ton, thy; son, his or her, are used instead of ma, ta, sa, before feminine words commencing with a vowel, or an & mute, in order to prevent the meeting of two vowels, or of a vowel and an A mute; thus we say :

mon épée, my sword, and never ma épée.
ton épouse, thy wife, instead of ta épouse.
son armée, his army, but never sa armée.

C'en est fait, mon heure est venue.
BOILEAU.

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continue to harass the Carthaginians by war, that they would strive to return the favour with increase; no one has lived too short a time who has performed a work of perfect virtue; wise men despise the appearances in a dream; as soon as we have arisen, we despise the appearances in a dream; Aristotle, Zeno, and innumerable others, having gone out of their country, never returned home; there is no plague so detestable, which is not pro duced by man against man; I am not born for a corner; this whole world is my country; the seeds of virtue are inborn in our nature; Hannibal fought with the Romans in Italy; Hannibal, having fought with the Romans, always came off conqueror; Hannibal, as often as he fought with the Romans in Italy, came off conqueror.

Page 38, col. 1, vol. II.-LATIN-ENGLISH.

The mind of every most excellent man chiefly strives after immortal glory; the enemies were wearied by the length of the conflict; the enemies, wearied by the length of the conflict, left the (field of) battle; he acquired virtue; in whatever part of the world a good man is, he will be loved by friends; he who has acquired virtue, in whatever part of the world he is, will be loved by us; courage is eager for danger; courage does not reflect on what it may be about to suffer; courage (virtus) is eager for danger, and whither it turns, does not think of what it will suffer; Augustus did not suffer himself to be called a lord; some animals are destitute of reason, others use reason; the soul having escaped, the body is worth nothing; the memory of illustrious men, even when dead, has influence with us; it is worthy of a king to aid the fallen; it is peculiar to folly to perceive the faults of others and to forget its own; we ought to do our best to benefit very many persons; to be angry with those whom we ought to love is wickedness; friendships, acquaintances, and neighbourhoods, contain some pleasure (something of pleasure); we understand our advantages better by being without them, than by enjoying them; what plea sure friendships, acquaintances, and neighbourhoods contain, we understand better by being without them, than by enjoying them; fresh men always succeeded wearied ones.

Page 38, col. 1, vol. II.-ENGLISH-LATIN. Felicitas virtute nititur; nititur ne hominibus felicitas ? non, felicitas Deo nititur; excolere virtutem eniti debemus; pater filium complexus est; filius patris mortem ultus est; rex praemium pollicitus est; sorori tuae regina pollicita est ne praemium? milites cumulatam gloriam adipisci nitentur; mane experrecti sunt, et discessere; bene vitae officiis functi sunt; Aristoteles et Zeno tent? heri domum reverterunt; e patria profecti sunt, et nunquam praeceptorum officiis functi sunt; quando amici tui domum rever. revertent; pestis haec hominum in animis nata est (born); ubi est patria? patria mea est mundus; in animis mortalibus sunt semina innata vitiorum; dux cum hostibus congressus est; quotiescunque duces Anglici cum hostibus congressi sunt, semper discessere superiores; optimi cujusque pueri animus maxime parentes suos amat; boni in salutem animae nituntur; lacte pueri et puellae vescuntur; discipuli officiis suis functi sunt; O' Deus, miserére lapsorum; succurite pauperibus; proprium est stultitiae nulli prodesse.

Page 39, col. 1, vol. II.-LATIN-ENGLISH.

Caesar feared to oppose his army to a river of such magnitude; Caesar is of opinion that it should be attempted, and a trial made; Caesar, although he feared to oppose his army to a stream of such magnitude, yet is of opinion that it should be attempted and a trial made; nor did they fear that they should be surrounded; they said that they feared not the enemy; they said that they feared the narrow road; they said that they feared that corn was not supplied conveniently enough; they said that they feared not the enemy, but the narrow road, and that they were afraid that provisions could not be supplied conveniently enough; be not

afraid, the ship is safe; I fear greatly on account of the republic; he had no fear on account of his own peril and the peril of the legion; you are not afraid you will lose the place; he feared he should not succeed.

