Oldalképek
PDF

TWO VOICES.

KEY TO EXERCISES IN LESSONS IN LATIN,-XVIII, 1. Active. 2. Passive.

EXERCISE 69.-LATIN-ENGLISH. Deponent belonging to the passive in form and to the active in meaning. 1. There is no firm friendship among the bad. 2. I hasten to death.

3. The Gauls dwell beyond the Rhine. 4. We have no weapons against SIX TENSES.

death. 5. A generous man is mild toward the conquered. 6. Comets 1. Present; 2. Perfect; 3. Imperfect; 4. Pluperfect; 5. First Future ;

are admirable on account of their rarity and beauty. 7. Slaves obey

ou account of fear, the good from a regard to duty. 8. Sailing along 6. Second Future, or Future Perfect.

the shore is often dangerous. 9. No one is happy before death. 10. THREE MOODS.

On what account dost thou laugh ? 11. Below the moon all things 1. The Indicative. 2. The Subjunctive. 3. The Imperative.

are perishable. 12. Thou dwellest many years among barbarians, 13.

The kingdom of Pluto is placed under the earth. 14. The government FOUR OTHER FORMS.

of nations is in the power of kings. 15. Fish die out of water. 16.

The thing happened contrary to expectation. 17. The camel bears 1. The Infinitivo. 2. The Participle. 3. The Gerund. 4. The Supine.

supine. hatred to horses. 18. Painted garments are mentioned with (in) In all, fifteen varieties of expression enter into the Latin verb. | Homer. 19. Many animals congregate and fight against other animals. You are not to suppose from this that every verb has all these 20. The hippopotamus feeds on the corn-fields around the Nile, forms. Even when the Latin was a living language, many

EXERCISE 70.-ENGLISH-LATIN. verbs were defective, that is, lacked some of the ordinary 1. Inter malos nulla est firma societas. 2. Contra mortem nulla forms. We, however, are bound to write the language as we habet homo arma. 3. Ultra mortem est vita. 4. Ad Rhenum profind it written in the remains of Roman literature, and so are peramus. 5. Ante domum sunt amici. 6. Apud me sunt filii mei. restricted to forms which actually occur in extant Latin writings; 7. Apud te suntne filii vestri? 8. Mitis erga victos est rex. 9. Post and as poetry has its licences, so are we obliged, in order to be mortem boni sunt felices. 10. Quid est infra terram ? 11. Deus est

12. Infra nubes habitant homines. 13. correct to confine ourselves to the usages of the best prose super omnia et per omnia.

Penes me mei sunt liberi. 14. Apud Ciceronem sunt multa pulchra writers. In general, the Latin of Cicero is the model to be

dicta. 15. Rus propter te amo. 16. Intra muros sunt milites. followed. Verbs which have been above described as active, may also

EXERCISE 71.-LATIN-ENGLISH. be called transitive; that is, active in voice, and transitive in

1. Poison is for (acts as) a remedy sometimes. 2. An infant has no

power without another's aid. 3. Eagles do not build in trees. 4. import; thus, laudo puerum, I praise the boy, is a transitive

The cuckoo lays in the nests of other birds. 5. By old age our senses verb, because the action of the verb passes over (trans, across,

grow dull. 6. Some men are born with teeth. 7. Xerxes fled from over, and eo. I go) to the object, puerum. As some verbs are Greece with very few soldiers. 8. Metellus leads elephants in triumph. transitive, others are intransitive or not transitive. Such is 9. The traveller sings in presence of the robber. 10. The stars move dormio, I sleep, in which no action passes over to an object from the east (rising of the sun) to the west (setting of the sun). 11. Intransitives are sometimes called neuters; that is, neither Britain was discovered by the Phoenicians. 12. Bees cannot exist active nor passive. When they have a passive form, they bear without a queen. 13. It is sweet to die for one's country. the name of neuter passives; as, ausus sum, I have ventured ;

EXERCISE 72.- ENGLISH-LATIN. gavisus sum, I have rejoiced. Sometimes a verb, in the passive l. Estne aliquando venenum pro remedio ? 2. In Græciã pugnat form, has a reflective force, and may be Englished by a neuter | Xerxes. 3. In senectute visus et auditus hebescunt. 4. Paritne in

alieno nido coccyx ? 5. Soror tua coram multis cantat. 6. Ab ortu or intransitive verb; as, moveor, I move myself, or simply, I

solis ad occasum properant. 7. Græciā proficiscens exercitus in Italiam more. A few active forms have a passive signification; as,

properat. 8. Metellus cum multis militibus est in Britannia. 9. Tapalo, I am beaten; veneo, I am sold. Somewhat similar is

