Third person imperatives are as common in Euclid as they are rare in the usual Greek texts, and that means very common indeed. We usually think of an imperative as giving an order or command, and this is true in the first and second persons, where you or I are ordering someone around. The third person imperative is quite different. It is a statement that something should exist, or an action should be taken. The subject is in the nominative case, and is the person or thing involved. The subject must be specified, unlike as in the second person, where it rarely is. First-person commands or exhortation are in the subjunctive. In English, the best we can do is say "let there be", which is more or less subjunctive, or appeal to the reader with "suppose there is" or "draw a ...". Euclid uses the third person imperative instead of all these circumlocutions that are necessary in English. The only other place where third person imperatives were commonly used was in the statements of laws and other legal writing.
For "let there be", Euclid uses e/)stw or e/)stwsan in the singular and plural, respectively. This is the present tense, active voice, indicative mood, which is appropriate for forms of "to be". Euclid says "epezeu/xqw AB" for "join AB" or "let AB be joined", which simply means that a straight line is drawn from point A to point B. This is aorist tense, passive voice, indicative mood. It is aorist because it is a single action, passive because line AB receives the action.
Be aware that every imperative has a subject in the nominative case, expressed or implied. When we say in English, 'join AB,' AB is the object of the verb join, not its subject. When Euclid says 'epezeu/xqw AB,' AB is the subject of the verb, as in 'let AB be joined.' Try to translate it without putting it in English if you can, to enjoy its conciseness. If you can't do this, express it in the second person. Otherwise, you will be led to clumsy expressions like 'Let AB have been joined, and then let AB be extended to K' instead of the elegant Greek. The best idea, of course, is to come to understand it directly without translation.
Imperatives found in Book I of Euclid are shown in the box on the right. The verb from which each is derived is shown, together with a hint of the meaning. The actual meanings will be clear when you encounter them in the text. As you can see, most are passive, but a few active imperatives also are there. Present, aorist and perfect tenses are all represented. In the present and perfect tenses, the ending is -sqw, and in the aorist tense, the most-used, simply -qw. Note that θ is a sign of the passive. The active imperatives have a τ instead. For the plural, Euclid adds -san to the singular. This plural ending is typical of the koinh/, and differs from that shown in many grammars, which are older forms of what was quite rare anyway. The aorist tense refers to a single action finished and complete, and is the most common in Euclid. The present tense refers to some current action, as a step in the course of a proof, while the perfect refers to some prior action that has established the conditions for a following one. Here, the presence or lack of a σ distinguishes perfect from aorist. Actually, the aorist is usually better characterized by augment of the verb stem (lengthening of the initial vowel), and the perfect by reduplication. There are, of course, both strong and weak aorists to contend with. In cases of uncertainty, look up the principal parts of the verb. The sixth principal part is the aorist passive.
How the imperative mood is formed in general is shown in the box at the left, with examples in the third person singular. The basic scheme is quite simple. Only three tenses are involved, the Present for continuing, habitual actions, the aorist for single, definite actions, and the Perfect for actions done and over, as a presupposition. The perfect imperative is very rare. The aorist is the most common. The tenses have no time significance. The tenses are distinguished by tense signs, which are in red in the box, while person, number and voice are given by the endings, in blue. Only the aorist distinguishes middle and passive. The variable vowel ο/ε is shown in red here. The perfect has no tense sign, just reduplication, and the aorist no augment. The endings for active and middle are shown in individual boxes for both persons and numbers. The aorist active uses -ον in the second person singular, while the present uses -σο, which in every case contracts with the ε to give -ου. These second-person forms are not used in Euclid, but it is nice to be able to recognize them anyway. There are slight changes, as usual, for -μι verbs, for contract verbs, and for stems ending in liquids or π, κ and τ that complicate the simple scheme, but the endings are still generally recognizable. Second (strong) aorists have the same endings as the present. They weaken the stem and do not use the σα as the first (weak) aorists do. Look out for this stem change when you see something that looks like a present imperative. The classical example is lei/pw, "leave", whose aorist is e/)lipon. The aorist imperative is lipe/tw (note that the augment is dropped), the present leipe/tw. The third person plural endings shown in the small boxes are those of Attic Greek, and are the ones usually found in grammars.
Remember that the active imperatives end in -tw in the singular, and -twsan in the plural. For example, e/)xetw means "let have", from e/)xw, "have". e/)xetw o( ku/klos ke/ntron A means "let the circle have a centre A", where there is both an object and a subject, in accusative and nominative, respectively. Present is used because the circle continuously has a centre. Having and being are like this. sune/statw is an aorist (ε in place of ι is the augment) identified by stem change, a special case like strong aorist. It means "let be put together (constructed)".
If something is not to be done, the negation is expressed by μη, not ου. In the aorist, the subjunctive is used, not the imperative, for negative commands. A negative command expresses the action as an idea only, not to be carried out. The present still uses the imperative, but be aware of the implication of continuous (lack) of action in this case.
Composed by J. B. Calvert
Created October 2000
Last revised 16 June 2002