Page 39, col. 1, vol II.-ENGLISH-LATIN.

Tin eo ne operam perdideris; timeo no domus cadat; timeo ut frumentum in urbem supportetur dux; metuebat ut exercitus ejus veniret; de suâ puellula pulchrâ metuunt; de fortunâ tuâ nihil timeo; rex ducesque timent ne circumveniantur; Cicero experiendum judicat; timeo ut experiri possit,

Page 54, col. 2, vol. II.-LATIN-ENGLISH.

The forehead, the eyes, and the countenance often lie, but the spech lies very often; whatever arises has its origin from nature; the sun bestows the same light and the same warmth on all; how many are unworthy of light! and yet the day arises; whence, at length, do you appear to us so suddenly? O soldiers, if we break out in fierce assault upon the enemy, the victory is in our hands; while we attempted to assault the city, the enemies attacked us from behind; each one measures dangers by his own fear; the wise man both remembers past things with pleasure, and so possesses present things, as to perceive how great and how pleasant they are; take care you do not obtain honours by flattery; orators, before they begin, premise certain things; in all matters, before we begin, we should employ careful preparation; all the citizens had adorned and clothed their houses with flowers and wreaths, because they were waiting for the king; while the hostile army was demolishing the private and public buildings of the city, the citizens were filled with the greatest grief; while the enemies were dividing the spoil amongst themselves, we charged them with the greatest impetuosity; the general exhorted the soldiers, that they should try all methods by which they might relieve the city from the blockade; because a fierce tempest arose, great fear seized upon all the sailors.

Page 55, col. 1, vol. II.-ENGLISH-LATIN.

Page 55, col. 2, vol. II.-LATIN-ENGLISH.

The arts we support themselves; shall always pity wretched men; when you are sick, you ought to comply with the instructions of the physician; foolish men perceive the faults of others, (but) forget their own; the principal charm of youth springs from modesty; O boys, reverence old age; O boy, I confess the truth; take pity on the destitute; let the scholars reverence their teachers; I doubt not that you will promise me your protection; we behold (intuemur) with great pleasure the noble examples of virtue which have been recorded in history; who knows not how many abuse eloquence? we have enjoyed peace during many years; all the citizens fear that the enemies wil attack the city; as soon as we have arisen, we proceed to our business; the citizens, having obtained liberty, will enjoy the greatest pleasure; aid the fallen; converse as boldly with your friend as with yourself; be not angry with those whom you ought to love; if we always pursue the path of virtue, access to heaven will sometimes lie open to us; perform your part we!!; by concord small things increase, by discord the greatest things fail to pieces: glory, like a shadow, follows virtue; do not flatter bad men; we flatters our senses; I fear that my friend is dying. measure great men by their worth, not by their fortune; pleasure

Page 55, col. 2, vol. II.-ENGLISH-LATIN.

Heri amicus meus mortuus est; metuo ne amicus tuus moriturus sit; ne largitor malis pueris; Deus piis largietur; aditus in coelum semper bonis patet; metuo ut aditus in coelum Alexandro pateat; quamdiu patria tua pace fruebatur? quamdiu regis exercitus in patriâ nostrâ erit, pace fruémur; esne munere functus ? ne abutere patris gratiâ; loquar tecum, sed non tibi blandiar; regi blanditus, laudem adeptus est; filius ne laudem adipiscétur ? filius meus gloriam maximam adeptus est; gloria virtutem eximiam sequitur; se rediturum esse, mihi pollicitus est; ille rediit; non, cras redibit; pueri se ipsi tuentur; pueri se ipsi tueri debent; misereor et miserebor miserorum; ne obliviscere vitiorum tuorum ; intra paucos dies proficiscar; quando revertes? veremini senes, pucri, veremini patrem; veremini Deum; peccatum suum fassus

CORRESPONDENCE.

