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rocks, they are never found associated with recent accumula- The grains of these minerals exhibit no signs of the action of tions, but they have a far wider range, from the Silurian forma- water. They are not water-worn, neither is there any appear. tion up to the Tertiary, both inclusive. But the division between ance of stratification. The nearest approach to it is in the case volcanic and trap rocks is more one of position than distinct of graphic granite, the vertical section of which is drawn in Fig. mineralogical character. This was expressed by Sir James Hall 24, and the horizontal section in Fig. 25. when he said, “I am confident there is not a lava of Mount Etna It will be seen that the black mica in the horizontal section to which a counterpart may not be produced from the whin- has some resemblance to Hebrew characters, hence its name stones of Scotland," which are traps.

graphic. The traps are decidedly of igneous origin; we find them Syenite, named from Syene, an Egyptian city, has four condisrupting strata, and filling up the fissures, while the rock in stituents; the mica is in a very small quantity, and has been the neighbourhood exhibits marks of induration, and other almost wholly replaced by hornblende. alterations by heat. The trap rocks bear a general division Protogine, or “first-formed”- -80 called from an erroneous into feldspathic and ougitic traps.

supposition that it was formed before granite-has talc in its FELDSPATHIC TRAPS.

composition instead of mica. In these rocks feldspar predominates. Felstone, or compact

Granitic rocks have evidently never cooled at the surface, for feldspar, is almost a pure mass of this mineral; it is a compact all is hard and compact. That they were once in a molten con

we never find any ashes, or anything corresponding to pumice; flinty rock. Its colour is either grey, of various shades, or a greenish white; this latter kind is often translucent at the dition seems an inevitable conclusion, when we inspect such edges.

diagrams of granitic veins as those taken from Lyell's Pitchstone is a variety of felstone having a resinous lustre, “ Elements,” and drawn in Figs. 26 and 27. hence its name.

These veins are never found traversing rocks higher than the Felstone porphyry has a basis of compact feldspar, with large cretaceous, and instances are found in Norway where the crystals of the same mineral disseminated through the mass. granitic vein penetratos the strata without dislodging it or The rock to which the term porphyry was originally, and is still altering its dip; so that either the fissure must have been made applied, was of this very nature, the basis being of a dark by the shrinkage of the rock, on account of the proximity of brick-red colour, and the crystals white, or more generally of a heat, or else that after the upheaval took place the strata filesh-colour. The appearance of such a rock is indicated by returned to its normal position. Fig. 23. AUGITIC ROCKS.

LESSONS IN GREEK.-XXVIII. In these the mineral augite is the chief ingredient. Augite and hornblende are considered by many mineralogists as The student will find an advantage in comparing together the synonymous terms.

three voices. The relation of their leading parts may be seen Basalt, which we have briefly described, is a prominent trap in the following rock, and the basalts of the north of Ireland are of this augitic

CONSPECTUS OF THE THREE VOICES. class.

INDICATIVE MOOD, FIRST PERSON SINGULAR. Greenstone is applied to a large class of trap rocks. Their

Active Voice, Middle Voice. Passive Voice. colour is a dark green, owing to the presence of hornblende in

Present. great quantity. They are less compact than the basalts, and

λυ-ω,

λυ-ο-μαι. exhibit distinct crystals of their several ingredients. They are

Imperfect. €-λυ-ον,

E-λυ-ομην, known in Scotland as whinstones.

Future. λυ-σ-ω,

λυ-σομαι,

λυ-θή-σ-ομαι. When the composition of greenstone is mainly feldspar and

First Aorist. E-du-o-a, E-λυ-σάμην,

E-λυ-θην.

First Perfect. Ne-lu-koa, augite, then it is called dolerite.

λε-λυ-μαι. Serpentine, so much used to make ornamental vases, pillars,

First Plup. ε-λε-λυ-κ-ιν,

E-λε-λυ-μην. and mantelpieces, belongs to this class of rocks, though some

Second Perf. πε-φην-α, P.F. λε-λυ-σ-ομαι. geologists class it with the granites.

Second Plup. E-Te-on-elv,

Second Aor. The enclosed minerals we shall treat of in another place.

ε-λιπ-ον,

ε-λιπ-ομην, E-τρι-βην. Second Fut.

τριβ-ησ-ομαι. THE GRANITIC ROCKS.

GENERAL CONSPECTUS OF THE GREEK VERB. These rocks superabound in silica. The volcanic and trap

ACTIVE VOICE. rocks are chiefly classed according to the quantity of silica they contain, but it is always compounded with some base, such as

Indic. Subj. Opt. Imp. Infin. Part.

λυω. potash, soda, alumina, or magnesia. But in the granites there Pres.

λυω, λυοιμι, λνε, λυειν,

λυων.

