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fare
altro, other
arciduca, archduke
ancora, yet, still
udire, to hear

Nuova Jork, Neojorca, New
York

da gran tempo, long since
far parola, to talk, speak (fac-
cia, present subj.)

sue a person, enter a suit
against him
consiglio, counsel, advice
che what

cosa,

injure a person
seco (for con se), with him, her,
one's seif

andarsene, to go away
scusarsi, to excuse one's self
subito, immediately
vogliono, they are willing
rivenire, to return
divenire, to become
in breve, in a short time
dacchè, since, as

80, I know

legnajuolo. joiner, carpenter movie (past part. morto), to

die

aver da dare, to owe, be in medicina, medicine, physic

debt for

te, thee

sappia, pres. subj. from sapere,

to know

di più, further
mancò poco, ch' io, etc., non, I,
was very near, I, etc.
had like (i. e. little was

etc.,

Si dí-ce, che la si-gró-ra Johnson si ma-ri-te-à. Al canto si co- ó-sce uc-cê-lo. Si mangia e si bé-ve bê-ne in quest' o-ste-ri-a. Si co-nó-sco-no gli a-mi-ci rẻ-le dis-gia-zie. Si cér-ca quá-si rên-pre la for-ú-na, dőv'é--sa non è. In Eu. rò-pa si pár-la-no cin-quan-ta tre lingue. Si de-sí-de-ra-no spé...so cô...se che -6-nó n Si cô-pro-no qualche -cé-vo-li. vôl-ta i té -ti di rá-me e di la-á-gna. Si è desto, ch' E'l-la si-a am-ma-la-ta; è é-zli vé-ro? Non si è ma-i fe-li-ce a spé-se del tên ês-se-re dé-li á -tri. Non si cé-de, che l' Ar- far processo ad uno, to indict or ci-dú-ca sí-a an-co-ra am-ma-lá-'o. A-vé-te voi u-di-to quél-lo. che si racconta d' ú-na ra-gáz-za di Nuô-va Jork (Neo-jûrca)? Non se ne pár-la più. Se ne par-la da gran tên-po. Non vô-glio, che se ne faccia pa-rô-la. Gli si fé-ce pro-cês-so. Mi si di-ce, ch' E'l-la si ma-ri-te-rà. Ci viê-ne rac-con-tá-to m6l-to, che non è vé-ro. Non vi si cà al-cún buôn eon-sí-glio. Che cô-sa si ha da dá-re a te? Ci si la 6-a. Non vi si vé-de niên-te. Bá-sta, ch' io lo sáp-pia. Non ocóre. che di più ve ne pár-li. Ci man-cò pô-co, ch' i-o non ca-dé-si Fa d' uô-po che lo sco-iá-re si-a o-gnó-ra at-lên-to. E' pec-cáto che mi-o cu-gí-no non pôs-sa ve-ni-re. Co-min-cia a far-si Non Bá-sta sa-per-lo. Non oc-cor-re an-dar.vi. giá no. gio-va dis-cor-re-re. Che cô-sa b-6-gna fá-re per im-pe-dí-re úa tal dis-grá-zia? Bi-s6-gna sêm-pre la-vo-rá-re, non bixố-gna êu-ser pi-gro. Bio-ghe-d a-ver pa-ziên-za. Che cô-sa fa Ella? Bi--6-gna ch' í-o scií-va. Bi-so-gná-va ch' í-o scrivé-si ú-na lêt-te-ra. Bi-so-gne-à ch'í-o lê-ga quel -bro. Bi-6-gna che nói seri-viá-mo. Bi-6-gao che i miêi fran ề li la-16-ri-no. Bi--6-gna sên-pre a-dem-pí-re il sú-o do-vé-re. Non bi-6-gna far má-le ad al-cú-no. Bi-so-gne-iêb-be tê-ne dir-glie-lo. Bi--6-gna ch' egli non ab-bia a-vi-to da-na-ci Se ne va ré-co. Vo-lé-te ac-com-pignár-mi? Me ne v E-la già? Bi-só-gna ch'i-o me ne vá-da. La di Lê-i má-dre non se ne va an-có-ra. Mi scú-si, mí-a ma-ire se n'è già an-da-a, ed i miêi fran ê li se ne an-dián-no sú-hi-to. A-pê-ti an-6-ra un mo-mén-to, ce ne an-die-mo in-sie-ne. Vat-te-ne. An-da-te-ve-ne con Di-o. E'gli-no non vô-glio-no an-dar-sp.ne. Non me ne vô an-có-ra, mà me ne an-drò phê. sto. Dó-po a-vér é-gli dét-to qué-sto, se ne an-dò sén-za piên de-re con-gê-do. S'é-gli se n'è an-dá-to, me ne an-drò anch' 1-0. An-diá-mo-ce-ne, si-gnó-ri. Se 16-si ve-nú-to un pô-co più tardi, sa-1ê-i ve-nú-to cól-le vô-stre so-e-le. Son ve. nú-to a di-man-dár-le, quân-do è El-la ri-ve-nú-ta? Qué-sto mer- án-te è di-ve-nu-to he co in biệ-ve. Dac chè non 1 hộ ve-dú-to, non số, che cô-sa sf-a di-ve-nú-to di lúi. $6-no ôgoại u-sci-to un po' più tar-di. E'l-la è u-sci-ta sén-za air-me-lo. Se fós-si u-sf-to, Glié-lo a-vrê-i dec-to. E-ra El-la in chiê-sa? Si, ne son u-í-to in qué-sto mo-mén-to. Cré-de E'l-la, che il le-gna-juô-lo sf-a già môr-to? E'-gli sa-rêb-be môr-to, se non a-vé-se pré-so me-di-cf-na. E'-gli m' ha di-man-da-to la mí-a ta-buc-chiê-ra, ma non ghẻ-la pre-te-rò. La la-van- a-ja mi ha di-m n-dá-to un scel.lí-no, glié-lo man-de-ro Ha Ella ren.dú.to_i }{.bri a mí-a so.rêl-la? Nô, gliédi ren.deò dimá-ni. Perchè è E'l-la co-ì triesta? Io Gliélo hô già dét-to. Non Glé-io o di-maneda.to. Che Ghé-ne på-re? A.é-te com-prá-o déle nó-ci da qué-sta dôn.na, paiga.te.

