Module 29

δείκνυμι and φημί

© 2021 Philip S. Peek, CC BY 4.0 https://doi.org/10.11647/OBP.0264.35

The Verb

In Greek and in English verbs have the same definitions and functions. Verbs are words that represent actions (throw) and states of being (be or exist). They differ in the same fundamental way that Greek nouns differ from their English counterparts: they use endings to create meaning in a way that English does not. The Greek verb (ῥῆμα) in its finite form has an ending that indicates what person and number the subject is. The Greek infinitive has an ending that indicates that it is unmarked for person and number.

The μι-Verbs δείκνυμι and φημί

Though not as numerous as ω-verbs, μι-verbs occur frequently. μι-verbs conjugate differently from ω-verbs in some tenses, typically the present, imperfect, aorist, and sometimes the perfect. In conjugating these verb forms, learn which stem to combine with which ending. The stem is the base of the word to which the ending is joined. Once you have the correct stem and ending, combine them to create the correct form. You may memorize the stems and endings or you may learn how to combine stems and endings so that you can recognize the forms as you encounter them.

Present and Imperfect Tense Stems

Use the long vowel grade stem for the singular (I, you, he, she, it) and the short vowel grade for the plural (we, you, they). Note that the stems differ even within the same tense, mood, and voice.

long vowel grade stem

short vowel grade stem

(use for the singular)

(use for the plural)

δεικνῡ-

δεικνυ-

φη-

φα-

Present and Imperfect Tense Endings

Add to the correct tense stem.

Primary Active

(use for the present)

S

Pl

1st

-μι

-μεν

2nd

-ς

-τε

3rd

-σι (ν)

-ᾱσι (ν)

Secondary Active

(use for the imperfect)

S

PL

1st

-ν

-μεν

2nd

-ς

-τε

3rd

---

-σαν

Infinitive Active

-ναι

Primary Middle and Passive

(use for the present)

S

Pl

1st

-μαι

-μεθα

2nd

-σαι

-σθε

3rd

-ται

-νται

Secondary Middle and Passive

(use for the imperfect)

S

Pl

1st

-μην

-μεθα

2nd

-σο

-σθε

3rd

-το

-ντο

Infinitive Middle and Passive

-σθαι

The Conjugation of δείκνυμι

The principal parts are these:

δείκνῡμι δείξω ἔδειξα δέδειχα δέδειγμαι ἐδείχθην

Remember that to conjugate correctly, you need to combine the correct stem with the correct endings.

Present Indicative Active of δείκνῡμι

Singular: long vowel grade, δεικνῡ-, + primary active endings. Plural: short vowel grade, δεικνυ-, + primary active endings.

Verb Form

English Equivalent

Person and Number

δείκνῡμι

I show

1st person singular

δείκνῡς

you show

2nd person singular

δείκνῡσι (ν)

he, she, it shows

3rd person singular

δείκνυμεν

we show

1st person plural

δείκνυτε

you show

2nd person plural

δεικνύᾱσι (ν)

they show

3rd person plural

Present Infinitive Active of δείκνῡμι

Short vowel grade of the stem, δεικνυ-, + -ναι.

δεικνύναι

to show

unmarked

  1. Note that infinitives with the ending -ναι are ALWAYS accented on the penult. Thus, its accent is persistent. Remember that final -αι and -οι count as short for purposes of accentuation except in the optative, a mood learned in Part II of the 21st-Century series.

Present Indicative Middle of δείκνῡμι

Short vowel grade of the stem, δεικνυ-, + primary middle and passive endings.

Verb Form

English Equivalent

Person and Number

δείκνυμαι

I set

1st person singular

δείκνυσαι

you set

2nd person singular

δείκνυται

he, she, it sets

3rd person singular

δεικνύμεθα

we set

1st person plural

δείκνυσθε

you set

2nd person plural

δείκνυνται

they set

3rd person plural

Present Infinitive Middle of δείκνῡμι

Short vowel grade of the stem, δεικνυ-, + -σθαι.