, was not sufficient of those bases for the silica to take up; hence

Imp. ελυον, . it separated out, and can be distinguished in the rock in grains

Fut. λυσω, ,

λυυοιμι, ,

λυσειν, , 1 Aor. ελυσα,

λυσω, of transparent quartz.

, λυσαιμι, λνσον, λυσαι, λυσα5.

λελυκος. . True granite is readily recognised; as the derivation of the 1 Perf. λελυκα, λελυκω, λελυκοι- λελυκε, λελυκεword indicates (granum, a grain), it is constituted of grains,

1 Plup. ελελυκειν.

Mb,

vai, very perceptible.

2 Perf. πεφηνα, πεφηνω, πεφηνοι- πεφηνε, πεφηνε- πεφηνάς. In a typical specimen those grains are-1. Quartz. 2. Feld. 2 Plup. EneonveLv.

Mi,

vai,

2 Aor. ελιπον, λίπω, , λιπoιμι, , spar. 3. Mica.

λιπε, , λιπειν, , λιπων. . 1. The quartz is commonly colourless, very rarely brown; it

MIDDLE VOICE. is easily recognised, being not unlike a piece of glass.

Pres. λυομαι, λυωμαι, λυοιμην, λυου, λυεσθαι, λυομενος. 2. The feldspar may be orthoclase, or potash feldspar, which

Imp. ελυομην. is generally flesh-coloured; or albite, or soda feldspar, which is Fut.

λυσομαι,
λυσοίμην,

λυσεσθαι, λυσομενος usually dead white. These distinctive minerals are, however, only 1 Aor. ελυσαμην,λυσωμαι, λυσαιμην, λυσαι, λυσασθαι, λυσαμένο the heads of two classes, which contain a great variety, and 2 Aor. ελιπομην, λιπωμαι, λιπoιμην, λιπου, λιπεσθαι, λιπομενος which are found frequently mixing.

PASSIVE VOICE. 3. Mica is sometimes in small colourless plates, which give to the granite of which the houses in Dublin are built its 1 Aor. Elvonu, Avew, λυθειην, λυθητι, λυθηναι, λυθεις. spangled appearance; more generally it is black, and between 1 Fut. Luongo

λυθησοι

λυθησεσ. λυθησοthese extremes is found in every shade of grey.

Mal,
μην, ,

θαι, , To gather the relative proportions of these constituents, we

Perf. λελυμαι, λελυμε- λελυμε

λελυσο, λελυσθαι, λελυμενος give this analysis of Wicklow granite by Professor Haughton :- Plup. ελελυμην. νος, -ω, VOS,-€171',

P. Fut. λελυσομαι,

λελυσοιFeldspar

61.18 Quartz

θαι,
μην,

,
24.98
13.37

2 Aor. ετριβην, τριβω, τριβειην, τριβηθι, τριβηναι, τριβεις.
2 Fut. τριβησο-

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LEVOS.

λελυσεσ. λελυση

HeYos.

Mica.

.

τριβησ- τριβησο

τριβησοι99-53

μαι, ,

μην,
,

εσθαι, ,

juevos.

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κεισαν. .

a

re

We present another arrangement, showing the number of The original form of the first person plural active indicative each tense in the Greek verb.

was ues instead of pev, resembling the Latin termination mus.

Thus the Dorians said TUTTONES, ?ce strike, instead of TUTTOMEV: NUMBER OF EACH TENSE.

so in the Latin, percutinus ; so also ypad-o-jes, we write (in Present, 2, namely, Present Active and Present Middl

Latin, scrib-i-mus). Imperfect, 2, Imperfect Active and Imperfect Middle.

The original form of the third person plural of the principal Future, 5, Future Active, Fut. Mid., Fut. Perf., 1st tenses, active voice, ended in yti: the r passed into o, and the

Fut. Pass., 2nd Fut. Pass. Aorist,

νwas dropped, and so βουλευοντι becaine first βουλευονσι, and Aor. 1st Act., 2nd Act., 1st Mid., 2nd Mid., then Boulevovói, they advise. 6, 1st Pass., 2nd Pass.

In the first person singular of the pluperfect active the Perfect, 3, Perfect 1st Act., 2nd Act., Perf. Pass.

Attic writers, besides the form given in the paradigm, namely, Pluperject, 3, Pluperfect 1st Act., 2nd Act., Plup. Pass.

AFAukelv, had another forin in n (contracted from the Ionic

εα), 1s ελελυκη. The εισαν of the third person plural is com21 tenses in all.

monly shortened into εσαν: thus, ελελυκεσαν instead of ελελυWe remarked before in page 26 of this volume on the close connection in sense between the passive and middle. Thus The Æolic elas, ele(v), elav, instead of aes, ai, aley of the optawe find the present and imperfect the same in both; and, in tive first aorist active, is more usual than the form given in the the same way, the perfect and pluperfect passive, as well as the paradigm. futare perfect, often bear a middle signification.