tobacchiera, snuff-box
lavandaja, washer woman
noce, walnut
disegno, design, drawing
donare, to give, present with
(a gift)
ombrella, umbrella.

LESSONS IN GREEK.-No. XLV.
By JOHN R. BEARD, D.D.
VERBS IN CONSIDERED IN DETAIL.

Verbs in μ which, after adding the syllable vvỷ or vỷ to the stem-
vowel, append the personal endings.

Formation

of the verbs in a. &, o, and of those whose stem

terminates in a consonant.

a. Verbs with a stem ending in a, e, o.

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follows: PRESENT TENSE. IND.-V6 vá do) tá i va, an-did-mo, an-dd te,
The irregular tenses of andare, to go. required for this exercise are as
cá da-no. FUTURE-An-dro.
dú-ce, vá-da-no.

gliesle. Mi-o fra:ê-lo ha di-man-dá-to il vô-stro di sésgno, | rân no. PRES. TENSE, SUBJ➡ På da, vâ-da, vá da an did mo, an-did-te,

donasterglielo. A-véte pré-so l' om-brêl-la di mi-o zíso, ren dé-te-glie-la.

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2. ζε-ννύμι, 1 boil (transitive), f, ζεσω, 2. εξεσα, pf. m. or p. εξεσμαι, a. p. εξεσθην (ξεω is commonly intransitive).

3. σβεννύμι, I extinguish, f. σβέσω ; aor, εσβεσα ; 2 a. εσβην, I went out, I was extinguished; pf. εσβηκα, I have been put out ; midl, σβεννυμαι, I go out ; pf. m. or p. εσβεσμαι; a. p. εσβέσθην. There is no other verb in ννύμι, except this, with a Second Aorist.

4. στορε-ννῦ-μι, I spread over, f. στορεσω, Attic, στορῶ ; a.

εστόρεσα.

The stem ends in o, lengthened into w→

1. ζω-ννῦ μι, Ι gird, f. ζωσω ; a. εξωσα ; mid. I gird myself, a. εξωσάμην ; pr. m. or p. εζωσμαι.