δείκνυσθαι

to set

unmarked for person & #

  1. Remember that final -αι and -οι count as short for purposes of accentuation except in the optative, a mood learned in Part II of the 21st-Century series.

Present Indicative Passive of δείκνῡμι

Short vowel grade of the stem, δεικνυ-, + primary middle and passive endings.

Verb Form

English Equivalent

Person and Number

δείκνυμαι

I am shown

1st person singular

δείκνυσαι

you are shown

2nd person singular

δείκνυται

he, she, it is shown

3rd person singular

δεικνύμεθα

we are shown

1st person plural

δείκνυσθε

you are shown

2nd person plural

δείκνυνται

they are shown

3rd person plural

Present Infinitive Passive of δείκνῡμι

Short vowel grade of the stem, δεικνυ-, + -σθαι.

δείκνυσθαι

to be shown

unmarked for person & #

  1. Remember that final -αι and -οι count as short for purposes of accentuation except in the optative, a mood learned in Part II of the 21st-Century series.

Imperfect Indicative Active of δείκνῡμι

Singular: long vowel grade, δεικνῡ-, + past indicative augment and secondary active endings. Plural: short vowel grade, δεικνυ-, + past indicative augment and secondary active endings.

Verb Form

English Equivalent

Person and #

ἐδείκνῡν

I was showing, used to show

1st singular

ἐδείκνῡς

you were showing, used to show

2nd singular

ἐδείκνῡ

he, she, it was showing, used to show

3rd singular

ἐδείκνυμεν

we were showing, used to show

1st plural

ἐδείκνυτε

you were showing, used to show

2nd plural

ἐδείκνυσαν

they were showing, used to show

3rd plural

Imperfect Indicative Middle of δείκνῡμι

Short vowel grade stem, δεικνυ-, + past indicative augment and secondary middle and passive endings.

Verb Form

English Equivalent

Person and #

ἐδεικνύμην

I was setting, used to set

1st singular

ἐδείκνυσο

you were setting, used to set

2nd singular

ἐδείκνυτο

he, she, it was setting, used to set

3rd singular

ἐδεικνύμεθα

we were setting, used to set

1st plural

ἐδείκνυσθε

you were setting, used to set

2nd plural

ἐδείκνυντο

they were setting, used to set

3rd plural

Imperfect Indicative Passive of δείκνῡμι

Short vowel grade stem, δεικνυ-, + past indicative augment and secondary middle and passive endings.

Verb Form

English Equivalent

Person and #

ἐδεικνύμην

I was being shown, used to be shown

1st singular

ἐδείκνυσο

you were being shown, used to be shown

2nd singular

ἐδείκνυτο

he, she, it was being shown, used to be shown

3rd singular

ἐδεικνύμεθα

we were being shown, used to be shown

1st plural

ἐδείκνυσθε

you were being shown, used to be shown

2nd plural

ἐδείκνυντο

they were being shown, used to be shown

3rd plural

The Conjugation of φημί

The principal parts are these:

φημί φήσω ἔφησα ------ ------ ------

φημί does not have a middle or a passive voice. It has active forms in the present, imperfect, future, and aorist. It uses μι-verb endings for the present and imperfect and ω-verb endings for the future and first aorist.

Remember that to conjugate correctly, you need to combine the correct stem with the correct endings.

Present Indicative Active of φημί

Singular: long vowel grade, φη-, + primary active endings. Plural: short vowel grade, φα-, + primary active endings.

Verb Form

English Equivalent

Person and Number

φημί

I say

1st person singular

φής, φῄς, φῇσθα

you say

2nd person singular

φησί (ν)

he, she, it says

3rd person singular

φαμέν

we say

1st person plural

φατέ

you say

2nd person plural

φᾱσί (ν)

they say

3rd person plural

Present Infinitive Active of φημί

Short vowel grade, φα-, + -ναι.

φάναι

to say

unmarked

  1. Note that infinitives with the ending -ναι are ALWAYS accented on the penult. Thus its accent is persistent. Remember that final -αι and -οι count as short for purposes of accentuation except in the optative, a mood learned in Part II of the 21st-Century series.