In the second person singular indicative present and future, A glance at the general conspectus will show that this large middle or passive, the Attics, in addition to the form in D,

have array of separate tenses is not complete in all its parts. The another form in ει, ας λυη 2nd λυει, λυση 2nd λυσει, λελυτη right to appear in the conspectus may be disputed in the and λελυσει, λυθηση and λυθησει, τριβηση 2nd τριβησει. This instance of the perfect subjunctive and optative of the passive form in ec is cxclusively used in the three following verbs, voice, inasmuch as they have no separate and independent namely:forms, but are each made up of a participle and a part of the

βουλομαι, I will; Bovilet, thou willest (subj. βουλη). Verb ειναι.

οιoμαι, I think;
0191, thou thinkest

(subj. oin). Verify the statements made as to the number of each tense

oyouci, I shall see; Oyel, thou shalt sec (subj. oyn) by writing out in full the several tenses in the order observed above.

In addition to the termination of the third plural imperative, Form for yourself, solely by the aid of memory, a general active and passive, in etwoav, atwoav, odwoav, there oxists an

termed Attic, conspectus of the Greek verb, in imitation of the ono just given, abbreviated form in ovrwv, avtwv, odwv, which taking as your verb

as being frequently used by writers in the Attic dialect. These πιστευω (I believe), πιστευσω, πεπιστευκα, πεπιστευμαι.

abbreviated Attic imperatives correspond in all the tenses,

except the perfect, with the genitive plural of the participle of ETYMOLOGICAL VOCABULARY,

each tense ; and the middle form, odwv, corresponds with the Aww, I loose, unbind. , Avolouos, breaking Autpwrns, -ov, d, a third person of the dual voice :Auris, a loosing. the law (νομος, -ου, ransomer,

Present Active, βουλευτωσαν and βουλευοντων. Λυσιθριξ, τριχος, ,hav. d, law).

deemer.

Perfect Active, πεποιθετωσαν and πεποιθοντων ing the hair loose Autopios, loosing, re- ATO-duw, I buy off.

(Gen. of the part. TETTOIOOTwv). (θριξ, τριχος, ή, deeming, healing. Ala-duw, I separate. Aorist First, βουλευσατωσαν and βουλευσαντων. . hair). Aurpov, loosing. Kara-duw, I dissolve,

Present Middle, βουλευεσθωσαν and βουλευε σθων. Λυσιμαχος, putting money, a ransom. break.

Aorist Middle, σκεψασθωσαν 2nd σκεψασθων. an end to the fight Aut pow, I buy off, Napa-Avw, I remove,

When in the future of the active and middle ow, comida, in (uaxn, -75, ñ, bat- ransoni.

destroy; hence our tle). Λυτρωσις, εως, ή, α word paralysis.

roots of two or more syllables, a short vowel, o, e, i, precedes Auriuos, loosing.

the o, the o in many verbs is dropped, and a new form is pro

duced, ending in W, ovuar (mark the circumflex); thus, claw Each of these various compounds of auw, namely, anoiva, (commonly davvw), I drive, eraow, edaw, e1w: and so in the Frapuavw, etc., has its own set of derivatives. The student, other persons, elậs, erậ, edwuev, etâte, elwor. This abbreviated then, in making himself thoroughly acquainted with Aww, has form bears the designation of the Attic future, because employed taken steps towards the acquirement of an immense number of by Attic writers. Here are some other examples of Greek words.

THE ATTIC FUTURE. THE PRESENT, IMPERFECT, FUTURE, AND FIRST AORIST

TeNew, I end, τελε-σ, Attic τελώ, «είς, -εί, -ούμεν, -είτε, TENSES, ACTIVE VOICE.

-ούσι: τελε-σ-ομαι, τελούμαι, , -είται, etc. A few remarks on some of the forms of the verb, of which a Kouifw, I carry, κυμισω, Attic κομιώ, -ιείς, -ιεί, -ιούμεν, -ιείτε, full paradigm has been given, may be of service to the student

-ιούσι: κομιούμαι, -ιεί, -ιείται, -1ουμεθα, of these lessons.

etc. In the conjugation w the person-endings in the course of time Bißacw, I step, stride, Bißaow, Bibaw, B13W, BIBWuev, etc. minderwent changes, as may be learnt from the older conjugation, namely, that in ui, as well as from the dialects, or forms infinitive, and the participlo ; thus, te@, Teleâv, Tedw. The

These contracted futures are found only in the indicative, tho of the language in use among the Dorians, the Æolians, etc.- verbs which take this form are-i, edaw (edavvw), Tedew, and forms more ancient than the Attic, in which Xenophon wrote, katew (I call); 2, all verbs in afw: 3, a few in a w: 4, of the whose Greek is considered the standard for ordinary prose. In verbs in u, all that end in avrude, together with appleruume, I the first person singular indicative and subjunctive of the active voice ue has been dropped, and ti in the third person

put on (clothes), auqiw. singular; thus the forms originally were Avous or Auwur instead ing the parts of the verb required in the exercises that ensue.