2. ῥω ννύμι, Ι strengthen; f. ρωσω ; 2. εῤῥωσα : pf. m, or p. εῤῥωμαι, (εῤῥωσο, vale, farewell); iut. εῤῥωσθαι ; a. p. εῤῥωσθην.

3, στρωννύμι, Ispread out ; f. στρωσω ; a. εστρωσα, etc., se

στορέννυμι.

Another form of the Present and Imperfect is, σκεδαννύω, 4. χρωννύμι, I colour, f. χρώσω; 9. έχρωσα; pf. m. or pe

ε-σκεδαννύον: κορε-ννύω, ε-κορε-ννυον: στρωννύω, 4-στρω νννον: the v being always short.

b. Verbs with a stem terminating in a consonant, as ολ-λυ-μι (ΟΛ.), I destroy, and oμ νϋ-μι (ΟΜ.), I swear.

Pres. ολλύ με (Lat. perdo) | ομ-νῦ· μι:

ωμ-νῦν :

(ΟΛΕΩ) | ομ-ωμο-κα:

ολ-λύ μαι (pereo)

Imp. ωλλύν

1 Perf, ολωλε κα

perdidi

2 Perf, ολωλα, perii

1 Plpt, ωλ ωλε κειν,

perdid. | ομωμο-κειν:

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(ΟΜΟΩ)

ομοῦμαι, ἢ

ωμο-σα :

Of the Present and Imperfect there is

ομνύμαι

ωμνύ μην ομ-ωμο-σ-μαί,

ομωμο σμην

ωμο-σάμην

1 A. P. ωμο-σ-θην

1 F. Ρ. ομο-σθησομαι. another form with the

v short, namely, ολλυ ω, ωλλυ-ον, ομνυ· ω, ωμνυον. The present, the first perfect, and the first pluperfect have a transitive signification ; thus, pres. I destroy, i perf. I have destroyed, 1 pipt. I had destroyed, and the 2 perf. and 2 plupt. have an intransitive meaning, as 2 perf. 1 have perished (I am lost, it is all over with me), 2 plpf. I perished. The middle of ολλυμι, nam ly, ολλυμαι, signities I am perishing.

Ολ-λυ-μι has arisen by the assimilation of v to x, from ολ-νυμι. The perfect participle middle or passive of ομνυμι 15 ομωμοσμενος. The other forms of the perfect and pluperfect are in the Attic writers generally without the 6, as ομωμόται, όμωματα.

In partimular instances belonging to this class of verbs the stem ends, i, in a vowel, and takes vvv.

The stem ends in a

1. κεραννύμι, I mia, f. κεράσω, Attie κερῶ ; a. εκερᾶσα ; pf. κεκράκα; mid. I mix for myself, a. εκερασαμην, pf. nuid. or pass. κεκρᾶμαι; a. p. εκρᾶθην (by metathesis), also εκερασθην.

2. κρεμαννύμι, I hang, f. κρεμάσω, Αtt. κρεμῶ; a. εκρεμάσα md, or pass. κρεμαννυμαι, 1 hang myself or am hanged, but κρεμᾶμαι, I hang ; f. μ. κρεμασθήσομαι, a. εκρεμασθην, 1 toas hanged or I hung (intrans.)

3. πεταννύμι, I spread out, I open; f. πετᾶσω, Αtt. πετῶ ; pt. in, or p. πεπτᾶμαι (by syncope), a. p. επετασθην.

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κεχρωσμαι; Imp. εχρώσθην.

ii. Verbs whose stem ends in a consonant and take vv.

1. αγνύ μι, I break ; f. αξω : a. εαξα; inf. αξαι; pf. ελγα, Ι have been broken; a. p. εάγην.

2. είργνυμι (ως είργω), I restrain, enclose ; f. είρξω; a. είρξα ; α. μ. είρχθην ; pr. m. or p. είργμαι (but ειργω, ειρξω, ειρξα, I exclude).

3. ζευγνύ μι, I yoke, sind, f. ζεύξω ; 2. εξευξα; mid. I bind for myself; a. εξευξαμην; pf. m. or p. εξευγμαι; a. p. εξευχθήν; and more commonly εζύγην.