Filius meus sine dentibus est natus. 10. Estne exercitus sine ele. fio (factus sum, fieri), I become, I pass from one state into another; phantis ? 11. Elephanti in triumpho a duce ducuntur. 12. Dulcene I am made.

est pro patriâ mori? 13. Quid sine Dei ope sunt mortales ? 14. The tenses may be divided into three classes; thus :

Omnesne aves in arboribus nidificant? 15. Clam patre est puer in

domo. 16. Infantes in gremio matris felices est dulce videre. 17. I PRESENT THE I the action incomplete Present,

Tecumne est soror tua ? 18. Sine patre nihil potest puer, 19. Mecum the action complete Perfect.

est filia mea. 20. Quot liberi tecum sunt ? 21. Quot homines sunt II. PAST TIME. the action incomplete Imperfect.

in Britannia ?
the action complete Pluperfect.
III. FUTURE TIME 3

the action incomplete First Futuro.
7 the action complete Second Future.

LESSONS IN GEOMETRY.-XIX. You thus see that there are three forms of complete action, and The following method of constructing a regular pentagon three of incomplete :

involves the use of the circumscribing circle, on the circumference

of which the angular points of the pentagon may be marked. (1 scribo, I rrite or am writing

PRESENT. INCOMPLETE 2 scribebam, I did writo or was writing

We have added this to the modes of construction given in the

IMPERFECT. (3 scribam, I shall write or shall be writing FUTURE.

last lesson to show the student that there are many ways of (1 scripsi, I have written

PERFECT.

constructing each of the regular polygons, and to urge him to COMPLETE 2 scripseram, I had written

PLUPERFPCT. exercise his ingenuity in finding out other methods for the con(3 scripsero, I shall have written

SECOND (or struction of the hexagon, heptagon, etc., than those we are

PERFECT) FUTURE. about to give him in this and the following lessons. The natural sequence of our ideas requires a corresponding se- PROBLEM L.--To construct a pentagon on a given straight quence of tenses. We do not in thought suddenly pass from line (another way). the present to the past in the same sentence, or in the same

Let A B (Fig. 68) member of a sentence. Consequently, we must avoid doing so be the

be the given straight the employment of the tenses. The tenses may be divided | line on which the reinto pairs-namely, similar and dissimilar; for example:

quired regular pen

tagon is to be deSIMILAR TENSES.

DISSIMILAR TENSES,

scribed. At the point Present Present.

Present
Imperfect.

A, in the straight
Present Perfect present. Perfect present Imperfect.

line A B, draw A C, Imperfect Imperfect.

Pluperfect Perfect present. Imperfect Pluperfect.

of indefinite length,

perpendicular to AB, 1 Now similar tenses should follow each other, and not dissimilar and produce A B inde. *

AD ones. That is, if you use one present, use another; if you use finitely both ways to

Fig. 68. & present, do not let an imperfect immediately follow.

wards x and y. Bisect Observe, however, that the present infinitive may come after A B in D, and along AC set off A E, equal to AD. Join B E, and a finite verb in the imperfect tense, as solebat scribere, he was produce it indefinitely to F, and set off E G along E F, equal to EA wont to write. The rule I have now given relates to what is or AD. Then from A as centre with the distance A G, describe the called the consecutio temporum, or sequence of tenses. Compare semicircle XGH, and from B as centre, with a distance equal to Exercise 75 (Latin-English), in the next lesson.

| AG, describe the semicircle KLY, and let the semicircles x G H,

e de

The first song is taken from the “Hymns for Infant the potential mood, and even the optative mood; but these are Minds," by Jane Taylor and her sister, Mrs. Gilbert, a work, mere figments; they have no corresponding reality in the lanlike all by the same authors, of priceless value in aid of edu- guage. Another form of the verb has a better claim to be cation in school or family. But for the sake of those who termed a mood; I allude to what is called the infinitive, as would sing this tune to a sacred hymn, we add the exquisite legěre, to read. This, however, might probably be more rightly words composed for this tune by the late Thomas Rawson described as the verb in its abstract form. If, however, it is Tavlor of Bradford. Yorkshire-hitherto treasured, like his acknowledged to be a mood, then we must say that the Latins other poems, by a select circle, but henceforth, we trust, more have four moods, the indicative, the subjunctive, the imperative, widely to be known. This tune must be thoroughly sol-faed and the infinitive. The infinitive, however, must stand in the “by heart," like the rest, and the pupil must point to the notes class of dependent modes of utterance, since it makes no sense on the modulator as he thus sol-faes.