Saeva tempestas coorta est; saeva tempestas coorietur; saeva tempestas cooritur; saevae tempestates cooriebantur; saeva tem-est; tempestate coortâ, pavor animos nostros occupavit. pestas cooriebatur; nautae multos labores experti sunt; hostes domum tuam demolientur; meam sororem opperiar; mater mea heri me opperiebatur; illi eblanditi sunt honores; honores eblandieris ne? nolo honores cblandiri; prius quam odiaris, adhibenda tibi est industria; tellure potitur; omni urbe potitus est; libris patris mei potiar; mi puer, cave ne mentiaris; solum mali mentiuntur; malum est mentiri; O pater, nunquam mentiar; illi mentiti et puniti sunt; turpe est mentiri; sol et bonis et malis oritur, tanta bonitas Deo est; rex fortibus militibus honores largi. tur; inter duo filios bona partitus est; quicquid a tellure critür, venit a manu divinâ.

Page 55, col. 1, vol. II.—LATIN-ENGLISH.

Those are to be laughed at, who teach others that which they themselves have not tried; every animal loves itself, and as soon as it appears, aims at preserving itself; nature has bestowed so great a productive power on the conveniencies and necessaries of men, in order that those things which are begotten may seem to have been given to us advisedly (consulte), and not to have arisen by chance; Herodotus passed through many lands, and certainly (quidem) related many marvellous things, but these he himself invented not, but others (invented them) from whom he heard them; now, for three months we had been waiting for a friend, when his death was announced to us; Sulla suddenly appeared to the Romans, and began a most frightful civil war; a wise man will never flatter bad men, never invent any false thing, never occasion injury to others; if we attack the enemy quickly, there is no doubt that in a short time we shall get possession of the city; as soon as the sun has risen, we shall set out; take care that you do not flatter bad men; the enemies hastened to get possession of the city; an even number is easy to divide; the sun rising, we set out; a fierce tempest having arisen, great fear seized all the sailors; with the greatest pleasure we behold the sun when about to rise (oriturum).

Page 55, col. 1, vol. II.—ENGLISH-Latin.

Sole oriente, tenebrae diffugiunt; solem oriturum magnâ cum voluptate specto; coortâ tempestate, naves nostrae sparsae sunt; nulli calamitatem moliar, non etiam malis; ortusne est sol? horâ octava sol orietur; repente hostem adortus est; meam ordiar orationem; orator orationem ordiebatur, quum judex intrabat; non est dubium quin tuis potituri sitis; simula que nati sumus, move mus; omnes homines se ipsos diligunt, ac simulatque facultatibus potiti sunt, inter se eas partiri debent; inter egentes facultates partitus est; multi Britanniam emensi, ignorant quam sit felix potensque; spero te nunquam mentiturum esse; tempestas orietur; omnes existimant, tempestatem coorituram esse.

THE LEAN HORSE.

SIR,-Permit me to lay before your readers an answer to the question about the horse, proposed in No. 42, p. 240 of the POPULAR EDUCATOR.

The gentleman who bought the horse,
Which was so poor and lean;

Had spared no cost in keeping him,

'Tis plainly to be seen.

The feeding of the animal,

Till he got sound and well,

Cost eighteen pound and one bob more,
And then he did him sell.

The half of which if added to
One fourth of the prime cost,
Is just exactly what the gent.
By the transaction lost.

Wood Hall Colliery, 1st February, 1853.

A. THOMSON.

The same answer was given, with correct solutions, by W. GIBBONS (Pimlico): G. WILD (Dalton-on-Tees): G. ARCHBOLD (St. Peters): DAWSON (Knaresborough): PHILO (Berwick-ouTweed): F. II. (Brightwell): B. B. (Yorkshire); G. W. C.; JAMES WILKINSON (Low Moor): and others.

