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21 определение
definition, determination, examination, identification, computation• (Нам) необходимы более точные определения, потому что... - More exact definitions are necessary because...• Вспомним некоторые определения. - Let us recall some definitions.• Давайте начнем с более тщательного определения того, что мы понимаем под... - Let us begin by defining more carefully what we mean by...• Дадим теперь более точное определение. - A more precise definition is as follows.• Данное определение применимо даже тогда, когда... - This definition is applicable even when...• Для наших целей подходит следующее достаточно грубое определение. - For our purposes the following rather rough definition is adequate.• Из определения очевидно, что... - It is evident from the definition that...• Из определения понятно, что It is plain from the definition that...• Из этих определений видно/понятно, что - It is clear from these definitions that...• Используя определения F и G, легко показать, что... - It is a simple matter, using the definitions of F and G, to show that...• Мы можем дать альтернативное определение... - It is possible to give an alternative definition of...• Мы можем дать неформальное определение, сказав, что... - We can express the definition informally by saying that...• Нам необходим критерий для определения, действительно ли... - We need a criterion for determining whether...• Нам необходимо одно определение. (= Мы нуждаемся в одном определении. ) - We need a definition.• Не существует систематического способа определения... - There is no systematic way of determining...• Однако, строго говоря, такое определение является бессмысленным, поскольку... - Strictly speaking, however, such a definition is meaningless because...• Определение констант будет дано в Приложении. - The determination of the constants will be given in Appendix.• Отметим отличие в определениях... и... - Let us contrast the definitions of... and...• Очень трудно, если вообще возможно, дать удовлетворительное определение... - It is difficult if not impossible to give a satisfactory definition of...• Перед тем как продолжить (изучение и т. п.), нам необходимо ввести еще одно определение. - We need one more definition before proceeding with...• Предыдущие определения являются прямыми обобщениями... - The above definitions are straightforward generalizations of...• С другой стороны, из определения F следует, что... - On the other hand, it follows from the definition of F that...• Следующая теорема показывает, как можно сделать это определение строгим. - The following theorem shows how this notion can be made precise.• Следующие примеры покажут важность данного определения. - Examples will bring out the significance of this definition.• Сначала нам необходимы несколько дополнительных определений. - A few more definitions are required first.• Существенный интерес представляет задача определения... - It is a problem of considerable interest to determine...• Существует простая геометрическая интерпретация этого определения. - There is a simple geometrical interpretation of this definition.• Существуют различные способы определения... - There are various ways of defining...• Теперь мы выведем простое правило для определения... - We now derive a simple rule for determining...• Теперь мы готовы ввести основное определение. - We are now ready for a basic definition.• Теперь мы собрали воедино основные определения и результаты (теории и т. п.)... - - We have now assembled the main definitions and results of...• Ценность этого определения, безусловно, заключается в его полезности. - The merit of this definition lies, of course, in its usefulness.• Это вытекает непосредственно из определения оператора D/Dt. - This follows at once from the meaning of the operator D/Dt.• Это завершает определение (= нахождение)... - This completes the determination of...• Это не особо полезное определение, так как... - This is not a particularly useful definition, since...• Это прямое следствие определения. - It is an immediate consequence of the definition.• Это обычные (= стандартные) определения для... - These are the usual definitions for...• Это определение не влечет за собой, что... - This definition does not imply that...• Это определение неудовлетворительно по нескольким причинам. - This definition is unsatisfactory for several reasons.• Это определение основано на следующих соображениях. - This definition is based on the following considerations.• Это полезное определение, поскольку... - This is a useful definition because...• Это придает смысл определению (= введению)... - This gives a means of defining...• Этот подход доказал свою полезность в определении ранних стадий... - This approach has proven useful in identifying the early stages of... -