unless when joined to a verb in another mood. Thus, vult Our pupils must expect no explanation, at this stage of legere, he wishes to read. Here legere has meaning by being the course, of the sharps, or flats, or clefs, introduced at the united with vult. Vult is said to be a finite word, as legere is beginning of the old notation staff. A proper explanation now said to be an infinitive; finite and infinitive are the opposites would be lengthy and out of place. They are introduced thus of each other. The two words come from the same Latin word early for the sake of those who play on instruments. It is finis, end or limit; the former, therefore, means the limited; enough for the singer that the square mark shows him the place the latter, having the prefix, in, not, means the unlimited; that of the key-note.

is, the definite and the indefinite mood.

Another form in which the verb appears is the participle. In

Latin there are four participles; 1, the active, ending in ns, as LESSONS IN LATIN.-XIX.

amans, loving ; 2, the passive, ending in tus, as amatus, loved; THE LATIN VERB.

3, the future, ending in rus, as amaturus, about to love; and 4,

the corresponding passive participle, which ends in dus, as In form, the Latin verb has two chief divisions-1, active; 2, amandus, to be loved—that is, he who ought to be loved. The passive. Thus, laudo is I praise, in the active voice, and laudor, usages connected with these participles will be set forth hereI am praised, in the passive voice. There are some verbs which, after. The Latins have no active participle of past time; they thongh passive in form, are active in signification; as hortor, cannot by means of a participle say having loved. But the I encourage. The ending in r shows that hortor is of the passive past participles of their deponent verbs have an active signifiform. This form the verb, so to say, lays down, or lays aside, cation, since the verbs themselves have an active signification ; and hence it is called deponent (from de, down, and pono, Ithus, hortatus means having exhorted, put). Deponent verbs, then, are verbs which, disregarding the Connected in form with the passive participle in dus, is what claims of their form, have an active import, just as if they were in Latin is called the gerund; as, amandum, which wears the active in form. As these verbs have an active meaning, their appearance of being the neuter singular of the participle past participle has an active meaning : thus, hortatus, the past amandus. The gerand exists in the nominative as amandum, participle of hortor, is not being encouraged, but having en. in the genitive as amandi, and in the dative and ablative 28 couraged. This past participle joins with parts of the verb amando. It is not easy to set forth the distinctive meaning sum, I am, to form the perfect tense: thus, hortatus sum means of the gerund in one English term. Its proper and full force I have encouraged. There are deponent verbs in all four con must be learnt in reading Latin prose. I place before you a jugations.

few instances of its use. The tenses of the verb in Latin are pretty much the same as

GERUND. in other languages. Thus we have PRESENT, amo, I love, or I am loving; IMPERFECT, amabam, I was loving, or I did love;

Scribendum est, one must write. PERFECT, amavi, I loved, or I have loved; PLUPERFECT, ama

Scribendi ars, the art of writing.

Scribendo aptus est, he is ready at writing. veram, I had loved ; FIRST FUTURE, amabo, I shall or will love;

Inter scribendum, during writing. SECOND FUTURE, amavero, I shall have loved.

Scribendo exerceor, I am exercised in triting. The present tense denotes either an action continued in the present time, or an habitual action. The imperfect tense denotes | Hence, you see that the gerund denotes under certain circuman action continued in past time. The perfect tense has two stances the whole act implied in the verb, as here the act of meanings : first, it signifies an action done and completed in writing. Yet is it nearly connected in meaning as in form with past time indefinitely, and from the period in past time being participles. Similar, indeed, is the case with our word writing; indefinite or undefined, it is called an aorist, or is said to have and generally our active participles in ing, besides having a an qorist import (aorist is a Greek word, denotes a tense of participial force, assume now a verbal, and now a substantare the Greek verb, and signifies undefined or indeterminate); in the force; a verbal, as in writing the letter, say, etc.—that is, while second place, the perfect tense indicates an action which in you write, or when you write; a substantive force, as, the writing itself, or in its consequences, continues from the past to the is bad. present, being somewhat the same as our phrase, I have dined • As in form the gerund, so also the supine is peculiar to the that is, I have just dined ; in contradistinction to the aorist i Latin tongue. There are two supines, one ending in urd, as dined—that is, yesterday, or some time in the past.