CONSTRUCTION OF THE VIOLIN. Sia,-In answer to one of your correspondents, who signs his name "John Stocking," I quote the following passage from "Ottó on the Violin."

The violin consists of 58 different pieces; the wood is generally of three sorts; the back, neck, sides, and circles, are of sycamore; the belly, bass-bar, sound-post, and six blocks, of deal; and the finger board and tail piece, of ebony. Six cremona violins (namely these made by Amati or Straduarius) that came in to my possession, were made after the following proportions. The belly was thickest where the bridge rests; then it diminished about a third at that part where the holes are cut, and where the belly rests on the sides it was half as thick as in the middle. The same proportion is observed in the length. The thickness is equally maintained all along that part in which the bass-bar is fixed;

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ANSWERS TO CORRESPONDENTS. ELSWICK: Right in the lean horse query.-A STUDENT IN ENGLISH, and his friends in Sheffield, are strongly advised to commit the lists of prefixes and affixes with their meanings to memory; this will give them such a hold, as it were, of the most important part of the language, as will enable them to speak and write with the greatest accuracy.-WALLASEY BIDETON (Liverpool): We hope that Mr. Cassel's Latin Dictionary, edited by Dr. Beard, will be the best and cheapest, when it is ready.-W. BUSH (Yarmouth) wishes to know where he can obtain designs for wood-carving.As an introS. HEATH (Barnetby) should read Virgil before Horace. duction to the Horation metres and style, he would do well to read George Buchanan's Latin translation of the Psalms of David, a most elegant book, and written in the purest Latin, that of the Augustan age: good copies of it may be had at any old book-stall in London for sixpence.-H. EAVES (Preston) wishes to know of some work on the art of grinding glasses for telescopes: can any of our readers assist him?

A SUBSCRIBER (in Buckingham) will have some lessons on Mapping, &c. in the P. E.-J. Y. (Preston) will find his wants supplied in the Lessons on Chemistry, when they appear.-AMICUS (Stepney): The subjects for Examination in Natural Philosophy, and Chemistry, in the University of London, are always the same, but the particular questions vary every year. The classical subjects for the Pass Examination in 1851 are stated in No. 41, p. 215, col. 2, line 34.-W. ASH (Holborn): His penmanship is really not so bad as he thinks; we advise him to buy two or three copybooks for large-hand, ready ruled, at a stationer's shop, and imitate our large coples by writing them from A to Z two or three times. Then, do the same with the half-tert hand; and, lastly, do the same with the small or court-hand, and he may rest assured that by slow and careful perseverance he must improve. He ought, of course, to read most carefully our instructions as to the mode of holding the pen and sitting at the table.-W. BUTLER (Southwark): The sentence I had known the deceased some years previous to his death," is the most correct.-A SUBSCRIBER (Isle of Man) should buy the latest edition of Smart's Walker's Dictionary. Encyclopædias very soon get out of date; we cannot recommend any one in particular, as you might be disappointed in the first article you turned up. The P. E. will be better than any encyclopædia.

Incola, the sentence beginning Regibus is quite right:-Agricola ought to have known that littera in the singular is a letter of the alphabet, and that a letter in the sense of an epistle is in Latin litteræ, being in the plural.-F. T. An adjective pronoun is a pronoun which, like an adjective, stands with a noun, as si qui (for si aliqui) homines, if any persons; the genitive case of the personal pronoun ego, that is mei, of me, or mine, denoting possession, and so is the same as mei of what is called the possession pronoun meus; they are indeed the same word; similar tenses are such as denoting corresponding times, may go together; dissimilar tenses are the reverse. responding times are such as in the nature of things stand in the same relation as the presents, and the presents hold the same position in time or in regard to eternity; in the same way are the past and the past related, the future and the future; the supine differs from the infinitive chiefly in form and in construction; the supines are really nouns, the one in the accusative case, the other in the ablative; the infinitive also has sometimes the force of a noun, as Amo legere libros, I love to read books, is the same as Amo lectionem librorum, I love the reading of books.