Imperfect Indicative Active of φημί

Singular: long vowel grade, φη-, + past indicative augment and secondary active endings. Plural: short vowel grade, φα-, + past indicative augment and secondary active endings.

Verb Form

English Equivalent

Person and Number

ἔφην

I was saying, used to say

1st person singular

ἔφης, ἔφησθα

you were saying, used to say

2nd person singular

ἔφη

he, she, it was saying, used to say

3rd person singular

ἔφαμεν

we were saying, used to say

1st person plural

ἔφατε

you were saying, used to say

2nd person plural

ἔφασαν

they were saying, used to say

3rd person plural

Practice Translating μι-Verbs. Translate the below sentences, adapted from a variety of ancient Greek writers. To come to an accurate understanding of the sentences, use your knowledge of endings and their functions. If you forget an ending or function, remember to use the Case and Function Chart in Appendix I and the Adjective, Adverb, Noun, and Pronoun Chart in Appendix VIII to assist you. After you finish translating each sentence, check your understanding with the answer in the Answer Key. After you have read through all of the sentences once, read them again at least two more times. In each subsequent reading your understanding improves.

  1. πόλεμος καὶ δυστυχία τὰς ὀργὰς τῶν βροτῶν τὰς αὐτὰς ταῖς συντυχίαις καθιστᾶσιν.
  2. γῆ μέλαινα πίνει· πίνει δένδρεα δαὖ γῆν· δἥλιος θάλατταν; τὸν δἥλιον σελήνη. φύσις καὶ τῶν ἀνθρώπων καὶ τῶν πάντων πίνειν. τί, ἑταῖροι, οὐ καλὸν καί μοι πίνειν (Anakreontic, anonymous poems written in the Anakreontic meter);
  3. ὅσῳ πέλας τὰ Μοίρας, μᾶλλον πρέπει τοῖς ἀνθρώποις τερπνὰ παίζειν· καὶ γὰρ Μοίρα ὡς τάχιστα τὰς τέρψεις τοῦ βίου δίδωσι καὶ λαμβάνει.
  4. Μοίρα δεσπότῃ ἔδωκε τὸ σῶμα Ζωσίμης, ψύχην ἀγαθῆς, καὶ νῦν θανάτῳ, πρὶν ἦν μόνῳ τῷ σώματι δούλη, καὶ τῷ σώματι εὗρεν ἐλευθερίην (Damaskios).
  5. παραὐτῷ Ζηνὶ πίμπλημι ἀμβροσίης ὅταν τὰ ὄμματα βλέπω ἧς ἐράω.
  6. ἐπεὶ ἀστέρας ἀναβλέπεις, Ἀστήρ, οὐρανός εἰμι καὶ πολλοῖς ὄμμασιν εἰς σὲ καταβλέπω.
  7. οὔτε γὰρ ἐλπίδἔχομεν γηράσαι οὔτε θανεῖν ὅτε ἐσμὲν ὑγιείας καλῆς· ἀλλὰ χρόνος βιότου θνητοῖς ὀλίγος.
  8. πῶς δὑγιείαν ἔδοτε αὐτοῖς, ὡς πάντες ὧν ψαύετε θνῄσκουσιν;
  9. αἰνίζειν μὲν ἄριστον· δὲ ψόγος ἔχθους ἀρχή· ἀλλὰ κακῶς εἰπεῖν Ἀττικὴν δίδωσί μοι τέρψιν.
  10. πάντα θεοῖς ἀνέθεσαν Ὅμηρός θἩσίοδός τε· κλέπτειν, μοιχεύειν τε καὶ ἀλλήλους ἀπατεύειν.

Adverbs and Verbs

αἰνίζω praise, approve

καταβλέπω look, look down

ἀναβλέπω look, look back

κλέπτω steal

ἀνατίθημι set up, establish, dedicate, offer

*λαμβάνω, λήψομαι, ἔλαβον take, receive; capture

ἀπατεύω deceive

*λέγω, λέξω or ἐρέω, ἔλεξα or εἶπον say, tell, speak

αὖ (adverb, postpositive) in turn, again

λύω (), λύσω, ἔλῡσα loose, free, destroy; (mid.) ransom

*ἄρχω, ἄρξω, ἦρξα rule, command; begin + gen.