The student should now have no difficulty in generally formof λυω, and λυετι instead

So y has been dropped in

It the first singular indicative of the first aorist, which was eavoav,

may,

however, be as well to enter a littlo into detail with the

tenses. instead of, as now, elvoa. In the second person of the imperative active, Oc was dropped, so that we have Ave instead of

KEY TO EXERCISES IN LESSONS IN GREEK.-XXVII. The second person singular active has the termination ola in

EXERCISE 76.-GREEK-ENGLISH. the following forms :-0100a (in Latin, nosti), thou knowest, from

1. I might loose myself. 2. I would loose myself. 3. I loose myself. the perfect olda, used with a present signification, as I know;

4. I may loose myself. 5. I was loosing myself. 6. I loosed myself. poella and noncia, the pluperfect to oda, used with an imper. seires. 10. They were loosing themselves.

7. I shall loose myself. 8. I remained behind. 9. They loose them

11. They loosed themfect meaning, as, thou knewest ; eonoda, thou saidst, imperfect selves. 12. You might have loosed yourselves. 13. I might have from onue, I say; noda, thou wast, imperfect from ciui, I am; remained behind. 14. To have remained behind. 15. Having re. pelota, thou wentest, imperfect from elul, I go.

mained behind. 16. To have loosed one's self. 17. To loose one's

ransoin.

λυει. .

λυεθι. .

F

B

с

D

M

H

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B

sell. 18. Loosing one's self. 19. Loose yourselves. 20. I may have But by Euc. I. 13, angles BCA, BCG are together equal to remained behind. 21. You loosed yourself. 22. He may have loosed two right angles, and BCA has been proved less than a right himself, 23. Let them both loose themselves. 24. You two might

angle. Therefore BCG is greater than a right angle. loose yourselves. 25. Of one loosing himself. 26. You were loosing

Again, by Euo. I. 17, BCG and coB are together less yourselves. 27. Having loosed themselves. 28. They might loose than two right angles, and BCG is greater than one right angle: themselves. 29. We might have loosed ourselves.

therefore B G C is less than a right angle. Therefore BCG is EXERCISE 77.-ENGLISH-GREEK.

greater than BGC; therefore side BG is greater than Bc. 1. Λυοιμην. 2. Λυοιτο. 3. Ανοιντο. 4. Λυεσθαι. 5. Λυομενος. 6. Αυσασθε. | Q. E. D. 7. Ελιποντο, 8. Λιπηται. 9. Λιπεσθε. 10. Λυσσιτο. 11, Ανέσθω. 12. Λνσω

PROPOSITION XVII.-In the figure of Euclid I. 16, if Ec be μεθα. 13. Δνσονται. 14. Ανηται. 15. Λυσαισθoν. 16. Λυση. 17, Λυσασθαι. equal to EF (Fig. 16), the angle A EXERCISE 78.-GREEK-ENGLISH.

ABC will be equal to the angle BCF. 1. He was rubbed. 2. Thou mayest be rubbed. 3. Thou wouldest For, by construction, A E= EC, be rubbed. 4. He would be rubbed. 5. They two might have been

BE=E F; therefore, if Ec=EF, loosed. 6. They might have been loosed. 7. Let him be loosed. 8. A E, E C, B E, and EF are all equal To have been loosed. 9. Being about to be loosed. 10. To have been (Axiom 1). Also it is proved in rubbed. 11. Being about to be rubbed. 12. Thou wast loosed. 13. Euclid I. 16, that angle BAE= Ye were loosed. 14. Thou shalt be loosed. 15. We may have been angle E CF. But since E AB is an loosed. 16. We might have been loosed. 17. They may have been isosceles triangle, angle EAB=EBA loosed. 18. Having been loosed. 19. To be about to be loosed. 20. (Euc. I. 5); therefore the angle ECF Having been rubbed. 21. Let him be rubbed. 22. I have been loosed. 23. I had been loosed.

But be24. I shall have been loosed. 25. They have is equal to angle E BA. 'been loosed. 26. They had been loosed. 27. Thou mightest have been

cause EBC is an isosc triangle, loosed.

angle ECB=angle E BC; and, from EXERCISE 79.-ENGLISH-GREEK.

above, angle ECF=angle E BA; 1. Ελυθη. 2. Αυθη. 3. Λυθειη. 4. Τριβησεται, 5. Λυθησονται. 6. Ετριβη. | therefore, adding equals to equals,

Fig. 16. 7. Δελνμαι. 8. Λελυμενος, -ης. 9. Λελνσονται.

whole angle A BC= whole angle BCF (Axiom 2).