22 принцип
principle, mode, consideration, concept, precept• Базовый принцип этого состоит в том, что... - The underlying idea is that...• В дальнейшем следует помнить этот важный принцип. - This is an important principle to be kept in mind as we proceed.• В принципе это подобно (че. иу-л). - This is similar in principle to...• В принципе, могло бы быть полезным... - In principle it may be advantageous to...• Важное применение данных принципов обнаруживается в... - An important application of these principles is to be found in...• Данный подход нарушает основной принцип... - This approach violates the basic principle of...• Данный принцип легко обобщается на... - The principle is readily extended to...• Данный принцип утверждает, что... - This principle states that...• Другой важный пример этого принципа встречается, когда... - Another important example of this principle occurs when...• Использующийся здесь принцип состоит в том, что... - The principle used here is...• Исходя из этого (общего) принципа... - With this (general) principle in mind...• Легко сформулировать весьма ясный общий принцип. - The general principle is quite clear and easy to state.• Метод основывается на принципе, что... - This method is based on the principle that...• Одно приложение данного принципа является особенно важным. - One application of this principle is especially important.• Оказывается, что эти же самые общие принципы применяются независимо от того, действительно ли... - It appears that these same general principles apply regardless of whether...• Отметим, что основные черты данного принципа состоят в... - The principal features to note are...• По крайней мере в принципе это позволяет нам (сказать и т. п.)... - At least in principle, this enables us to...• Подобные принципы доказали свою полезность при проектировании... - Similar principles prove helpful in the design of...• Полностью оценить смысл данного принципа можно лишь после того, как у нас имеется... - The full meaning of this principle can be appreciated only after we have...• Поучительно проверить этот результат, начиная с изначальных принципов. - It is instructive to verify this result from first principles.• Предыдущее описание просто иллюстрирует принцип... - The above description merely illustrates the principle of...• Предыдущие примеры иллюстрируют общий принцип, что... - The preceding examples illustrate the general fact that...• Применяя принцип виртуальных работ, мы... - By applying the principle of virtual work we...• Таким образом, в принципе необходимо только... - Thus, in principle at least, it is only necessary to...• Те же самые общие принципы выполняются, когда... - The same general principles hold when...• Теперь мы рассмотрим несколько фундаментальных принципов... - We now turn to several fundamental principles...• Тот же самый принцип применяется, когда... - The same principle applies when...• Третий пример иллюстрирует основной принцип, что... - Example 3 illustrates the general principle that...• Этот принцип был применен при производстве... - This principle has been applied to the manufacture of... -
23 рассмотрение
treatment, consideration, analysis, examination• Вдобавок, имеется одна фундаментальная причина для рассмотрения... - There is, in fact, one basic reason for considering...• Другим способом рассмотрения данной проблемы является следующий. - Another way of regarding this problem is as follows.• Другой предмет, напрашивающийся для рассмотрения, состоит в том, что... - Another subject that calls for consideration is that of...• Здесь мы представляем для рассмотрения две таких схемы. - Here we present two such schemes for consideration.• Из внимательного рассмотрения... видно, что... - Close inspection of... shows that...• Мы завершаем... рассмотрением частного класса (чего-л). - We conclude by considering a particular class of...• Мы заключим наше рассмотрение кратким обсуждением... - We conclude with a brief look at...• Мы начинаем с рассмотрения трех конкретных примеров. - We begin by looking at three concrete examples.• Мы начнем с рассмотрения... - We shall begin with consideration of...; Let us begin by considering...• Мы не будем входить в рассмотрение этого сложного вопроса. -We shall not enter into this complicated question.• Мы также исключим из рассмотрения два класса... - We also exclude from consideration two classes of...• Нашей целью не является развернутое рассмотрение (теории и т. п.)... - It is not our purpose to give an extensive treatment of...• Не вдаваясь в строгие рассмотрения, обсудим вкратце... - Without giving a rigorous treatment we briefly discuss...• Обсуждение начнется с рассмотрения простейшего типа... - The discussion will be initiated by considering the simplest type of...