4. μιγανῦ· μι, Ι mir ; f. μίξω ; Α. έμιξα, μιξαι; pf. μεμίχα; pf. m. or μ. μεμιγμαι; a. p. εμιχθην, εμίγην ; f. p. μιχθήσομαι, μιγήσομαι, 3. Ι. μεμιξομαι.

5. οιγ-νῦ μι, Ι open, commonly as a compound, ανοιγνυμι (for which, however, ανοιγω is more usual in the present, and in the imperfect ανεωγον is always used); f. ανοιξω ; 2. ανεψξα, ανοίξαι ; 1 μι. ανερχα, I have opened ; 2 pf, ανεωγα, I stand open (tor which the Artie ανεφγμαι); impt. ανεφγομην; a. p. ανεψχθην, ανοιχθῆναι.

β.

7.

8.

ομοργνυμι, I wipe off, f. ομορξω; a. ωμορία; mid. I wipe off for myself, f. ομορξομαι ; 8. ωμερξαμην; a. p. ωμορχθην.

πηγνύ μι, Ifasten, f. πηξω, a. επηξα; 1 pf. πεπηχα, I have fastened; 2. pr. πεπηγα, I am fast; mid, πηγνυμαι, I remain just ; pf. πεπηγμαι, I am fast ; a. p. επάγην ; f. p. παγήσομαι.

ῥηγ νῦ μι. I break, I tear, f. βήξω; a. εῤῥηξα : 2 p. εῤῥωγα, I am brchen; a. m. εῤῥηξαμην; a. μ. εῤῥᾶγην; Ι. Ρ. ράγησομαι.

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388

ώμοσαν τας συνθηκας φυλάξαι. Ξενοφάνης έλεγε την γῆν ἐξ αέρος και πυρος συμπαγῆναι. Σωκράτης, ιδων Αντισθένη το διεῤῥωγος ἱματιου μέρος αει ποιουντα φανερον· Ου παύση, έφη. εγκαλλωπιζόμενος ἡμῖν; Ψευδόρκον στυγεῖ θεος όςτις ομεῖται. Ζευς ανδρ' εξολέσει Ολύμπιος, ός τον έταιρον μαλθακα κωτίλλων εξαπατᾶν εθελει.

ENGLISH-GREEK.

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append the person-endings immediately to the stem. All other parts of these verbs, however, follow the formations The formation of this second aorist active corresponds in all the moods and the participle, to that of the second aorist active of the verbs in μι. The characteristic vowel is length. ened throughout, as in εστην, ἅ and e being changed into η, ο into w, and y into ῦ; and so remains, as in εστην, through all the indicative, imperative, and infinitive. The imperative termination, not, in verbs with a for the characteristic vowel is abridged into a, as προβᾶ instead of προβηθι.

Char. a
ΒΑ Ω
βαινω
I step, I go.

He mixes. We mix. They mix. It was mixed. It has been mixed. They hang. They will hang. They have hung. I spread out. Thou wilt spread out. He has clad. They have clad. I shall clothe myself. We shall clothe ourselves. He boils. They will boil. He extinguishes, I am extinguished. Thou wilt gird. I shall strengthen. They will strengthen. I have been strengthened. They have coloured. He will colour. He is broken. They will break. They will yoke. He has yoked. I have been voked. He opens. They He has open. Thou hast opened. He will wipe away. I went. wiped away. Thou wilt fasten. He will fasten. I am broken. Ο boy, boil the water. The boy cannot boil the water. The S. 1. ε-βη-ν 2. ε-βης boys boiled the water. The garment is torn. The doors stand The wine will be mixed with water. (are) open. cup is broken. The light is put out. They put out the light. I swear not (subj. aor.) rashly. Pride will destroy you all Put out (aor) the light. The women in grief (grieving) tore (aor. mid.) their garments.

The

Inflexions of the tuo Present perfect forms, κείμαι, I lie, and ήμαι, I sit.

κείμαι, the perf. mid. or pass. means properly I have laid
myself, and so, as the result of so doing, I lie. κεῖμαι,
then, is perfect in form and present in signification.
Perf. Ind. κείμαι, κεῖσαι, κεῖται, κεῖμεθα, κεῖσθε, κεῖνται; subj.
κεώμαι, και, κέηται, etc.; impr. κεῖσο, κείσθω, etc. ; inf.
κεῖσθαι, part. κείμενος.