PROPOSITION XVIII.-In the figure of Euclid I. 22, if the EXERCISES IN EUCLID.-III.

circles cut again in L (Fig. 17), D K shall be equal to DL. Join

FL, GL; then, since FK, FL are radii of the same circle, FK= PROPOSITION XIII.-In a triangle A B C (Fig. 13), if BO, CO, FL (Def. 15); and, since GK, G L are radii of the same circle, bisecting the angle A B C, BCA, and meeting in o, be equal, then

GK=GL (Def. 15). shall A B be equal to AC. For since OB=0C, angle o BC=

Hence, in the triangles angle o CB; but angle o Bc is equal to half-anglo ABC, and

FGK, FGL, because angle o C B equals half-angle

GK=GL, and FG is AC B; and, by Axiom 7, the

common, also base FX halves of equal things are equal;

= base FL, therefore therefore angle ABC= angle

angle PGK=

angle ACB. Therefore, by Euo. I. 6,

FGL (Euc. I. 8). A B=AC. Q. E. D.

Again, in the triPROPOSITION XIV.-In a tri.

angles DGK, DGL, angle A B C, if Bo, co, bisect

Fig. 17.

because GK=GL, and Bing the angles A B C, BCA, and

DG is common, also inFig. 13.

meeting in o, be equal, then Ao cluded angle DG K has been proved equal to included angle

will bisect the angle BAC. DGL, therefore, base DK= base D L. Q. E. D. Taking the figure of the last proposition, we have proved that NOTE ON EUCLID I. 22.-Of the three straight lines, A, B, C, if o B, oc be equal, then a B, A c are equal. Hence, since it is necessary that any two should be greater than the third, AB=AC, and A o is common, also ba BO= base co; thero- because, by Euc. I. 20, any two sides of a triangle are greater fore, by Euc. I. 8, angle BAO = angle cao; i.e., A o bisects than the third. The necessity will also appear from the figure ; angle BAC. Q. E. D.

for if the large circle cut DE in M, G H must evidently be greater PROPOSITION XV.-In the figure of Euclid I. 1, if the circles than GM, or the small circle will not cut the large, and the concut again in F (Fig. 14), and

struction will fail. CA produced meet the circle

If ah be greater than gm, then gu is greater than the again in , then ch is greater

difference of FM and FG; c is greater than the difference of a than CF. Join H F, AF; then,

and B; i.e., C with either is greater than the third ; and since since Ah is equal to AF, being radii of the same circle (Def.

A, B, C, are in order of magnitude, A with either of the others is

greater than the third. 15), the angle AHF = angle

The proposition that any two sides of a triangle are greater AFH (Euc. I. 5). But the

than the third is obvious if a straight line be defined as the angle cry is greater than

shortest distance between two points; from which it follows the angle A FH (Axiom 9);

that a broken line between two points must be longer than therefore the angle cyl is

a straight line. greater than the angle CHF.

Fig. 14,

Hence two sides Therefore, by Euc. I. 19,

are greater than the side c H is greater than the side CF. Q. E. D.

the third. Corollary.--Hence it is obvious that the diameter is the PROPOSITION

longest line that can be drawn within a XIX.- At
circle ; for if CAU be a diameter, and F given point in
any point on the circumference, the angle a given straight
CFH will be greater than the angle A FI; line, to make an
å.c., than the angle CHF. Therefore ca angle equal to a
will be greater than c F.

given rectilineal
PROPOSITION XVI.-In the figure of angle.
Euclid I. 5 (Fig. 15), prove that BG must This is the

Fig. 18. be greater than BC. By Euc. I. 17, any two same as Euc. Fig. 15. E angles of a triangle are together less than 23, but the solution there given being of little use for prso.

two right angles; therefore A B C and A CBtical purposes, the following modified form of it is sug. are together less than two right angles. But they are equal; gested : -Let A (Fig. 18) be the given point in the given therefore each of them is less than one right angle. Therefore straight line A B, and DC E the given rectilineal angle. In CD, BC A is less than a right angle.

CE take two points, D, E, such that cD=0E, and join De

A

A

D

B

D

G

D

F

G

с

E

B

D

20

NOTES.

ACB or ABC.

From A B cut off AF equal to CD (Euc. I. 3), and from centre A, / most part his writings are easy and graceful, and but few at distance A F, describe a circle (Post. 3). With f as 'centre, of the Odes present any but ordinary ditficulties to the reader. and radius FG equal to D Е, describe a circle, cutting the last The following extract is the ninth ode of the first book; it is described circle in G, G'. Join AG, AGʻ; thon FAG, FAG' shall addressed to his friend Thaliarchus, and requires no further be the angles required. For in the triangles FAG, FA G', since introduction. It is in the Alcaic measure, so called from the AF, A G, A G' are all equal, being radii of the same circle, and Greek poet Alcæus, who employed it, and was credited with that A F is equal to c D or C E, therefore A F, AG, A G' are equal its invention :to CD or C E. Also, because FG, F G' are equal, being radii of

HORACE.-Book I., ODE ix. the same circle, and F G is equal to D Е, therefore FGʻis equal to

Vides ut altà stet nive candidum DE. Hence, since AF, AG and AF, A G' are equal to cd and

Soracte, nec jam sustineant onus CE, also bases FG and FG' are equal to D Е, therefore included

Silvæ laborantes, geluque angles FAG, F A G' are equal to included angle DCE. Q. EF.