• Особое рассмотрение должно быть дано... - Special consideration must be given to...• Относительно более исчерпывающего рассмотрения... читатель отсылается к... - For a more exhaustive treatment, the reader is referred to...• Перед тем как вернуться к рассмотрению этих проблем, нам необходимо (изучить и т. п.)... - Before returning to these matters, it is necessary to...• Предварительное рассмотрение данного предмета было бы неполным без... - A preview of this subject would be incomplete without...• Представленное здесь рассмотрение было чисто формальным. - The treatment given here has been purely formal.• При более тщательном рассмотрении выясняется, что данная теория... - On closer examination this theory is noted to be...• Рассмотрение ведется на поверхностном уровне. - The treatment is at a superficial level.• Решение подобной проблемы легко выводится из рассмотрения... - The solution to such a problem is readily deduced by considering...• Случай... требует специального рассмотрения. - The case of... requires special consideration.• Строгое рассмотрение задачи показывает, что... - A rigorous treatment of the problem shows that...• Существо данного рассмотрения заключается в том, что... - The essence of the matter is that...• Эти данные нуждаются в дальнейшем рассмотрении. - The data need further consideration.• Это приводит к рассмотрению темы... - This leads into the topic of...• Этот результат заслуживает более пристального рассмотрения. - This result is worth a more careful look. -
24 свойство
property, character, feature, behavior, quality• Будет обнаружено, что это свойство присуще (и)... - It will be found that this property is shared by...• В данном параграфе мы обсуждаем некоторые простые свойства и примеры (чего-л). - In this section we discuss some simple properties and examples of...• В следующей теореме мы устанавливаем дополнительные свойства... - In the next theorem we obtain further properties of...• В соответствии со свойствами... возникают четыре разных случая. - Four distinct cases arise according to the nature of...• В таблице 2 сведены воедино свойства (чего-л). - Table 2 summarizes the properties of...• В этом параграфе мы подведем итог относительно некоторых свойств (чего-л). - We summarize in this section some of the properties of...• Все действительные числа обладают следующими свойствами... - All real numbers have the following properties:...• Выясняется одно замечательное свойство... - A remarkable feature emerges:...• Данное свойство является основой одного метода нахождения... - This property provides one method of determining...• Затем вы выводим некоторые из элементарных свойств... - We next derive some of the elementary properties of...• Материал не меняет своих свойств в широком температурном диапазоне. - The material retains its properties over a wide temperature range.• Мы будем изучать свойства... - We shall study the properties of...• Мы выведем теперь некоторые элементарные свойства... - We shall now obtain some elementary properties of...• Мы можем использовать эти же свойства, чтобы определить... - We can use these same properties to define...• Мы начинаем с того, что установим свойства... - We begin by establishing the properties of...• Мы обсудим асимптотические свойства... - We will discuss the asymptotic properties of...• Мы уже вывели некоторые свойства (чего-л). - We have deduced some of the properties of...• Наиболее точной формулировкой этих свойств является следующая. - The most concise statement of these properties is as follows.• Но сначала мы установим некоторые фундаментальные свойства (оператора и т. п.). - But let us first establish some fundamental properties of...• Новое свойство возникает, когда мы рассматриваем... - A new feature appears when we consider...• Огромный интерес вызывают свойства этого нового материала. - Great interest is focused on the properties of this new material....• Одним интересным свойством этих результатов является то, что они указывают... - One interesting feature of these results is that they indicate...• Относительно соотношения (12) заметим, что его интересным свойством является, что... - The interesting feature to notice about (12) is that...• Подытожим наиболее важные свойства... - We summarize the most important properties of...• При выводе большинства этих свойств отправной точкой служит наблюдение, что... - In establishing most of these properties the starting point is the observation that...• Рассмотрим два свойства... - Let us consider two properties of...• Результат, представленный формулой (9), очень полезен при выводе свойств (чего-л). - The result (9) is very useful for deducing properties of...• Следующая теорема обобщает хорошо известное свойство... - The following theorem generalizes a well-known property of...