amatum, in order to love ; the other ending in u, as amatu, to The Latin has three moods, the indicative, or the mood of I love or to be loved; the former is called the first or active supine ; reality, the mood of simple statement; the subjunctive, or mood | the latter, the second or passive supine. The former is used after of dependence; and the imperative, or mood of command. Mood verbs of motion ; the latter is used after certain adjectives ; is a Latin word (modus), signifying measure or manner. It is

thus:found in the French term mode, sometimes used in English.

SUPINES. The term mood, therefore, denotes the modes or manners in

1st. Venio rogatum, I come in order to ask. which a statement is made. All propositions may be reduced

2nd. Jucunda auditu, pleasant to hear or to be heard. to two general classes; they are either independent or dependent. You may see here an illustration of the propriety of my ques. The independent are in the indicative mood; that is, the mood / tioning whether the infinitive should be designated & noo. which simply indicates or points out. The dependent are in the | If it is a mood, is not the supine equally a mood? And if you subjunctive. The word subjunctive (Latin, sub, under or to, and admit the claims of the supine, can you deny the claims o. jungo, I join) signifies that which is subjoined; that which is gerund? But if the gerund is a mood, equally is the partie connected in the way of dependence. The subjunctive mood, Ta mood. Properly there can be no mode or manner of attesa consequently, is the mood which is dependent on the indicative. / where there is not a complete utterance; that is to say, mo The imperative mood, though differing in form from the other | imply propositions, for without a proposition there is no 1 two, may logically be considered as a subdivision under the sub- | If so, the infinitive can be called a mood only by some lat junctive. How closely the subjunctive and the imperative are of expression. allied, may be seen in the fact that the subjunctive is often used. These, then, are the forms of the verb which you have for the imperative; it is so used when a kind of softened com- understand, to recognise, to construe, to form, and to empty mand is desired. In the older Latin grammars, you will find Latin. I will here recapitulate them;

[ocr errors]

TWO VOICES.

KEY TO EXERCISES IN LESSONS IN LATIN.-XVIII. 1. Actite. 2. Passive.

EXERCISE 69.-LATIN-ENGLISH. Deponent belonging to the passive in form and to the active in meaning.

1. There is no firm friendship among the bad. 2. I hasten to death.

3. The Gauls dwell beyond the Rhine. 4. We have no weapons against SIX TENSES.

death. 5. A generous man is mild toward the conquered, 6. Comets 1. Present; 2. Perfect; 3. Imperfect; 4. Pluperfect; 5. First Future;

are admirable on account of their rarity and beauty. 7. Slaves obey 6. Second Future, or Future Perfect.

on account of fear, the good from a regard to duty. 8. Sailing along

the shore is often dangerous. 9. No one is happy before death. 10. THREE MOODS.

On what account dost thou laugh? 11. Below the moon all things 1. The Indicative. 2. The Subjunctive. 3. The Imperativo.

able. 12. Thou dwellest many years among barbarians. 13.

The kingdom of Pluto is placed under the earth. 14. The government FOUR OTHER FORMS.

of nations is in the power of kings. 15. Fish die out of water. 16.

The thing happened contrary to expectation. 17. The camel bears 1. The Infinitive. 2. The Participle. 3. The Gerund. 4. The Supine.

hatred to horses. 18. Painted garments are mentioned with (in) In all, fifteen varieties of expression enter into the Latin verb. Homer. 19. Many animals congregate and fight against other animals. You are not to suppose from this that every verb has all these 20. The hippopotamus feeds on the corn-fields around the Nile. forms. Even when the Latin was a living language, many

EXERCISE 70.-ENGLISH-LATIN. verbs were defective, that is, laoked some of the ordinary | 1. Inter malos nulla est firma societas. 2. Contra mortem nulla forms. We, however, are bound to write the language as we habet homo arma. 3. Ultra mortem est vita. 4. Ad Rhenum profind it written in the remains of Roman literature, and so are peramus. 5. Ante domum sunt amici. 6. Apud me sunt filii mei. restricted to forms which actually occur in extant Latin writings; 7. Apud te suntne filii vestri? 8. Mitis erga victos est rex. 9. Post and as poetry has its licences, so are we obliged, in order to be

mortem boni sunt felices. 10. Quid est infra terram ? 11. Deus est

super omnia et per omnia, 12. Infra nubes habitant homines, correct, to confine ourselves to the usages of the best prose

13.