Flumina constiterint acuto. Both positions, G, Gʻ, are given, since the enunciation does not

Dissolve frigus, ligna super foco

5 state on which side of A B the angle is to be. PROPOSITION XX.-In the figure of Euclid I. 15, if EF, EG

Large reponens, atque benignius (Fig. 19) be drawn at right angles

Deprome quadrimum Sabina,

O Thaliarche, merum diota.
respectively to A B and cd, the anglo
FEG is equal to the angle BED or

Permitte divis cætera, qui simul
A EC; for since A E F is a right

Stravere ventos æquore fervido

10 angle, and the angle C E G is a right

Deprceliantes, nec cupressi angle, therefore A EF=CEG. From

Nec veteres agitantur orni. cach take the common part, C EF,

Quid sit futurum cras, fuge quærere; et then the remainder A EC= remain.

Quem sors dierum cunque dabit, lucro der FEG. But, by Euclid I. 15, A EC

Appone : nec dulces amores

15 Fig. 19. =BED; i.e., angle F E G is equal to

Sperne puer, neque tu choreas. angle A EC or B ED. Q. E. D.

Donec virenti canities abest Our next article will extend as far as Euclid I. 32, and we

Morosa. Nunc et campus, et areæ, shall prove the following propositions :PROPOSITION XXI.-Given two straight lines, A B, AC, meet

Lenesque sub noctem susurri

Composita repetantur hora. ing in A, and another line, D E, of limited length. Required to describe an isosceles triangle, A LM, such that Al may coincide

Nunc et latentis proditor intimo with A B, and AM with AC, and LM may be equal to D E.

Gratus puellæ risus ab angulo, PROPOSITION XXII.-If A B C be an isosceles triangle of

Pignusque dereptum lacertis, vertex A, with the base B C produced to D, and if from centre

Aut digito male pertinaci.
C, at distance C A, a circle be described cutting BA produced in
E, then the angle ECD shall be equal to three times the angle

1. Stet, stands out, owing to the greater clearuess of the atmosphere.

In summer the outline of the hills would be dim and hazy. PROPOSITION XXIII.-In the figure of Euclid I. 5, draw CL

2. Soracte, a hill in the territory of the Falisci, about twenty-. at right angles to c B, meeting B A produced in L, and prove four miles from Rome, now called Monte di S. Oreste. AL=AC

4. Acuto. So Pindar speaks of xróvos oferus, and we use the phrase , PROPOSITION XXIV.—If in the figure of Euclid I. 5, the “piercing cold.” Constiterint, as having a passive sense, “have been angles FBC, BCG be bisected by the lines co, B0, meeting in o, stopped," takes gelu as a kind of ablative of the agent. then o A shall bisect the angle BAC.

7. Sabina, generally described by Horace as & poor wine, rilo PROPOSITION XXV.-In the figure of Euclid I. 1, if the Sabinum” (Ode I. xx. 1), but this would be mellowed by having been

kept four circles cut again in F, and ca produced cut the circle in H, then

years (quadrimum).

8. Diota, a two-landled jar (drs, o's, wios, the car), abl. of the IF will be equal to A B.

place whence a thing proceeds. PROPOSITION XXVI.—If in a triangle ABC, BC be bisected 9. Simul more generally would be simul ac stravere, as 80012 as the į in G, and AG joined, and the angle B AG be equal to the angle have quieted. CAG, then B A shall be equal to ca.

10. Æquore, abl. of place. PROPOSITION XXVII.-Given two straight lines, AB, AC, 11. Deproeliantes, fighting it out. The de has a sense of completing meeting in A, and another straight line, D, of limited length. a thing, doing it thoroughly. Required to form a right-angled triangle, of which the base 13. Fuge quærere, seek not to know. The infinitive is used as shall coincide with a c, one side shall coincide with A B, and the

the object of (accusative case after) fuge, by a frequent construction

borrowed from the Greek. other side be equal to D.

So Virg. Æn. ix. 200, "adjungere rebus.

Nise fugis ? " where adjungere is the object of fugis. PROPOSITION XXVIII.-If in the figure of Euclid I. 1, A B

14. The construction is quem cunque (diem) dierum Fors dabit, produced cut the circles in D, E, and the circles cut again in F, whatever sort of day Fortune gives, count it a gain. Lucro appone, set it the figure CEFB is a rhombus, having each of the angles at D down to the profit side of the account. and e double the angles at c and F.

18. Areæ, open places, around temples, for example.
20. Repetantur, be sonight for at the appointed hour.
23. Pignus, either a bracelet (lacertis) or a ring (digito).