• Следующие свойства (чего-л) совершенно очевидны... - The following properties are immediately evident:...• Смит [1] сообщает, что это свойство могло бы иметь полезные практические приложения, что и показывается ниже. - Smith [1] suggests that this property may have a useful practical application as follows.• Таким образом, важно узнать основные свойства... - Thus, it is important to understand the basic properties of...• Теперь мы можем найти некоторые дополнительные свойства... - We are now in a position to determine some further properties of...• Топология имеет дело со свойствами... - Topology deals with the properties of...• Частицы с конечной массой не обладают этим свойством. - This property is not shared by particles with a finite mass.• Читатель поймет, что данные свойства прямо связаны с... - The reader will realize that these properties are directly connected with...• Эти свойства, безусловно, могут применяться в... - These properties can of course be applied to...• Это подходящее место, чтобы обсудить некоторые свойства, связанные с... - This is a good place to review a number of properties connected with...• Это приводит нас к важному свойству... - This leads us to an important property of...• Это свойство известно под названием... - This property is known as...• Это свойство может быть использовано, чтобы вывести... - This property can be used to derive...• Это свойство особенно полезно, когда... - This feature is particularly useful when...• Это свойство позволяет найти... - This property enables one to find...• Это свойство является почти очевидным как следствие того факта, что... - This property is almost evident from the fact that...• Это свойство является следствием следующей теоремы. - This property is a consequence of the following theorem. -
25 факт
(см. также данные, результат, вариант, версия, случай) fact, case, one point• Благодаря этому факту усиленно напрашивается, что... - This fact strongly suggests that...• В свете всех этих фактов становится естественным (вычислить и т. п.)... - In view of all these facts it becomes natural to...• В связи с тем фактом, что..., очевидно, что это невозможно. - This is obviously impossible in light of the fact that...• В этом параграфе мы устанавливаем основные факты относительно... - In this section we establish the basic facts about...• Важность этого факта станет понятна после того, как мы обсудим... - The importance of this fact will become clear when we discuss...• Внимание читателя привлекается к тому факту, что... - The reader's attention is drawn to the fact that...• Вряд ли необходимо еще подчеркивать тот факт, что... - It is hardly necessary to stress the fact that...• Данная теория также объясняет тот факт, что... - This theory also explains the fact that...• Данное утверждение интуитивно очевидно, если исходить из факта, что... - The proposition is intuitively obvious from the fact that...• Данный подход должен быть изменен так, чтобы он учитывал факт, что... - The approach must be modified to accommodate the fact that...• Добавьте к этому тот факт, что... - Add to this the fact that...• Его принципиальная важность заключается в том факте, что... - Its principal importance lies ultimately in the fact that...• Задача усложняется тем фактом, что... - The problem is complicated by the fact that...• Замечательным фактом является то, что... - It is a remarkable fact that...• Замечательным фактом является, что... - It is a remarkable fact that...• Здесь принимается во внимание тот факт, что... - This takes account of the fact that...• Зная этот набор фактов, мы понимаем, что... - With this framework before us, we realize that...• Из этого факта, совместно с (1), вытекает, что... - This fact, taken together with (1), implies that...• Интересным и полезным фактом является то, что... - The interesting and useful fact is that...• Исключительным фактом является то, что... - It is an extraordinary fact that...• Мы используем этот факт в дальнейшем. - We shall make use of this fact later.• Мы можем использовать преимущество, предоставляемое этим фактом, чтобы... - We can take advantage of this fact to...• Мы можем объяснить этот факт тем, что... - We can explain this fact by...• Мы привлекаем внимание к факту, что... - We call attention to the fact that...• Мы примем этот важный факт без доказательства. - We shall accept this important fact without proof.• На некоторое время мы пренебрегаем тем фактом, что... - We neglect, for the time being, the fact that...• На этом этапе мы хотим привлечь внимание к тому факту, что... - At this point, we wish to call attention to the fact that...• На этом этапе необходимо указать очень важный факт. - At this stage a very important fact must be pointed out.