Penes me mei sunt liberi. 14. Apud Ciceronem sunt multa pulchra writers. In general, the Latin of Cicero is the model to be

dicta. 15. Rus propter te amo. 16. Intra muros sunt milites. followed. Verbs which have been above described as active, may also

EXERCISE 71,-LATIN-ENGLISH. be called transitive; that is, active in voice, and transitive in

1. Poison is for (acts as) a remedy sometimes. 2. An infant has no

power without another's aid. 3. Eagles do not build in trees. 4. import; thus, laudo puerum, I praise the boy, is a transitive

The cuckoo lays in the nests of other birds. 5. By old age our senses verb, because the action of the verb passes over (trans, across,

I grow dull 6. Some men are born with teeth. 7. Xerxes fled from over, and eo, I go) to the object, puerum. As some verbs are Greece with very few soldiers. 8. Metellus leads elephants in triumph. transitive, others are intransitive or not transitive. Such is 9. The traveller sings in presence of the robber. 10. The stars move dormio, I sleep, in which no action passes over to an object. from the east (rising of the sun) to the west (setting of the sun). 11. Intransitives are sometimes called neuters; that is, neither Britain was discovered by the Phænicians. 12. Bees cannot exist active nor passive. When they have a passive form, they bear without a queen. 13. It is sweet to die for one's country, the name of neuter passives ; as, ausus sum, I have ventured;

EXERCISE 72.- ENGLISH-LATIN. gavisus sum, I have rejoiced. Sometimes a verb, in the passive 1. Estne aliquando venenum pro remedio? 2. In Græciā pugnat form, has a reflective force, and may be Englished by a neuter

Xerxes. 3. In senectute visus et auditus hebescunt. 4. Paritne in or intransitive verb; as, moveor, I move myself, or simply, I

alieno nido coccyx ? 5. Soror tua coram multis cantat. 6. Ab ortu move. A few active forms have a passive signification; as,

solis ad occasum properant. 7. Græcií proficiscens exercitus in Italiam

properat. 8. Metellus cum multis militibus est in Britannia. 9. Tapalo, I am beaten; veneo, I am sold. Somewhat similar is

Filius meus sine dentibus est natus. 10. Estne exercitus sine elefio (factas sum, fieri), I become, I pass from one state into another;

phantis ? 11. Elephanti in triumpho a duce ducuntur. 12. Dulcene I am made.

est pro patriã mori? 13. Quid sine Dei ope sunt mortales ? 14. The tenses may be divided into three classes; thus :

Omnesne aves in arboribus nidificant? 15. Clam patre est puer in

domo. 16. Infantes in gremio matris felices est dulce videre. 17. 1. PRESENT TIME the action incomplete Present,

Tecumne est soror tua ? 18. Sine patre nihil potest puer, 19. Mecum the action complete Perfect.

est filia mea. 20. Quot liberi tecum sunt? 21. Quot homines sunt II. PAST TIME. the action incomplete Imperfect,

in Britannia ?
the action complete Pluperfect.
III. FUTURE TIME

the action incomplete First Futuro.
the action complete Second Future.

LESSONS IN GEOMETRY.—XIX. You thus see that there are three forms of complete action, and THE following method of constructing a regular pentagon three of incomplete :

involves the use of the circumscribing circle, on the circumference (1 scribo, I writo or am writing

of which the angular points of the pentagon may be marked.

PRESENT. INCOMPLETE < 2 scribebam, I did write or was writing IMPERFECT.