Pipf. Ind. εκείμην, εκεῖσο, εκεῖτο, pl. έκειντο; opt. κεοιμήν,
Κέδιο, κέοιτο, etc.

Fut. κείσομαι

Compounds, ανακειμαι, κατακειμαι, κατακείσαι, etc., inf. κατακεῖσθαι; impr. κατάκεισο, εγκεισο.

Ημαι, I sit,

3. ε-βη

D. 2. ε-βη-τον

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3. ε-βη την

εσβητην

Εγνω την

Ρ. 1. ε-βη- μεν

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εδυμεν

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εδύτε

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εδύσαν

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Ημαι, a perfect passive form, signifying I have seated myself,
or I have been sealed, and so coming to signify I sit. P.
The stem is 'ΗΔ (compare ήσεται instead of ήδεται, and
the Latin sed-eo, where the s represents the aspirate in
'ΗΔ; compare also the Greek έδρα, a seat )

Perf. Ind. ήμαι. ἦσαι, ἧσται, ἡμεθα, ἦσθε, ἤνται; impr. ἦσο,
ἦσθω, etc. ; inf. ἦσθαι; part, ἦμενος.

Pipt, ήμην, ἦσο, ἦτο, ἤμεθα, ἦσθε, ἤντο.

As the perfect form has a present meaning, so in
both verbs the pluperfect is equivalent to the
imperfect.

Instead of the simple ἦμαι in prose, we find καθημαι,
the inflexions of which vary in this, that in the
3rd person singular of the perfect, it never takes
. and in the pluperfect only then when it has
the temporal argument.

Perf. κάθημαι, καθησαι, καθηται; sub, καθώμαι, καθῇ, καθῆται;
impr. καθησο; Iut. καθῆσθαι; p. καθημενος.
Plpf. εκαθημην and καθήμην, εκαθησο and καθησο, εκάθητο and
καθηστο; opt. καθοίμην, καθοιο, καθοιτο.

The forms wanting in ήμαι are made up by έζεσθαι οι
ΐζεσθαι (prose καθέζεσθαι, καθίζεσθαι).

Verbs in a which in the Second Aorist Active and Middle follow the Analogy of the Verbs in μια

Several verbs, having the characteristics a, ɛ, o, v, form a second aorist active and middle after the analogy of the forma tions in u, since those tenses want the mood-Towel, and

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σβεσης
σβειη
σβείητον
and εἶτον
σβειη την
and ειτην
σβειημεν
and εἶμεν
σβειητε
and είτε
σβειες

γνοίην

γνοίης
γνοιη
γνοιήτου
and οἶτον
γνοιητην
and οιτην
γνοίημεν
and οἶμεν

Imperative.

σβῆθι, ητω

γνοίητε

and οἴτε

γνοιεν

γνῶθι, γνωτω δῦθι, δὕτω σβῆτον, ήτων γνωτον, ωτων δύτον, ὕτων σβητε

γνῶτε

σβητώσαν γνώτωσαν

δύτε

δύτωσαν

and σβεντων and γνοντων and δύντων

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βας, ᾶσα, αν σβεις, εῖσα, εν γνους, οὖσα, ον ους, ὖσα, ἔν G. δύντος G. βαντος G. σβεντος G. γνοντος

The subjunctive βω. βῆς, βῇ, etc., appears in the compounds, as, αναβώ, αναβῇς αναβή, εις, αποσβῶ, διαγνῶ, αναίνω. The imperative βηθι, βητω, ete, appears in the compounds ανάβηθι αναβᾶ, ανάβητε, αποσβηθι, διαγνωθι; αναδύθι. In ordinary style the second aorist middle is found in very few verbs, as πέτομαι, Ιfy; πρίασθαι, I purchase. Besides the verbs just adduced, some others follow this formation, as,

1. dugar, commonly amodiopaero (with acc.), I run aicity

from; a. (ΔΡΑ) απεδρᾶν, ας. ᾶ, ἅμεν, ᾶτε, ᾶσαν ; subj. αποδρῶ, δρᾷς, δρᾷ, δρῶμεν, δρᾶτε, ὁρῶσι(ν) : ορι δραιην; imp. αποδράθι, ατω ; iut. αποδράναι, part. δρᾶς, ᾶσα, αν. 2. πετομαι. Ι fy; a. (ΠΤΑ) επτην; imp. πτῆναι ; p. πτας, 3, m. επτάμην, inf. πτασθαι (by syncope).