• Наиболее важным является тот факт, что... - Most important is the fact that...• Нам всем (хорошо) известен тот факт, что... - We are all familiar with the fact that...• Некоторые из этих проблем возникают из того факта, что... - Some of the problems arise from the fact that...• Немедленным следствием предыдущего результата является тот факт, что... - An immediate corollary of the above result is the fact that...• Необходимо заметить, что в той же мере важным является тот факт, что... - But equally important, one should notice, is the fact that...• Неожиданным фактом является то, что... - An unexpected fact is that...• Однако имеет смысл использовать факт, что... - But the sensible thing is to use the fact that...• Однако при вычислении величины W мы должны принять во внимание тот факт, что... - In computing W, however, we must take into account the fact that...• Очевидно, что этот ответ обязан быть следствием факта, что... - The answer must obviously be sought in the fact that...• Подтверждение такой точки зрения вытекает из того факта, что... - Confirmation of this view is found in the fact that...• Позднее нам будут необходимы несколько фактов относительно... - Later on we shall need certain facts about...• Полезно помнить следующий факт:... - A useful result to remember is that...• Поразительным фактом является то, что... - A striking fact is that...• Предыдущие примеры иллюстрируют общий факт, что... - The preceding examples illustrate the general fact that...• Причиной этого является факт, что... - The reason for this lies in the fact that...• Простейшим объяснением всех этих фактов является... - The simplest explanation for these facts is...• Рассмотрим некоторые важные факты относительно... - Let us review some important facts regarding...• Следует уделить внимание тому факту, что... - Attention should be paid to the fact that...• Таким образом, мы возвращаемся к факту, что... - We thus recover the fact that...• Твердо установленным фактом является, что... - It is a well-established result that...• Тот факт, что..., ничего не говорит о... - The fact that... says nothing about...• Тривиальным фактом здесь является... - It is a trivial observation that...• Тщательное сравнение затрудняется тем фактом, что... - Careful comparison is somewhat hampered by the fact that...• Учитывая эти факты, мы можем... - Taking these facts into account, we can...• Фактом чрезвычайной важности является то, что... - This is a fact of tremendous importance to...• Фундаментальным фактом является то, что каждый... - It is a fundamental fact that every...• Чтобы сделать это, мы используем тот факт, что... - То do this, we make use of the fact that...• Чтобы учесть данный факт, Максвелл предположил, что... - То account for this fact, Maxwell supposed that...• Экспериментально обнаружено, что... - It is found, as an experimental fact, that...• Эти важные факты можно подытожить следующим образом. - The relevant facts may be summarized as follows.• Эти факты могут быть объяснены, если... - These facts can be explained if...• Эти факты позволяют нам... - These facts allow us to...• Это выливается в не что иное как простое переформулирование факта, что... - This amounts to no more than a restatement of the fact that...• Это иллюстрирует тот факт, что... - This illustrates the fact that...• Это могло бы показаться довольно неопределенным в свете того факта, что... - This may seem rather pointless in light of the fact that...• Это могло бы показаться парадоксальным в свете факта, что... - This may appear to be paradoxical in view of the fact that...• Это необходимое следствие того факта, что... - This is a necessary consequence of the fact that...• Это очевидным образом вытекает из того факта, что... - This is clearly borne out by the fact that...• Это предположение игнорирует тот факт, что... - The assumption ignores the fact that...• Это происходит вследствие того факта, что... - This arises from the fact that...• Это просто другой способ выражения того факта, что... - This is just another way of expressing the fact that...• Это просто последствие того факта, что... - This is simply a consequence of the fact that...• Это связано с тем фактом, что... - This is connected with the fact that...• Это следует из нашего обсуждения соотношения (4), а также из того факта, что... - This follows from our discussion of (4) and the fact that...• Это совершенно очевидно следует из того факта, что... - This is at once obvious from the fact that...• Это соответствует тому факту, что... - This corresponds to the fact that...• Это справедливо, несмотря на тот факт, что... - This is so despite the fact that...• Этот пример иллюстрирует основной факт, что... - This example illustrates the general fact that...• Этот результат более или менее ожидаем, если исходить из факта, что... - This result is more or less to be expected from the fact that...• Этот результат было необходимо ожидать, исходя из факта, что... - This result was to be expected from the fact that...• Этот результат согласуется с тем фактом, что... - This result is in agreement with the fact that...• Этот факт был отмечен без доказательства в главе 4. - This fact was noted without proof in Chapter 4.• Является интересным тот факт, что... - It is an interesting fact that... -