We have added this to the modes of construction given in the (3 scribam, I shall write or shall be writing FUTURE.

last lesson to show the student that there are many ways of (1 scripsi, I have woritten

PERFECT.

constructing each of the regular polygons, and to urge him to COMPLETE 32 scripseram, I had written

PLUPERFECT. exercise his ingenuity in finding out other methods for the con(3 scripsero, I shall have written

SECOND (or struction of the hexagon, heptagon, etc., than those we are

PERFECT) FUTURE. | about to give him in this and the following lessons. The natural sequence of our ideas requires a corresponding se

PROBLEM L.-To construct a pentagon on a given straight quence of tenses. We do not in thought suddenly pass from line another way). the present to the past in the same sentence, or in the same

Let A B (Fig. 68) member of a sentence. Consequently, we must avoid doing so

be the given straight in the employment of the tenses. The tenses may be divided line on which the reinto pairs-namely, similar and dissimilar; for example:

quired regular pen-
| tagon is to be de-

VE ME
SIMILAR TENSES.

DISSIMILAR TENSES.

scribed. At the point Present Present. Present Imperfect.

A, in the straight Present Perfect present. Perfect present Imperfect.

line A B, draw AC, Imperfect Imperfect. Pluperfect Perfect present.

of indefinite length, Imperfect Pluperfect.

perpendicular to AB, . Now similar tenses should follow each other, and not dissimilar and produce A B inde. ones. That is, if you use one present, use another; if you use finitely both ways to

Fig. 68. a present, do not let an imperfect immediately follow.

wards x and y. Bisect Observe, however, that the present infinitive may come after A B in D, and along A C set off A E, equal to AD. Join B E, and & finite verb in the imperfect tense, as solebat scribere, he was produce it indefinitely to F, and set off E G along EF, equal to E A wont to write. The rule I have now given relates to what is or AD. Then from A as centre with the distance AG, describe the called the consecutio temporum, or sequence of tenses. Compare semicircle XG H, and from B as centre, with a distance equal to Exercise 75 (Latin-English), in the next lesson.

A G, describe the semicircle KLY, and let the semicircles XG H,

EL.

KLY intersect in the point Q. From the centre Q, with the dis- order, in such patterns as his taste and fancy may dictate. tance Q A, or Q B, describe the circle A N B, and along its circum- for models of tesselated pavement, marquetry, and parquetry. ference set off the arcs A M, MN, N o, each equal to A B, to deter- | An illustration of our meaning will be found in Fig. 72, a design mine the angular points M, N, o of the pentagon A MNOB, which which consists of perpendicular lines of pentagons, black and is completed by joining the straight lines A M, MN, NO, O B. white in alternation, the lozenges or rhombuses (see Definition 30,

The student who is acquainted with the method of drawing Vol. I., page 53) being divided by transverse perpendicular and the equilateral triangle, square, and regular pentagon, will readily horizontal lines into right-angled triangles, which are also black

see that the construction of figures, and white in alternation as they are
the number of whose sides are mul. contiguous to a white or black pen-
tiples of 3, 4, and 5, depends merely on tagon respectively. The designs
the repeated bisection of arcs of made by the learner, for pavement,

circles or angles, as may be seen by may be done in pieces of red, black,
M an inspection of Figs. 69, 70, and 66. and white paper, or in paper coloured

In Fig. 69, A B C is an equilateral to imitate various kinds of marble, triangle, or trigon, inscribed in the pasted together on cardboard. The circle ABC. By bisecting the arcs patterns for marquetry, which conA B, BC, CA, in the points D, E, F, and sists of various kinds of ornamental joining A D, D B, BE, E C, C F, and F A, wood cut in small pieces and veneered

Fig. 72. Fig. 19.

we get the hexagon ADBECF, the on a flat surface of deal or some com

number of whose sides is 3 x 2, mon timber, to form the top of a table or the panel of a cabinet; or 6. If the arcs AD, D B, BE, EC, CF, and FA, were again and those for parquetry, or blocks of wood about an inch in thickbisected in the points G, H, K, L, M, N, we should get a dodecagon, ness, put together in symmetrical patterns to form floors, may or twelve-sided figure, the number of whose sides is 3 x 2 x 2 be cut out in paper stained in imitation of various kinds of =12; by joining the extremities of the arcs AG, G D, etc., or wood. It may be said that coloured paper in imitation of wood drawing chords subtending these arcs, and by another bisection may be purchased of any one who sells materials for bookbind. of the twelve arcs, into which the circle is divided by the angu. ing, while paper in imitation of marble may be procured at the lar points of the dodecagon, we should get a twenty-four-sided same place for fine work, and from the paper-hanger for making figure. The same results would be obtained by bisecting in suc- designs on a large scale. We have called the attention of the cession the angles at the point o, the centre of the circle, and reader to the method named above of making geometrical dedrawing chords, as before, to the aros obtained by the successive signs in coloured paper, to show him how readily a knowledge bisections of the angles at the centre and the consequent bi- of geometry may be applied to art purposes. sections of the arcs on which they stand.