μοιχεύω commit adultery; debauch

βλέπω, βλέψω, ἔβλεψα see, have the power of sight

νεύω, νεύσω, ἔνευσα nod

γηράσκω, γηράσομαι, ἐγήρᾱσα grow old, become old

παίζω, παίξομαι or παιξέομαι, ἔπαισα, play, sport, dance

*δίδωμι, δώσω, ἔδωκα give; allow ‘x’ in dat. or acc. + inf., ἐμὲ (έμοί) εὐτυχέειν δίδως you allow me to prosper

πειράω, πειράσω, ἐπείρασα, attempt, undertake; (mid. and pass) try, make an attempt; make trial of, test + gen.

*εἰμί, ἔσομαι be, be possible

πέλας nearby

ἐράω love; long for, desire + gen.

πίμπλημι fill, fill up; fill ‘x’ (a person or thing) in acc. with ‘y’ a thing in gen.; be full of + gen.

*εὑρίσκω, εὑρήσω, ηὗρον find out, discover

πίνω, πίομαι or πιέομαι, ἔπιον drink; drink of + gen.

*ἔχω, ἕξω or σχήσω, ἔσχον have, hold; be able + inf.; καλῶς ἔχειν to be well

πρέπω, πρέψω, ἔπρεψα be clearly seen, resemble, seem; be fitting; liken

*θνῄσκω, θανέομαι, ἔθανον die, perish

τάχιστα most quickly

*καθίστημι appoint, establish, put into a state; (intrans.) be established, be appointed

ψαύω, ψαύσω, ἔψαυσα touch + gen.