26 основной
Основной - basic, major, principal, fundamental, underlying, key, primary, mainWhether in recognition of this or for less incisive reasons, no distinctions is often made between the tip coefficient and that for the principal surface.This criterion of permitting inspection of the primary-flow measuring device is fundamental to an acceptance test with no measuring tolerance (... является основным для приемочного испытания...).These many examples show that one underlying mechanism persists.—обращать основное внимание на—основное внимание обращается на—основное внимание при измерениях было сосредоточено на—основной упор в работе сделан на—останавливаться в основном наРусско-английский научно-технический словарь переводчика > основной
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27 hollandaise sauce
This is the most basic of the egg and oil emulsified sauces. The only flavoring is fresh lemon juice. This sauce must be kept warm, as excessive heat will cause it to break. Because this is kept warm, it is not safe to keep it for long periods of time and should never be reused from another meal period.HomogenizeTo create an emulsion by reducing all the particles to the same size. The fat globules are broken down mechanically by heating them quickly and then forcing them under extreme pressure through tiny holes of equal size until they are evenly distributed throughout the liquid. Homogenized milk and some commercial salad dressings are two examples of homogenized foods. Horn of Plenty ( A Mushroom)- This is a wild mushroom with a hollow, funnel- shaped cap and is dark grey or black in color. Because of this, it also has the name " etrumpet de deathe ".This particular mushroom is somewhat stringy, but has a robust flavor and may be used to flavor sauces, soups, or any other mushroom preparation. -
28 ἀπό
ἀπό (Hom.+) prep. w. gen. (see the lit. on ἀνά, beg., also for ἀπό: KDieterich, IndogF 24, 1909, 93–158; LfgrE s.v.). Basic sense ‘separation from’ someone or someth., fr. which the other uses have developed. In the NT it has encroached on the domain of Att. ἐκ, ὑπό, παρά, and the gen. of separation; s. Mlt. 102; 246; Mlt-Turner 258f.① a marker to indicate separation from a place, whether person or thing, from, away fromⓐ w. all verbs denoting motion, esp. those compounded w. ἀπό: ἀπάγεσθαι, ἀπαλλάσσεσθαι, ἀπελαύνειν, ἀπέρχεσθαι, ἀπολύεσθαι, ἀποπλανᾶσθαι, ἀποστέλλειν, ἀποφεύγειν, ἀποχωρεῖν, ἀποχωρίζεσθαι; but also w. ἀνίστασθαι, διαστῆναι, διέρχεσθαι, ἐκδημεῖν, ἐκκινεῖν, ἐκπλεῖν, ἐκπορεύεσθαι, ἐξέρχεσθαι, ἐξωθεῖν, ἐπιδιδόναι, μεταβαίνειν, μετατίθεσθαι, νοσφίζειν, παραγίνεσθαι, πλανᾶσθαι, πορεύεσθαι, ὑπάγειν, ὑποστρέφειν, φεύγειν; s. the entries in question.ⓑ w. all verbs expressing the idea of separation ἐκβάλλειν τὸ κάρφος ἀ. τοῦ ὀφθαλμοῦ remove the splinter fr. the eye Mt 7:4 v.l. (for ἐκ). ἐξέβαλον ἀπὸ τῆς πήρας αὐτῶν δῶρα they set forth gifts out of their travel bags GJs 21:3. ἀπολύεσθαι ἀ. ἀνδρός be divorced fr. her husband Lk 16:18, cp. Ac 15:33. ἀποκυλίειν, ἀπολαμβάνεσθαι, ἀποστρέφειν, ἐπιστρέφεσθαι, ἐπανάγειν, αἴρειν, ἀφαιρεῖν, ἀπολέσθαι, μερίζειν et al., s. the pertinent entries. So also κενὸς ἀ. τινος Hs 9, 19, 2. ἔρημος ἀ. τινος (Jer 51:2) 2 Cl 2:3. W. verbs which express the concept of separation in the wider sense, like loose, free, acquit et al. ἀπορφανίζειν, ἀποσπᾶν, διεγείρεσθαι, δικαιοῦν, ἐκδικοῦν, ἐλευθεροῦν, λούειν, λύειν, λυτροῦν, ῥαντίζειν, σαλεύειν, στέλλειν, σῴζειν, φθείρειν, s. the entries; hence also ἀθῷος (Sus 46 Theod. v.l.) Mt 27:24. καθαρὸς ἀ. τινος (Tob 3:14; but s. Dssm. NB 24 [BS 196; 216]) Ac 20:26; cp. Kuhring 54.ⓒ verbs meaning be on guard, be ashamed, etc., take ἀπό to express the occasion or object of their caution, shame, or fear; so αἰσχύνεσθαι, βλέπειν, μετανοεῖν, προσέχειν, φοβεῖσθαι, φυλάσσειν, φυλάσσεσθαι; s. 5 below.ⓓ w. verbs of concealing, hiding, hindering, the pers. from whom someth. is concealed is found w. ἀπό; so κρύπτειν τι ἀπό τινος, παρακαλύπτειν τι ἀπό τινος, κωλύειν τι ἀπό τινος; s. the entries.ⓔ in pregnant constr. like ἀνάθεμα εἶναι ἀ. τοῦ Χριστοῦ be separated fr. Christ by a curse Ro 9:3. μετανοεῖν ἀ. τ. κακίας (Jer 8:6) Ac 8:22. ἀποθνῄσκειν ἀ. τινος through death become free from Col 2:20. φθείρεσθαι ἀ. τ. ἁπλότητος be ruinously diverted from wholehearted commitment 2 Cor 11:3. Cp. Hs 6, 2, 4.