For filling up any space with small compartments all of the If the arcs AB, BC, CA, or the angles A OB, BOC, COA, were same size and form, the hexagon is the most convenient, because trisected, instead of being divided into two equal parts, and its shape assimilates more closely than either the equilateral trichords were drawn subtending the arcs thus subdivided, we angle or the square to that of the circle, the strongest form for should have & nonagon or enneagon, a polygon the number of the "arrangement of material to bear pressure, as in the case of whose sides is equal to 3x3, or 9, and by bisecting the nonagon the barrel drain or circular sewer. Less material, too, would be we should obtain an eighteen-sided figure, the number of whose used in forming a number of hexagonal compartments than in sides is equal to 3 x 3 x 2, or 18.

filling the same space with compartments in the form of equie Similarly in Fig. 70, in which the square ABCD is inscribed lateral triangles or squares having the same depth and area of in the circle A B C D, an octagon, A E B F C G D H, is obtained base as the hexagon. A remarkable instance in nature of the by bisecting the arcs A B, BC, CD, DA,

use of the hexagon for making the most of space for stowage, in the points E, F, G, H, and joining the

with the least possible quantity of material, is found in the honeystraight lines A E, E B, etc., the octagon

comb, of which the cells are hexagonal in form, terminating at being a figure the number of whose sides

the bottom in a roof or floor, consisting of three parallelois 4 2, or 8. A further bisection of

grams, the opposite angles of which are about 110° and 70' the aros A E, E B, etc., would give us a B

respectively. figure the number of whose sides is

The construction of a hexagon is easy enough, whether it be 4x 2 x 2, or 16; and so on.

required to inscribe it in a given circle, or to construct it on a In the same way, an inspection of Fig.

given straight line, because the radius of the circumscribing 66, in Problem XLVII., Page 149, shows

circle is always equal to the side of the hexagon that it surthat if we bisect the arcs A B, BC, CD,

Fig. 70.

rounds. Thus, if we have to inscribe a hexagon in the circle DE, EF, in the points R, S, T, P, Q, and join

ACE (Fig. 73), it is manifest that all we have to do is to open the their extremities, we get a decagon, or regular polygon, the compasses to the extent of A G, the radius of the circle AC number of whose sides is 5 x 2, or 10; while if the arcs AB, BC, I and divide the circumference into six equal parts by appe etc., were trisected, we should obtain a quindecagon, or regular | ing the opening of the compasses round the circumiere polygon, the number of whose sides is 5 x3, or 15. The learner and marking the points A, B, C, D, E, F, in succession. The can readily calculate for himself the results of further subdivisions hexagon is then completed by joining AB, BC, CD, DE, EL, of the arcs of the circle in the cases of the pentagon, decagon, F A, the chords of the six equal parts and quindecagon.

into which the circumference has The reader may have noticed already, that of all figures having been divided. equal sides and equal angles there are only three kinds that PROBLEM LI.-To construct a hexacan be fitted together so as to cover a flat surface without gon on a given straight line. Let AB

... any interstices or openings be- (Fig. 73) be the given straight line F

tween the pieces used. These on which it is required to construct
are the equilateral triangle, the a hexagon. From A and B as cen.
square, and the hexagon. This tres, with the distances A B and B A
number of regular figures that respectively, draw two arcs intersect-
will cover a flat surface with | ing each other in G. The point G is
out the addition of any other the centre of a circle circumscribing

Fig. 73.
figures, regular or irregular, may the required hexagon. From the cen.
Fig. 71.

be further reduced to two when tre G with the distance G a describe the circle A CE; then from LESSONS IN ARCHITECTURE.—VI. world. The architect who traced the plan of this temple was