Cor

HENRICUS (Taunton): Should write to Mr. Bagster for what he wants; Simeon's Hora Homiletica is the book he means, but we don't know any thing about prices. Your suggestion about publishing the figures of Euclid by themselves is good for many purposes; it will be taken into con sideration.-JOHN MCCULLOCH (Edinburgh): Thanks for his answers to Cassell's Arithmetic.-B. B. (Yorkshire): must really buy and read the Spectator for himself. Gregory's letters we doubt not are good, and recommendable to a student.-T. MORLEY (Bromley): Thanks for his answers to the questions in Cassell's Arithmetic.-E. SMITH (Little Cookham, Surrey) shall have the first copy of the answers to Cassell's Arithmetic.-GERMANICES, received and under consideration.- PHILO (Dundee): Right;

nous verrons.

GERMAN. EDWARD EVES should study more the rules of declension. In exercises 3, 4, and 10 you have made mistakes. The other sentences are very correct; every syllable beginning with an s must be written with a long -A SUBSCRIBER: Etcetera, &c. 2., is written in German generally u. f. w., but also like the English etcetera.-T. S. W. R. B. F. will find it in this week's lesson.-T. V.: Do not know; have never seen it.

S. DAVIES (Cayo): We believe Matthiae's Greek Grammar to be the most complete.-PHILOMATH (Bath): Received.-A STUDENT (Halifax): In the German, as in the French Lessons, there are references to the SECOND PART yet to come.-J. COLQUHOUN (Tolcross): Practice does wonders.-W. H. (Apsley-bridge) should write to the bookseller he mentions for his catalogue; he will be only too happy to send it to him.-A CONSTANT READER, &c. (Leeds), is informed that the two editions of the P. E. are exactly the same; the only difference is in the paper, and the heading of the first page.

ERRATA.

Vol. I. p. 411, Col. I. Exercises 2, line 2, for divitissime, read divitissimi, for dissisilim read dissimiles; Line 17, for modestur read modestior; line 18, Jor similissima read simillima; line 1, for contamus read cantamus.

LITERARY NOTICES.

GIN AND WATER; a pair of pictorial designs by Kenny Meadows, portraying the effects arising from the indulgence of those potent liquids. In the first, GIN, we have the interior of the drunkard's home, with a glimpse of the horrors which belong peculiarly to such homes; in the second, WATER, we see how comfort, cleanliness, and peace attend the steps of the temperate The contrast is well sustained, and the pictures-which measure man. 24 inches by 16 inches-cannot but be popular. We have had too many songs and pictures in praise of the drinking customs of our country, and we are glad to perceive that our poets and artists are beginning to discover that they may get inspiration even out of water"Wine, wine, thy power and praise Have ever been echoed in minstrel lays; But water, I deem, hath a mightier claim To fill up a niche in the Temple of Fame ?" These pictures, which should be framed and hung over every cottage chimney-piece, and on the walls of every factory, and workshop, and ragged school throughout all the land, can be obtained of every bookseller for one shilling. They are exquisitely engraved on wood, by Messrs. Henry Linton and William Measom.

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LESSONS IN DRAWING.-No. VII.

PERSPECTIVE.-SECTION I.

PREVIOUSLY to entering on the details of Perspective, we shall show, by a few easy lessons and experiments, that a certain knowledge of the principles of this department of the art of drawing may be readily acquired.