ⓕ as a substitute for the partitive gen. (Hdt. 6, 27, 2; Thu. 7, 87, 6; PPetr III, 11, 20; PIand 8, 6; Kuhring 20; Rossberg 22; Johannessohn, Präp. 17) τίνα ἀ. τῶν δύο; Mt 27:21, cp. Lk 9:38; 19:39 (like PTebt 299, 13; 1 Macc 1:13; 3:24; Sir 6:6; 46:8). τὰ ἀ. τοῦ πλοίου pieces of the ship Ac 27:44. ἐκχεῶ ἀ. τοῦ πνεύματός μου Ac 2:17f (Jo 3:1f). λαμβάνειν ἀ. τ. καρπῶν get a share of the vintage Mk 12:2 (cp. Just., A I, 65, 5 μεταλαβεῖν ἀπὸ τοῦ … ἄρτου).—Of foods (as in Da 1:13, 4:33a; 2 Macc 7:1) ἐσθίειν ἀ. τ. ψιχίων eat some of the crumbs Mt 15:27; Mk 7:28. χορτάζεσθαι ἀ. τινος eat one’s fill of someth. Lk 16:21. αἴρειν ἀ. τῶν ἰχθύων pick up the remnants of the fish Mk 6:43. ἐνέγκατε ἀ. τ. ὀψαρίων bring some of the fish J 21:10 (the only instance of this usage in J; s. M-EBoismard, Le chapitre 21 de Saint Jean: RB 54 [’47] 492).—Of drink (cp. Sir 26:12) πίνειν ἀπὸ τ. γενήματος τῆς ἀμπέλου drink the product of the vine Lk 22:18.② to indicate the point from which someth. begins, whether lit. or fig.ⓐ of place from, out from (Just., D. 86, 1 ἀπὸ τῆς πέτρας ὕδωρ ἀναβλύσαν ‘gushing out of the rock’) σημεῖον ἀ. τ. οὐρανοῦ a sign fr. heaven Mk 8:11. ἀ. πόλεως εἰς πόλιν from one city to another Mt 23:34. ἀπʼ ἄκρων οὐρανῶν ἕως ἄκρων αὐτῶν (Dt 30:4; Ps 18:7) from one end of heaven to the other 24:31, cp. Mk 13:27. ἀπʼ ἄνωθεν ἕως κάτω from top to bottom Mt 27:51. ἀρξάμενοι ἀ. Ἰερουσαλήμ beginning in Jerusalem Lk 24:47 (s. also Lk 23:5; Ac 1:22; 10:37). ἀφʼ ὑμῶν ἐξήχηται ὁ λόγος τ. κυρίου the word of the Lord has gone out from you and sounded forth 1 Th 1:8. ἀπὸ βορρᾶ, ἀπὸ νότου in the north, in the south (PCairGoodsp 6, 5 [129 B.C.] ἐν τῷ ἀπὸ νότου πεδίῳ; Mitt-Wilck. I/2, 11A col. 1, 12f [123 B.C.] τὸ ἀπὸ νότου τῆς πόλεως χῶμα; ln. 7 ἀπὸ βορρᾶ τῆς πόλεως; 70, 16 al.; Josh 18:5; 19:34; 1 Km 14:5) Rv 21:13.ⓑ of time from … (on), since (POxy 523, 4; Mel., HE 4, 26, 8; s. Kuhring 54ff).α. ἀ. τῶν ἡμερῶν Ἰωάννου from the days of John Mt 11:12. ἀ. τῆς ὥρας ἐκείνης 9:22. ἀπʼ ἐκείνης τ. ἡμέρας (Jos., Bell. 4, 318, Ant. 7, 382) Mt 22:46; J 11:53. ἔτη ἑπτὰ ἀ. τῆς παρθενίας αὐτῆς for seven years fr. the time she was a virgin Lk 2:36. ἀ. ἐτῶν δώδεκα for 12 years 8:43. ἀ. τρίτης ὥρας τῆς νυκτός Ac 23:23. ἀ. κτίσεως κόσμου Ro 1:20. ἀ. πέρυσι since last year, a year ago 2 Cor 8:10; 9:2.—ἀπʼ αἰῶνος, ἀπʼ ἀρχῆς, ἀπʼ ἄρτι (also ἀπαρτί and ἄρτι), ἀπὸ καταβολῆς κόσμου, ἀπὸ τότε, ἀπὸ τοῦ νῦν; s. the pertinent entries.β. w. the limits defined, forward and backward: ἀπὸ … ἕως (Jos., Ant. 6, 364) Mt 27:45. ἀπὸ … ἄχρι Phil 1:5. ἀπὸ … μέχρι Ac 10:30; Ro 5:14; 15:19.γ. ἀφʼ ἧς (sc. ὥρας or ἡμέρας, which is found Col 1:6, 9; but ἀφʼ ἧς became a fixed formula: ParJer 7:28; Plut., Pelop. [285] 15, 5; s. B-D-F §241, 2) since Lk 7:45 (Renehan ’75, 36f); Ac 24:11; 2 Pt 3:4 (cp. X., Hell. 4, 6, 6; 1 Macc 1:11). ἀφʼ οὗ (sc.—as in X., Cyr. 1, 2, 13—χρόνου; Att. ins in Meisterhans.3-Schw. and s. Witkowski, index 163; ἀφʼ οὗ is also a formula) since, when once (X., Symp. 4, 62; Demetr.: 722 Fgm. 1, 16 Jac.; Lucian, Dial. Mar. 15, 1; Ex 5:23 GrBar 3:6) Lk 13:25; 24:21; Rv 16:18 (cp. Da 12:1; 1 Macc 9:29; 16:24; 2 Macc 1:7; TestAbr B 13 p. 117, 23; GrBar; Jos., Ant. 4, 78). τρία ἔτη ἀφʼ οὗ (cp. Tob 5:35 S) Lk 13:7. ἀφότε s. ὅτε 1aγ end.ⓒ the beg. of a series from … (on).α. ἀρξάμενος ἀ. Μωϋσέως καὶ ἀ. πάντων τ. προφητῶν beginning w. Moses and all the prophets Lk 24:27. ἕβδομος ἀ. Ἀδάμ Jd 14 (Diod S 1, 50, 3 ὄγδοος ὁ ἀπὸ τοῦ πατρός [ancestor]; Appian, Mithrid. 9 §29 τὸν ἕκτον ἀπὸ τοῦ πρώτου Μιθριδάτην; Arrian, Anab. 7, 12, 4; Diog. L. 3, 1: Plato in the line of descent was ἕκτος ἀπὸ Σόλωνος; Biogr. p. 31: Homer δέκατος ἀπὸ Μουσαίου). ἀ. διετοῦς καὶ κατωτέρω Mt 2:16 (cp. Num 1:20; 2 Esdr 3:8).β. w. both beg. and end given ἀπὸ … ἕως (Sir 18:26; 1 Macc 9:13) Mt 1:17; 23:35; Ac 8:10. Sim., ἀ. δόξης εἰς δόξαν fr. glory to glory 2 Cor 3:18.③ to indicate origin or source, fromⓐ lit., with verbs of motionα. down from πίπτειν ἀ. τραπέζης Mt 15:27. καθεῖλεν δυνάστας ἀ. θρόνων God has dethroned rulers Lk 1:52.β. from ἔρχεσθαι ἀ. θεοῦ J 3:2; cp. 13:3; 16:30. παραγίνεται ἀ. τῆς Γαλιλαίας Mt 3:13; ἀ. ἀνατολῶν ἥξουσιν 8:11 (Is 49:12; 59:19); ἀ. τοῦ ἱεροῦ ἐπορεύετο 24:1; ἀ. Παμφυλίας Ac 15:38. ἐγείρεσθαι ἀ. τ. νεκρῶν be raised from the dead Mt 14:2.