24. Male pertinaci, that ill feigns resistance.
READINGS IN LATIN.-IV.

The following ode is addressed to some fickle fair one whoHORACE.

had betrayed the poet, who now congratulates himself on his QUINTUS Horatius Flaccus was born at Venusium in the escape :year 65 B.C., and died 8 B.C., in his fifty-seventh year.

HORACE.-OVES, I. v. the greatest of all the lyric poets of Rome, and his Satires,

Quis multâ gracilis te puer in rosa though not so biting and pungent as those

of Juvenal, the acknowledged master of that branch of literature, are marked

Perfusus liquidis urget odoribus

Grato, Pyrrha, sub antro? by as keen a sense of humour and power of observation. He

Cui flavam religas comam has left us four books of Odes and one book of Epodes in various lyric metres, two books of Satires, two books of Epistles,

Simplex munditiis ? Heu, quoties fidem 5 and the “ De Arte Poetica,” a treatise on the art and practice

Mutatosque Deos flebit, et aspera of versification, in hexameters. The Odes and Epodes are the

Nigris æquora ventis most beautiful of his works, though they are not the most

Emirabitur insolens, original , being, for the most part, formed upon Greek models.

Qui nunc te fruitur credulus anreâ ; There is an occasional obscurity in his language, and especially

Qui semper vacuam, semper amabilem 10 in the Satires and Epistles there are allusions to the events

Sperat, nescius auræ of his time to which it is difficult to find a key; but for the

Fallacis. Miseri quibus

He was

mus.

Intentata nites! Ne tabula cacer

Digna geri, promes in scenam; multaque tolles
Votiva paries indicat uvida

Ex oculis, quæ mox narret facundia præsens.
Suspendisse potenti
15 Nec pueros coram populo Medea trucidet,

185 Vestimenta maris Deo.

Aut humana palam coquat exta nefarius Atreus,

Aut in avem Progne vertatur, Cadmus in anguem.
NOTES.

Quodcunque ostendis mihi sic, incredulus odi.
1. In rosa, on a couch strern with roses.
5. Simplex munditiis, pain in thy neatness. Fidem, the confidence

NOTES. which he reposed in you deceiveil. Supply fælsam.

179. Aut acta refertur, or its occurrence is related. The drama con 6. Mutatos Deos, changed fortune.

sists partly of action, partly of narrative; and the action which the 7. Æquora. The poet compares Pyrrha's changing humours to the spectators see with their own eyes naturally impresses them more fickleness of the weather, Like many others, he has been ship-strongly than that of which they merely hear secondhand, Still, wrecked on her smiles, but he has got safely through it. Nigris, black there are subjects which, either from their being repulsive or unnatural, and scowling, probably as bringing up the black storm-clouds.

should be described rather than enacted, as the Greek poets have 8. Emirabitur, a strengthened form of miror, occurring only in done in the case of Medea's murder of her children, or Atreus this passage.

horrible feast, or the unnatural transformations of Progne and Cad. 13. Me tabula, etc. The construction is-Paries sacer indicat votiva tabulâ me suspendisse vestimenta uvida Deo potenti maris, and the 180. Segnius irritant, impress less vividly. allusion is to il custom of the Italian sailors, on escaping from ship- 181. Fidelibus, on the evidence of which he can depend, wreck, to put up a votive tablet in the temple of Neptune, or some 182. Quæ ipsi sibi tradit, and for which he is his own authority. Intos other sea deity, together with the clothes in which they were preserved. digna geri, things which ought to be kept behind the scenes.

16. Maris probably is governed by potens, according to a Greek 184. Mox, in due time. construction, by which verbs of ruling govern a genitive case-for 185. Pueros. In Euripides' play of “Medea," the cries of the children example, " Sic te Diva potens Cypri" (Odes, I. iii. 1).

are heard on the stage, but the actual murder is not shown. If you The next extract is from the Satires, and is the beginning of choose such subjects as Medea or Atreus, you must treat the horrors an amusing description of the way the poet was pestered in the

of the story in the same way as the old Greek poets did.

188. Quodcunque, etc., anything you show me in this ray is repugnant street, by a person who persisted in fastening on to him.

The to my reason and my taste. whole satire is peculiarly bright and vivid, and the description is so true to life, that it is as applicable at the present day as

Translation of SallusT—"CATILINA,” v. at the time when it was written.

(See page 124.) HORACE.--SAT. I. ix.