3. σκέλλω or σκέλεω, I dry, I dry up (hence our skeleton). 2. (ΣΚΛΑ) εσκλην, I am dried up; inf. σκλῆναι; opt.

σκλαίην.

4. φθα-νω (with acc.), I get before, I anticipate ; a. εφθην, φθω. φθαίην, φθῆναι, φθας.

5. καιω, I burn (transit.); a. (ΚΑΕ) εκαην, I burnt (intrans.), but 1 aorist εκαυσα (transit.), I set on fire.

6. ρέω, I flow; a. (ΡΥΕ), εῤῥνην, I flowed, f. ρυησομαι; pf, ερόνηκα.

7.

χαίρω, I rejoice ; a. (ΧΑΡΕ) εχρην.

|

8. άλισκομαι, I am taken, caught ; a. (ΑΛΟ) ήλων and ἑάλων. 9. βιοω, I live ; a. εβιων; subj. βιῶ, ῶς, , etc. ; opt. βιψην (not βιοιην, as γνοίην, to distinguish this part from the optative impf. βιοιην); inf. βιῶναι; part. βίους, οὖσα (the neuter does not occur); the cases, however, are supplied by the 1 aor. βιωσας (30, ανεβίων, I lived again, from αναβιωσκομαι). The present and in perfect are litre used by the Attics, instead of which they employ ζω (ζαω), | which on the other hand borrows the remaining tenses from βιοω, thus pres. ζῶ, impf. εζων, fut. βιωσομαι, a. εβιων, pt. βεβιωκα, pf. p. βεβιωται, part. βεβιωμένος. 10. φυω, I bring forth; 2 aor. εφῦν, I arose, came into being; οῦναι, φυς, subj. φυω (no opt. in Attic), 1 aor. εφύσα, 1 brought forth; f. φυσω, 1 shall bring forth. The perfect πεφύκα, I have come into being, I have become, is also intransitive. The mid. pres φνομαι, f. φυσομαι. Particular attention must be paid to a verb of frequent occurrence, namely, olda (stem EIA, vid-co in Latin), I know.

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του.

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Πτερυξ, υγος, ή, a wing.
Συλλας, ᾶ, ὁ, Sylla,
Νεκρος, α, ον, dead; ὁ νεκρος,

a corpse. Πτερον, ου, το, a wing. Πέλαγος, ου, τo, the sea. Προςθετος, η, ον, added (artiferally), adventitious, artificial. Άχρηστος, ον, useless, Οξυς, εία, υ, quick, feet, ex quisite.

Ακολαστως, unrestrainedly. Ώστε, so that (with infin. and indicat.)

EXERCISES-GREEK-ENGLISH.

Οι άνθρωποι την αληθειαν γνῶναι σπευδουσιν. Γνῶθι σεαυΓνῶναι χαλεπον (sc. εστι) μετρον. Η πολις εκινδύνευσεν ύπο των πολεμίων ἁλῶναι. Φεῦγε τους ακολαστώς βιωσαντας. Συγγνωθι μοι, ω πατερ. Εις τί καταδυς τοῦ κόσμου μερος και αποκρυψας σεαυτον πιστευεις, οτι τον Θεόν αποπεφευγας; Λιμος μεγιστον αλγος ανθρωποις εφυ. Οξεία ήδονη παραπτᾶσα φθανει. Ο δουλος ελαθεν αποδρας τον δεσπότην. Οἱ στρατηγοί εγνωσαν τοις πολιταις βοηθειν. Μηποτε σεαυτον απογνώς. Δαίδαλος ποιησας πτέρυγας προςθετας εξέπτη μετα τοῦ Ικάρου. Σύλλας ενέπλησε την πολιν φόνου και νεκρῶν, ώστε τον Κεραμεικον αἵματι ρυῆναι. Ικαρος, ὁ Λαίδαλου υἱος, τακέντος του κηρού και των πτερῶν περιῤῥυεντων, εις το πελαγος ενεπεσεν. Οἱ πολέμιοι την γῆν τεμοντες απέβησαν. Αχρηστον (sc. εστι) προειδέναι τα μέλλοντα. Οἱ αγαθοι παντων μέτρον ισασιν εχειν, Πολλοι ανθρωποι ούτε δικας ήδεσαν, ουτε νόμους.