Take your seat at a table, having a wall opposite to it, at the distance, say, of five feet from the eye, and having the edge of the table parallel to (that is, in every part equally distant from) the wall. Make a mark on the edge, in order to determine your position exactly, and to enable you to replace yourself in the same spot at pleasure. Now, using one eye only, make a mark on the wall directly opposite to the eyesuppose this point to be c, in fig. 71, your own position being at A. Next, lay a book near A, at right angles to the edge of the table, and the sides will appear to your eye to take such directions that, if they were sufficiently prolonged, they would meet in the point c. Take another book near B, also at right angles to the edge of the table, and consequently parallel to the first book near A, and you will find that its sides will in like manner appear to meet in the point c, if sufficiently prolonged. Lines which meet in one point in this manner, are said to converge to the point; and you will find, on laying another book beyond B, that its sides will also converge to c, if only it shall be parallel to the book A.

Points to which parallel lines appear to converge are called, in perspective, vanishing points; and you will perceive from the preceding observations, that for parallel lines at right angles to the wall, or, which is the same thing, at right angles to the edge of the table (these parallel lines being also in horizontal planes), the vanishing point is directly opposite the eye.

In the next place, take a book E, and place it on the book near B, so as to make an angle of 60°, with

the edge of the table. Place yourself as before, with the eye opposite to c, and you will find that at this angle of 60°, the vanishing point is no longer opposite to the eye, but that it lies in a horizontal line drawn through c, namely I ; and, supposing, as before, that the eye is about five feet from c, the new vanishing point v will be about three feet from c, in this horizontal line. Again, a book near G, placed parallel to E, will have the same vanishing point v. By a similar process, you will find that a book lying at an angle of 45° with the edge of the table, will have its vanishing point on the horizontal linе Hн, at the distance of about five feet from c. With these instructions you may continue similar observations on the convergency of the parallel lines of books placed at other angles. All the preceding examples are but particular instances of a general law about to be explained; it will,

VOL. II.

therefore, be sufficient to have indicated here a method by which the student may practically verify much of our observations, which will immediately follow, relating to vanishing points and vanishing lines.

[1.] If you look through a pane of glass at any object on the other side of it, and with a diamond, or any other suitable instrument, you trace upon the glass the apparent outline of the object, as it appears to the eye, it will be correctly drawn; and, if the colouring and shading were added, you would have upon the glass an exact image of the original. Perspective is generally divided into Linear and Aerial. Aerial Perspective relates to such changes as take place in the colour and the depth of shadow, according to the distance of any object from the eye, and other modifying circumstances. This branch of perspective will be treated of when considering COLOUR and CHIARO-SCURO, or LIGHT and SHADE. Linear Perspective explains the laws which modify such an outline as we have just supposed to be drawn upon a pane of glass. The end contemplated in this kind of perspective is to produce such

Fig. 71.
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an outline as shall convey to the mind a just idea of the original. Linear Perspective, then, the art by which upon a plane (such as the surface of a sheet of paper) an outline (or linear) representation may be drawn so as to produce the same image in the eye as the object itself would do, under certain given conditions.

[2.] Rays of light proceed from one point to another in straight lines. Upon this fact, and upon another, which the treatises on Optics explain, namely, that the rays from all objects to which we direct the eye converge to a point in the interior and at the back of that organ, the principles of perspective are founded. The

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Fig. 72.

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following remarks will illustrate this subject:In fig. 72, the triangle B C D is the object, and the lines BA, CA, DA, represent luminous rays proceeding to the eye at A. Rays of light proceed in all directions from any object whatever, but, on directing the eye to an object, we perceive it only by means of those rays which arrive at the eye, and are there converged. This being premised, the lesson conveyed by fig. 73, will be understood by the following explanations, and, as these contain the elements of the practical methods now in use for producing drawings in perspective, the student is requested to study them with attention. 50

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RG SG is the ground plane, or original plane. In this plane, by drawing v M at an angle of 60° with HH, bringing TN up to the plan of all original lines is to be found.

Fig. 73.

the ground line (that is, producing it to meet GG in P), and joining MP; VN and VT determining, as before, the length of

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HHGG is the plane of the picture, and is generally taken in a position vertical to that of the ground plane.