Adjectives, Nouns, Pronouns

*------, ἀλλήλων one another

*θεός, θεοῦ god, goddess, deity

*ἀγαθός, ἀγαθή, ἀγαθόν good, noble

θνητός, θνητή, θνητόν mortal

ἀμβροσία, ἀμβροσίας nectar of the gods

*καλός, καλή, καλόν beautiful, noble, good

*ἄνθρωπος, ἀνθρώπου human, person

μέλας, μέλαινα, μέλαν black, dark

ἄριστος, ἀρίστη, ἄριστον best, noblest

μοῖρα, μοίρας lot; portion; fate

*ἀρχή, ἀρχῆς rule, command; beginning; empire

*μόνος, μόνη, μόνον only, sole, alone, solitary; one

ἀστήρ, ἀστέρος star

Ὅμηρος, Ὁμήρου Homer

Ἀττικός, Ἀττική, Ἀττικόν Attic, Athenian

*ὀλίγος, ὀλίγα, ὀλίγον few

*βίος, βίου life

ὄμμα, ὄμματος τό eye

βίοτος, βιότου life

ὀργή, ὀργῆς impulse; passion, anger

βροτός, βροτοῦ mortal man; (adj.) mortal

*ὅσος, ὅση, ὅσον so many, as many as

*γῆ, γῆς land, earth

οὐρανός, οὐρανοῦ sky, heaven

δένδρεον = δένδρον, -ου τό (-ος, -ους (-εος) τό) tree

πέτρος, πέτρου rock

δεσπότης, δεσπότου master

*πόλεμος, πολέμου war

δούλη, δούλης slave

σελήνη, σελήνης moon

δυστυχία, δυστυχίας ill-luck, ill-fortune

στρατόπεδον, στρατοπέδου τό camp

ἐλευθερία, ἐλευθερίας freedom, liberty

συντυχία, συντυχίας incident; fortune

λπίς, ἐλπίδος hope, expectation

*σῶμα, σώματος τό body

ἑταῖρος, ἑταίρου comrade, companion

τερπνός, τερπνή, τερπνόν delightful, pleasant, agreeable, glad

χθος, ἔχθους (-εος) τό hate, hatred

τέρψις, τέρψεως pleasure, enjoyment τιμή, τιμῆς esteem, honor

Ζήν, Ζηνός Zeus

τιμή, τιμῆς esteem, honor

Ζωσίμη, Ζωσίμης Zosime

ὑγίεια, ὑγιείᾱς health, soundness

ἥλιος, ἡλίου sun

*φύσις, φύσιος (φύσηος, φύσεως) nature

Ἡσίοδος, Ἡσιόδου Hesiod, Greek poet c. 700 BCE

*χρόνος, χρόνου time

*θάλασσα (θάλαττα), θαλάσσης sea

ψόγος, ψόγου blame, flaw, censure

θάνατος, θανάτου death

*ψυχή, ψυχῆς life, soul, spirit

  1. The asterisk indicates the top 250 most frequently occurring vocabulary, which you are to memorize.

Practice Translating. Translate the sentences below, which have been adapted from Lucian’s The Lover of Lies (Φιλοψευδής). Remember the meanings and functions of the cases presented in Module 7. Use your memory to identify endings and their functions. If you forget an ending or a function, consult the Adjective, Adverb, Noun, and Pronoun Chart in Appendix VIII and the Case and Function Chart in Appendix I. Check your understanding with the translations in the Answer Key, making sure that you understand why each word translates as it does. Now go back and read each sentence two or three times, noticing with each rereading how much better your understanding of the sentence becomes. Make this a habit and you will improve quickly.

Εὐκράτης: κατ μικρὸν δὲ φιλοφρονούμενος οὐ πολὺ ἑταῖρος αὐτῷ καὶ συνήθης ἐγενόμην ὥστε πάντων ἐκοίνωσε μοι τῶν ἀπορρήτων. καὶ τέλος ἔπεισε με τοὺς μὲν οἰκέτας πάντας ἐν τῇ Μέμφιδι καταλιπεῖν, αὐτὸν δὲ μόνον ἀκολουθεῖν μεταὐτοῦ· μὴ γὰρ ἀπορήσειν ἡμᾶς ὅτι οἱ πολλοὶ ἡμῖν διακονήσονται. καὶ τὸ μετὰ τοῦτο οὕτω διήγομεν. ἐπεὶ ἤλθομεν εἴς τι καταγώγιον, ἔλαβεν ἀνὴρ τὸν μοχλὸν τῆς θύρας τὸ κόρηθρον καὶ τὸ ὕπερον καὶ τοῦτο περέβαλεν ἱματίοις. ἔπειτα ἐπιλέγει τινα ἐπῳδὴν καὶ τοῦτο ἐποίει βαδίζειν. δοκέει τοῖς ἄλλοις ἅπασιν ἄνθρωπος εἶναι. τὸ δὲ ἀπέρχεται ὕδωρ τε ἐμπίπλησι καὶ ἐσκεύαζε καὶ πάντα δεξιῶς ὑπηρέτεε καὶ διηκονέετο ἡμῖν. καὶ εἶτα ἐπεὶ ἅλις ἔχει τῆς διακονίας, δὲ Παγκράτης ἄλλην πῳδὴν ἐπιλέγων αὖθις κόρηθρον τ κόρηθρον ὕπερον τὸ ὕπερον ἐποίεε. τοῦτο ἐγὼ πάνυ ἐσπούδαζον κμανθάνειν παραὐτοῦ ἀλλὰ οὐκ εἶχον. ἐβάσκαινε γάρ, καίτοι πρὸς τὰ ἄλλα προχειρότατος ὤν. μιᾷ δέ ποτε ἡμέρᾳ λαθώνἐν σκοτεινῷ ὑφίστημιἐπήκουσα τῆς ἐπῳδῆς· ἦν δὲ τρισύλλαβος σχεδόν. καὶ μὲν ἐντέλλει τῷ ὑπέρῳ ταῦτα δεῖ ποιεῖν καὶ ᾤχετο εἰς τὴν ἀγοράν.

Adverbs and Verbs

ἀκολουθέω follow, accompany + dat.