[graphic]

we remember that the hexagon A and B as centres, with the radins A B and B A respectives: itself is composed of six equilateral triangles, as may be seen | draw arcs cutting the circumference of the circle ACE 1 from Fig. 71, in which the thick lines show how any number of points F and c; and from these points as centres, with the equilateral triangles regularly disposed in rows may be grouped | radius, draw arcs cutting the circumference in the points B into hexagons. The learner will find it a useful practice | D. Join A B, BC, CD, DE, E F, FA; A B C D E F is the helagu to make drawings of the various regular polygons arranged in required, for it is constructed on the given straight lino A B

he same

E and

Ctesiphon, who flourished about 552 B.C., and it was partly THE GREEK ORDERS OF ARCHITECTURE.

executed under his direction and that of his son Metagenes; The temple of Apollo Panionius, in Ionia, was built according but it was completed by other architects, who worked upon it to the Doric style (Fig. I.); but the Ionians, dissatisfied with after these for the space of more than two centuries. Vitruvius the simplicity of this order, invented another of a more delicate says that the form of this temple was dipterick (two-winged), character, and called it the Ionic order, after the name of their that is, surrounded with two rows of columns in the form of a country. They made the height of the column in this order double portico. It was 426 feet long, and 216 broad. In this greater in proportion to its diameter than in the Doric order. temple there were 127 columns of marble each sixty feet high, The form of the capital was totally different, having large volutes given by as many kings ! Thirty-six of these columns were at its corners, of which the spiral is often very finely sculp- carved by the most excellent artists of their times. Scopas, tured; the entablature was changed in its parts and proportions; one of the most celebrated sculptors of Greece, executed one and a base was added to the bottom of the column, in harmony | which was the finest ornament of this magnificent structure. with its capital (see Fig. II.). Of the origin of this order of All Asia had contributed with incredible ardour to the erection architecture we have no distinct account. Vitruvius states, and decoration of this temple. that as the Doric order was considered strong and masculine, Vitruvius informs us that Demetrius, whom he calls the like the form of Hercules, the Ionians modelled their new servant of Diana, and Paconius, the Ephesian, finished this

[graphic][graphic][ocr errors][ocr errors][merged small][subsumed][subsumed][ocr errors][merged small][merged small][merged small][ocr errors][graphic][subsumed][subsumed][graphic][merged small][merged small][merged small]

order according to the elegance and delicacy of the female temple, which was of the Ionic order. History records the figure, and that the volutes were taken from the curls of the remarkable fact that this temple was burned to the ground on hair on each side of the face. It is not easy to conceive how the day that Alexander the Great was born. This same the proportions of a Greek order of architecture could be Alexander, it is said, offered to rebuild it at his own expense, borrowed from that of the human figure, to which it has so provided that the Ephesians would consent that he should have little natural resemblance; and it has been ingeniously re- the sole honour of it, and that no name should be added to marked that it is more natural to trace the form of the volute his in the inscription to be put upon it. The Ephesians, not in the Ionic order to the curling of the bark of a rude upright approving this condition, concealed their refusal of his offer by post, crushed by a superincumbent weight greater than it could saying, “that it was not consistent for one god to erect a bear. In this order, continued subjects began to appear on the monument to another." This temple was rebuilt with still frieze, which in the Doric were considered the exception to the greater magnificence than at first. The truth of this may be rule. The cornice of the entablature was also enriched with gathered from the words of the sacred historian, in reporting exquisite mouldings, and decorated with sculptured ornaments. the speech of Demetrius the silversmith, who made silver

The edifices constructed after the Ionic order were numerous shrines of Diana, to the workmen of like occupation : “Sirs, ye and magnificent, such as the temples of Bacchus, at Teos; know that by this craft we have our wealth. Moreover, ye Apollo, at Miletus; Minerva, at Priene and Tegea; and of see and hear, that not alone at Ephesus, but almost throughDiana, at Magnesia and Ephesus. This order was also em out all Asia, this Paul hath persuaded and turned away much ployed in the construction of the Erectheum, or the temples of people, saying that they be no gods which are made with Minerva Polias and Pandrosus, in the Acropolis at Athens; hands : so that not only this our craft is in danger to be set at of the Delphic Apollo and of Æsculapias, in the same city ; nought ; but also that the temple of the great goddess D and in that of Juno, in Attica. The temple of Diana, at should be despised, and her magnificence should be destr Ephesus, was justly deemed one of the seven wonders of the whom all Asia and the world worshippeth.” Such was the VOL. U.

39

« ElőzőTovább »