VHH is the vanishing plane; it always passes through v, the place of the eye, and is always taken parallel to an original plane. The line in which the vanishing plane cuts the plane of the picture (or, as it is sometimes called, the plane of projection) is the vanishing line of an original plane.

The line H H is consequently the vanishing line of the ground plane, and of all planes parallel to the ground plane. It is commonly called the horizontal line; and in it are found the vanishing points of lines in the ground plane, making any angle whatever with Go, which we shall call the ground line. This line & a is evidently the intersection of the plane of the picture with the ground plane. HH being the vanishing line of planes parallel to the ground plane, the vanishing points of all lines lying in such parallel planes will also be found in н н.

[3.] The vanishing point of any original line, that is, a line lying in any original plane, as, for example, the line an is found by supposing a plane to pass through the line, and through the point v, the place of the eye; this plane evidently cuts the vanishing plane in a line parallel to the original line; for example, v c is evidently parallel to a R, and the point c, where this line vc meets the vanishing line of the plane in which on lies, is the vanishing point of a R, and of all lines in the same plane which are parallel to a R. As HH is the vanishing line of all planes parallel to RG so, it follows that the point is the vanishing point for all the lines in those planes which are parallel to a R. The image, or projection of the line QR, is at once ascertained when the vanishing point and the original line are given. Produce QR to the ground line, and join P, the point where it cuts this line, with o, the vanishing point; draw ay and a v, to the point v; then gris the projection or perspective representation of Q R.

nt the representation of T N. Now suppose the plane GGN to be turned round upon the line GG as on a hinge, until it is in the same plane with HHGG; and suppose also the plane и Vн to be turned in like manner on н н until it also is in the plane HHGG-the three planes are brought into one, and the lines VM, PN, retain their direction mutually parallel as before, the intersections also at P and м with the horizontal and the ground line have suffered no change. In fig. 75 is shown an arrangement very commonly adopted in perspective drawing founded upon this.

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preceding figures, the vanishing point of any line as TN making a given angle with the ground line, is found by drawing a parallel through v, the place of the eye, to cut the hor zontal line in м, bringing TN up to the ground line to cut i in F, joining P and M, and then determining the length of ta by lines drawn to v from T and N.

Go is the ground line; the line и н is determined by taking n G equal to the height of the eye above the ground line, thus Corresponding strictly with the lines HG in the two preceding figures; the line vc is the distance of the eye from the [4.] When the three planes are brought into one, in a man-plane of the picture, and in this arrangement, as in the two ner to be explained in the next section, these constructions are very easy, and if the reader familiarises himself with the figure referred to in [3.], all the practical methods in use will be understood without difficulty. Indeed, fig. 73, with the explanations now given, contains, in as concise a form as possible, the constructions on which all modern treatises on Perspective are founded; and forms the key to all that is to follow in this series of lessons. It is, therefore, recommended to the best attention of the student, with the assurance that a clear conception of its construction is in itself the substance of all theoretical perspective; for, by looking at any object through a pane of glass, and supposing it to represent H H G G, the plane of projection (confining, in the first place, his observations to lines at right angles to the ground line), he will see how consistent this construction is with the natural appearances.

[5.] In fig. 73, the vanishing point for a n at right angles to the ground line o o, was shown to be at c, the point where v o cuts Ha at right angles. In fig. 74, if TN is at an angle of 60° with the ground line, its vanishing point x will be found

HHGG is the picture, and the spaces above and below this are used for the necessary constructions effected by the parallel ruler, the set square, the r square, compasses, and other instruments described, with explanations of their uses, in the lessons on Practical Geometry in vol. I. of this work.

Lines at right angles to the ground line have their vanishing point in c, where a line from v the place of the eye, meets the horizontal line at right angles; this point is called the point of sight or the centre of the picture.

Lines parallel to the ground line or horizontal line, that is parallel to the plane of the picture, have no vanishing point, because a parallel drawn through v, as is at once evident, can never meet the horizontal line. Such lines in perspective will be parallel to their originals.

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