Lucius Catilina, the son of a distinguished house, was a man

endowed with great capacities, both of mind and body, but he had Ibam forte Via Sacra, sicut mens est mos,

a wicked and perverse disposition. From his boyhood he had Nescio quid meditans nugarum, et totus in illis :

revelled in the scenes of intestine strife, murder, rapine, and civil Accurrit quidam notus mihi nomine tantum,

broil, which became his pursuits on arriving at manhood. Gifted with Arreptaque manu, “ Quid agis, dulcissime rerum ?"

a constitution capable of enduring to an almost incredible degree, “Suaviter, ut nunc est," inquam; “et cupio omnia quæ vis." 5 fasting, cold, and want of sleep, with a mind courageons, cunning, Quum assectaretur, " Numquid vis?” occupo. At ille,

and shifty, capable of pretence or concealment to any extent; covetons “ Noris nos," inquit. “Docti sumus." Hic ego, “Pluris

of his neighbour's money, lavish of his own; outrageous in his Hoc," inquam,“ mihi eris.” Misere discedere quærens,

desires; with plenty of eloquence but little wisdom to guide it;

in his boundless ambition, ever straining after some extravagant Ire modo ocius, interdum consistere, in aurem

object beyond the belief or aim of ordinary men; this man, ever Dicere nescio quid puero; quum sudor ad imos

10 since Lucius Sulla's dictatorship, had been fired with an irresistible Manaret talos. "O te, Bolane, cerebri

desire to seize the reins of the state, and, provided he could gaio Felicem! aiebam tacitus; quum quidlibet ille

the regal power he aimed at, he cared not one jot by what mcans it Garriret, vicos, urbem laudaret. Ut illi

was to be attained. Day by day his views became more and in ore Nil respondebam, “Misere cupis," inquit, “abire;

outrageous, spurred on by his want of money and the recollection of Jamdudum video; sed nil agis, usque tenebo;

15

his crimes, to both of which results his former courses had code

tributed. An additional incitement was found in the corrupt state Persequar. Hinc quo nunc iter est tibi ?” “Nil opus est te

of morality in Rome, which was cursed by two abominable evils differ. Circumagi; quendam volo visere, non tibi notum ;

ing widely in their nature-luxury and avarice. Trans Tiberim longe cubat is, prope Cæsaris hortos." “Nil habeo quod agam, et non sum piger--usque sequar te.” NOTES.

LESSONS IN ALGEBRA.—XVIII. 1. Via Sacra, one of the principal streets of Rome, leading up to the Capitol through the Foruin, from where the arch of Constan

EXERCISE 30.-MISCELLANEOUS PROBLEMS IN SIMPLE tine now stands. It was called sacred as being the route followed

EQUATIONS. by triumphal processions and religious pageants.

1. What two numbers are those whose difference is 10; and 4. Quid agis. The common form of salutation in Rome. Where

if 15 be added to their sum, the amount will be 43 ? we say, “ How do you do ?" the Romans said, "What do you do?" Rerum goes with dulcissime, not quid.

2. There are two numbers whose difference is 14; and # 9 5. Ut nunc est, as times go.

times the less be subtracted from 6 times the greater, the re6. Occupo, I ask him at once.

mainder will be 33. What are the numbers ? 7. Pluris, etc. On this account, I reply, you will be more esteemed by 3. What number is that to which if 20 be added, and from me. Pluris is the gen, of price.

of this sum 12 be subtracted, the remainder will be 10 ? 10. Puero, the slave whom Horace had in attendance, according to 4. A and B lay out equal sums of money in trade; A gains the fashion of the day.

£120, and B loses £80; and now A's money is triple that 11. Bolane cerebri felicem, I wish you were here, Bolanus, toith your cool.

of B. What sum had each at first? ness, apostrophising some outspoken friend, who would have got rid of

5. What number is that, of which exceeds its | by 72 ? the fellow summarily. Cerebri, genitive, signifying with respect to. So Pliny has “Miseros ambitionis," and in Greek we find, eudaiuw tô v

6. There are two numbers whose sum is 37; and if 3 times λόγων. .

the less be subtracted from four times the greater, and the 15. Jamdudum, etc., l're scen it all along, but it's no uso.

remainder be divided by 6, the quotient will be 6. What are 17. Circumagi, there is no need for me to take you out of your way.

the numbers ? 18. Cæsaris hortos, the gardens on the Japiculum, which Cæsar, 7. A man has two children, to 4 of the sum of whose ages if when dictator, had assigued to the people as a public pleasure-ground 13 be added, the amount will be 17; and if from half the differ

The following are some of the canons for the treatment of ence of their ages 1 be subtracted, the remainder will be 2.
dramatic subjects which Horace lays down in the “ De Arte | What is the age of each ?
Poetica.”
HORACE.--DE ARTE POET., 179.

8. A messenger being sent on business, goes at the rate of €

miles an hour ; 8 hours afterwards, another is dispatched with Aut agitur res in scenis, aut acta refertur:

countermarding orders, and goes at the rate of 10 miles an Segnius irritant animos demissa per aurem,

180 hour. How long will it take the latter to overtake the former ? Quam quæ sunt oculis subjecta fidelibus, et que

9. To find two numbers in the proportion of 2 to 3 whose proIpse sibi tradit spectator. Non tamen intus

duct shall be 54.

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