ἐπακούω listen, hear, overhear

ἅλις sufficiently, enough

ἐπιλέγω say, utter, pronounce; pick out, choose; (mid.) think over, consider; read

ἀπέρχομαι, ἀπελεύσομαι, ἀπῆλθον depart, leave

*ἔρχομαι, ἐλεύσομαι, ἦλθον come, go

ἀπορέω, ἀπορήσομεν, ἠπόρησα be without means or resources; be at a loss, be in doubt; lack + gen.

*ἔχω, ἕξω or σχήσω, ἔσχον have, hold; be able + inf.; καλῶς ἔχειν to be well

αὖθις again, in turn, hereafter, in the future

καίτοι and indeed, and yet; though

βαδίζω, βαδιέω or βαδίσω, ἐβάδισα, walk, go

καταλείπω, -λείψω, -έλιπον leave behind

βασκαίνω slander, malign, bewitch; envy, grudge, keep to oneself

κοινόω, κοινώσω, ἐκοίνωσα communicate, impart; make common, share; (mid.) be partner, be sharer, be partaker + gen.

*γίγνομαι, γενήσομαι, ἐγενόμην be, be born

*λαμβάνω, λήψομαι, ἔλαβον take, receive; capture

*δεῖ, δεήσει it is necessary + dat. or acc. + inf.

οἴχομαι, οἰχήσομαι, ------ go, be gone, have gone

διάγω carry over; (intrans.) cross over; pass, spend; (intrans.) live

*πείθω, πείσω, ἔπεισα persuade, persuade ‘x’ in acc. + inf.; (mid. or pass.) listen to, obey + dat. or gen.

διακονέω, διακονήσω minister, serve, do service + dat.

περιβάλλω throw around

*δοκέω, δόξω, ́δοξα seem, think; seem best, think best + inf.

*ποιέω, ποιήσω, ἐποίησα do, make, cause; (mid.) consider

*εἰμί, ἔσομαι be, be possible

σκευάζω, σκευάσω, ἐσκεύασα prepare, make ready

εἶτα then, next, accordingly

σπουδάζω, σπουδάσω be serious, be earnest; be eager + inf.

ἐκμανθάνω learn, know, examine

σχεδόν near, roughly speaking, about, almost

ἐμπίμπλημι fill, fill up; fill ‘x’ (a person or thing) in acc. with ‘y’ a thing in gen.

ὑπηρετέω, ὑπηρετήσω serve as a rower; minister to, serve + dat.

ἐντέλλω order, enjoin, command

ὑφίστημι place under; put secretly in ambush; lie concealed

Adjectives, Nouns, Pronouns

ἀγορά, γορᾶς : agora, marketplace

Μέμφις, Μέμφιδος Memphis, an Egyptian city on the Nile river south of Cairo, the capital of Egypt c. 2700–2200

*ἄλλος, ἄλλη, ἄλλο another, other

*μικρός, μικρά, μικρόν small, little, short

*ἀνήρ, ἀνδρός man, husband

μοχλός, μοχλοῦ bar, lever, crowbar

*ἄνθρωπος, ἀνθρώπου human, person

οἰκέτης, οἰκέτου household slave

ἀπόρρητος, ἀπόρρητον forbidden, secret

Παγκράτης, Παγκράτου Pankrates

διακονία, διακονίας service

προχειρότατος, προχειροτάτη, προχειρότατον most at hand, ready

ἐπιλέγων, ἐπιλέγοντος speaking

σκοτεινός, σκοτεινή, σκοτεινόν dark

ἐπῳδή, ἐπῳδῆς enchantment, spell, charm

συνήθης, συνήθες living together; well-acquainted, intimate; accustomed, customary

ἑταῖρος, ἑταίρου comrade, companion

*τέλος, τέλους (-εος) τό: end, boundary; power; office; (acc.) finally

ἡμέρα, ἡμέρας day

τρισύλλαβος, τρισύλλαβον trisyllabic

θύρα, θύρας door

ὕδωρ, ὕδατος τό water

ἱμάτιον, ἱματίου τό cloak; piece of dress or cloth; (pl.) clothes

ὕπερον, ὑπέρου τό pestle

καταγώγιον, καταγωγίου τό lodging, inn, resting-place

φιλοφρονεόμενος, φιλοφρονεομένου treating or dealing with kindly + dat.