ENGLISH-GREEK.

They know. They knew. He may know. Thou knewest. He became. The woman will bring forth a child. They may live. I have lived. He is dried up. He went. They knew (resolved). He site. They sit. Thou liest. They lie. He will lie. He runs away. Go away, O, boy. The whole city flowed with blood. The bird flew away. The general determined to succour the city. The father pardoned the son. Do not live without restraint! The city was taken by the enemy. Let us not despair. The slave ran away from his master.

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But powers of different letters, and different powers of the same letter, are unlike quantities, hence they can be added only by writing them down with their signs.

9. The sum of a2 and a3, is a2 + a3.

neither twice the square of a. nor twice the cube of a. It is evident that the square cf a, and the cube of a, are 10. The sum of a3ba and Bal, is a + 30 6. From the preceding principles we deduce the following

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6. From 62(a + b) take a(a + b)1. 7. From 17a3+5xy take 12a2x3- 4zy2. 8. From 3a3 (68)3 take a3 (b2 — 8)3. 9. From a2b3+ x3y take ab — x2y3. 10. From 5+ y⁄4)3 — 3 (a2 — b3)5 take (x3+ y1)3.

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11. From 2x(a - b)3 + 3 (a - b)3 take x(a —b)3 + 3(a - b)3. 12. From (x+y)2 + (a + b)3 take (x + y)2 + (a+b).

MULTIPLICATION OF POWERS.

Powers may be multiplied, like other quantities, by writing the factors one after another, either with, or without, the sign of multiplication between them.

1. The product of a3 into b3 is a3b2; and 3 into am is amr3. 2. Mult. 5. a2b❜y2 a3by

Into

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3. Забу - 2x

4. dh3xa 4 by

If the quantities to be multiplied are powers of the same root, instead of writing the factors one after another, as in the last article, we may add their exponents, and the sum placed at the right hand of the root will be the product required.

The reason of this operation may be illustra ed thus: And aa aaa a2 X a3 is a2a3. But a2 aa, and a3 = aan. = aaaaa = a3. The sum of the exponents 2+ 3, is also б. So da da data.

N.B. The same principles hold true in all other powers of the same root.

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28. Mult. 3+ x2y + xy2 + y3 into x + y. Sab3 +1664 into a + 24. 29. Mult, a 2a3b+4a2b2

30. Mult. a+ ¿ into a2 — 8.

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The rule is equally applicable to powers whose exponents

are negative, i. e. to reciprocal powers.

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2. 12b3xn

3. a2b+3a2y1

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5. The quotient of a divided by a3, is

to a2. For in the series

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a1, a3. a2, a1, ao, a—1, a—a, a—3, a−4, etc., if any term be divided by another, the index of the quotient will be equal to the difference between the index of the diviend and that of the divisor.

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GENERAL RULE FOR DIVIDING POWERS.

A power may be divided by another power of the same root by subtracting the index of the divisor from that of the dividend, If the divisor and dividend have co-efficients, the co-efficient of the dividend must be divided by that of the div sor.

If the divisor and dividend are both compound quantities, the terms must be arranged, and the operation conducted in the șams manner, as in simple division of compound quantities.

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Thus yyyy. That is, yy

7. Divide an 8 by a.

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8. Divide

by 2a.

11.

12. a043

13.

12(6+y)

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[The above rule is equally applicable to reciprocal powers.]

ROOTS.

If we resolve b3, or bbb, into equal factors, viz. b, b and b, each of these equal factors is said to be a root of 63. So if we resolve 27 into is three equal factors, as 3 x 3 x 3, each of these equal factors is said to be a root of 27. And

factors, each of those factors is said to be a root of that

quantity.

A root of a quantity, then, is a factor, which multiplied into itself a certain number of times, will produce that quantity.

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