κόρηθρον, κορήθρου τό besom, broom

ὤν, ὄντος being

λαθών, λαθόντος secretly, by stealth

  1. The asterisk indicates the top 250 most frequently occurring vocabulary, which you are to memorize.

Practice Parsing Greek Sentences. Parse each word of the sentences found below. For nouns and pronouns, give their case and function. For verbs, give their person, number, tense, mood, and voice. For adverbs and conjunctions, identify them. For prepositional phrases, give the preposition and the preposition’s object. For adjectives, tell what noun they agree with in gender, number, and case.

ἓν δὲ βέλτιστον, ὃς κακὰ ἐμὲ ἐποίησε, τοῦτον δέννοις ἀντιδοῦναι κακοῖς.

ἔπειτα ἐπιλέγει τινα ἐπῳδὴν καὶ τοῦτο ἐποίεε βαδίζειν.

Check your answers with those in the Answer Key.

Eukleides (Euclid) of Alexandria (Εὐκλείδης c. 300 BCE). Born in Alexandria, Eukleides developed a conceptual system of geometry from a small set of axioms. His book, Elements, has been used to teach geometry up until 150 or so years ago. In Elements, Euclid discusses number theory, the connection between perfect numbers and Mersenne primes, the infinity of prime numbers, the uniqueness of prime factorization, and an algorithm for finding a common divisor of two numbers. Until recently Euclid’s geometry was the only geometry possible. As of the 19th century, mathematicans have discovered other geometries collectively referred to as non-Euclidean. Euclid and the non-Euclidean geometrical systems that followed are examples of discontinuities that created ways of knowing that were novel.

Herms and Phalloi

Fig. 4 Herm of Hermes from Pergamon. Copy of a herm attributed to the sculptor Alkamenes. Photograph by Kharmacher, 2020, Wikimedia, CC BY-SA, https://commons.wikimedia.org/wiki/File:20.12_Herme_Alkamenes.png

Fig. 5 A Roman gold phallic pendant, found in Essex. Photographed by Laura Pooley, Colchester Museums, 2006. The Portable Antiquities Scheme (PAS) is a voluntary programme run by the United Kingdom government to record the increasing numbers of small finds of archaeological interest found by members of the public. The scheme started in 1997 and now covers most of England and Wales. Finds are published at https://finds.org.uk. Wikimedia Commons, CC BY-SA, https://commons.wikimedia.org/wiki/File:A_Roman_gold_phallic_pendant_(FindID_144640-334389).jpg

Considered apotropaic (having the ability to ward off evil), the phallus appears on herms and as a pendant attached to chains and worn around the neck of children.

Module 29 Top 250 Vocabulary to be Memorized. Like learning the alphabet and endings, memorizing vocabulary is essential to acquiring language. The better you memorize the top 250 most frequently occurring vocabulary words the greater mastery of the language you will have.

Adjectives

ἑκάτερος, ἑκατέρᾱ, ἑκάτερον each

κοινός, κοινή, κοινόν shared, common; ἐκ τοῦ κοινοῦ shared in common; (n.) τὸ κοινόν the state

οἷος, οἵᾱ, οἷον such, such a kind; οἷός τέ εἰμι I am able, I am of such a kind to + inf.; οἷον or οἷα how, like, as, because

ὅλος, ὅλη, ὅλον whole, entire

Verbs

κρατέω, κρατήσω, ἐκράτησα, ------, ------, ἐκρατήθην be strong, powerful, rule + gen.

μανθάνω, μαθήσομαι, ἔμαθον, μεμάθηκα, ------, ------ learn; learn to, learn how to + inf.; understand

ὁμολογέω, ὁμολογήσω, ὡμολόγησα, ὡμολόγηκα, ὡμολόγημαι, ὡμολογήθην speak together; agree; admit

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