ⓑ lit., to indicate someone’s local origin from (Hom. et al.; Soph., El. 701; Hdt. 8, 114; ins [RevArch 4 sér. IV 1904 p. 9 ἀπὸ Θεσσαλονίκης]; pap [HBraunert, Binnenwanderung ’64, 384, s.v.; PFlor 14, 2; 15, 5; 17, 4; 22, 13 al.]; Judg 12:8; 13:2; 17:1 [all three acc. to B]; 2 Km 23:20 al.; Jos., Bell. 3, 422, Vi. 217; Just., A I, 1 τῶν ἀπὸ Φλαουί̈ας Νέας πόλεως; s. B-D-F §209, 3; Rob. 578) ἦν ἀ. Βηθσαϊδά he was from B. J 1:44; cp. 12:21. ὄχλοι ἀ. τῆς Γαλιλαίας crowds fr. Galilee Mt 4:25. ἄνδρες ἀ. παντὸς ἔθνους Ac 2:5. ἀνὴρ ἀ. τοῦ ὄχλου a man fr. the crowd Lk 9:38. ὁ προφήτης ὁ ἀ. Ναζαρέθ Mt 21:11. οἱ ἀ. Κιλικίας the Cilicians Ac 6:9. οἱ ἀδελφοὶ οἱ ἀ. Ἰόππης 10:23 (Musaeus 153 παρθένος ἀπʼ Ἀρκαδίας; Just., A I, 58, 1 Μακρίωνα … τὸν ἀπὸ Πόντου). οἱ ἀ. Θεσσαλονίκης Ἰουδαῖοι 17:13. οἱ ἀ. τῆς Ἰταλίας the Italians Hb 13:24, who could be inside as well as outside Italy (cp. Dssm., Her. 33, 1898, 344, LO 167, 1 [LAE 200, 3]; Mlt. 237; B-D-F §437).—Rather denoting close association οἱ ἀ. τῆς ἐκκλησίας members of the church Ac 12:1; likew. 15:5 (cp. Plut., Cato Min. 4, 2 οἱ ἀπὸ τ. στοᾶς φιλόσοφοι; Ps.-Demetr. c. 68 οἱ ἀπʼ αὐτοῦ=his [Isocrates’] pupils; Synes., Ep. 4 p. 162b; 66 p. 206c; PTebt 33, 3 [112 B.C.], Ῥωμαῖος τῶν ἀπὸ συγκλήτου; Ar. 15, 1 Χριστιανοὶ γενεαλογοῦνται ἀπὸ … Ἰησοῦ Χριστοῦ; Ath.).—To indicate origin in the sense of material fr. which someth. is made (Hdt. 7, 65; Theocr. 15, 117; IPriene 117, 72 ἀπὸ χρυσοῦ; 1 Esdr 8:56; Sir 43:20 v.l.) ἔνδυμα ἀ. τριχῶν καμήλου clothing made of camel’s hair Mt 3:4.ⓒ fig., w. verbs of asking, desiring, to denote the pers. of or from whom a thing is asked (Ar. 11, 3): δανίσασθαι ἀπό τινος borrow fr. someone Mt 5:42. ἐκζητεῖν ἀ. τῆς γενεᾶς ταύτης Lk 11:51. ἀπαιτεῖν τι ἀπό τινος Lk 12:20. ζητεῖν τι ἀπό τινος 1 Th 2:6. λαμβάνειν τι ἀπό τινος Mt 17:25f; 3J 7.ⓓ fig., w. verbs of perceiving, to indicate source of the perception (Lysias, Andoc. 6; Ps.-Aristot., De Mundo 6, 399b ἀπʼ αὐτῶν τῶν ἔργων θεωρεῖται ὁ θεός; Appian, Liby. 104 §493 ἀπὸ τῆς σφραγῖδος=[recognize a corpse] by the seal-ring; Demetr.: 722 Fgm. 2, 1 στοχάζεσθαι ἀπὸ τῶν ὀνομάτων; Just., D. 60, 1 τοῦτο νοοῦμεν ἀπὸ τῶν λόγων τῶν προλελεγμένων; 100, 2 ἀπὸ τῶν γραφῶν): ἀ. τῶν καρπῶν αὐτῶν ἐπιγνώσεσθε αὐτούς by their fruits you will know them Mt 7:16, 20. μανθάνειν παραβολὴν ἀ. τῆς συκῆς learn a lesson from the fig tree 24:32; Mk 13:28. ἀπὸ τῶν σπερμάτων μὴ ποιεῖσθαι τὴν παραβολήν if we are not to derive our parable solely from reference to seeds (cp. 1 Cor 15:37) AcPlCor 2:28.—Also μανθάνειν τι ἀπό τινος learn someth. fr. someone Gal 3:2; Col 1:7.ⓔ γράψαι ἀφʼ ὧν ἠδυνήθην, lit., write from what I was able, i.e. as well as I could B 21:9 (cp. Tat. 12, 5 οὐκ ἀπὸ γλώττης οὐδὲ ἀπὸ τῶν εἰκότων οὐδὲ ἀπʼ ἐννοιῶν etc.).④ to indicate distance fr. a point, away from, for μακρὰν ἀ. τινος far fr. someone, ἀπὸ μακρόθεν fr. a great distance s. μακράν, μακρόθεν. ἀπέχειν ἀπό τινος s. ἀπέχω 4. W. detailed measurements (corresp. to Lat. ‘a’, s. B-D-F §161, 1; Rob. 575; WSchulze, Graeca Latina 1901, 15ff; Hdb. on J 11:18; Appian, Bell. Civ. 3, 12 §42; CB I/2, 390 no. 248) ἦν Βηθανία ἐγγὺς τῶν Ἱεροσολύμων ὡς ἀπὸ σταδίων δεκατέντε Bethany was near Jerusalem, about 15 stades (less than 3 km.) away J 11:18. ὡς ἀπὸ πηχῶν διακοσίων about 200 cubits (c. 90 meters) 21:8. ἀπὸ σταδίων χιλίων ἑξακοσίων about 1600 stades (c. 320 km.) Rv 14:20; cp. Hv 4, 1, 5 (for other examples of this usage, s. Rydbeck 68).—Hebraistically ἀπὸ προσώπου τινός (Gen 16:6; Jer 4:26; Jdth 2:14; Sir 21:2; 1 Macc 5:34; En 103:4; Just., A I, 37, 1 ἀπὸ προσώπου τοῦ πατρὸς ἐλέχθησαν διὰ Ἠσαίου … οἵδε οἱ λόγοι ‘in the name of the father … through Isaiah’; 38, 1 al.)=מִפְּנֵי פ׳ ( away) from the presence of someone 2 Th 1:9 (Is 2:10, 19, 21); Rv 12:14 (B-D-F §140; 217, 1; Mlt-H. 466).⑤ to indicate cause, means, or outcomeⓐ gener., to show the reason for someth. because of, as a result of, for (numerous ref. in FBleek on Hb 5:7; PFay 111, 4; POxy 3314, 7 [from falling off a horse]; Jdth 2:20; 4 [6] Esdr [POxy 1010]; AscIs 3:13; Jos., Ant. 9, 56) οὐκ ἠδύνατο ἀ. τοῦ ὄχλου he could not because of the crowd Lk 19:3; cp. Mk 2:4 D. οὐκ ἐνέβλεπον ἀπὸ τῆς δόξης τοῦ φωτός I could not see because of the brilliance of the light Ac 22:11. ἀ. τοῦ πλήθους τ. ἰχθύων J 21:6 (M-EBoismard, ad loc.: s. 1f end). ἀ. τοῦ ὕδατος for the water Hs 8, 2, 8. ἀ. τῆς θλίψεως because of the persecution Ac 11:19. οὐαὶ τῷ κόσμῳ ἀ. τ. σκανδάλων Mt 18:7 (s. B-D-F §176, 1; Mlt. 246). εἰσακουσθεὶς ἀ. τῆς εὐλαβείας heard because of his piety Hb 5:7 (but the text may be corrupt; at any rate it is obscure and variously interpr.; besides the comm. s. KRomaniuk, Die Gottesfürchtigen im NT: Aegyptus 44, ’64, 84; B-D-F §211; Rob. 580; s. on εὐλάβεια).ⓑ to indicate means with the help of, with (Hdt. et al.; Ael. Aristid. 37, 23 K.=2 p. 25 D.; PGM 4, 2128f σφράγιζε ἀπὸ ῥύπου=seal with dirt; En 97:8) γεμίσαι τὴν κοιλίαν ἀ. τ. κερατίων fill one’s stomach w. the husks Lk 15:16 v.l. (s. ἐκ 4aζ; cp. Pr 18:20). οἱ πλουτήσαντες ἀπʼ αὐτῆς Rv 18:15 (cp. Sir 11:18).ⓒ to indicate motive or reason for, from, with (Appian, Bell. Civ. 5, 13 §52 ἀπʼ εὐνοίας=with goodwill; 1 Macc 6:10; pap exx. in Kuhring 35) κοιμᾶσθαι ἀ. τῆς λύπης sleep from sorrow Lk 22:45. ἀ. τῆς χαρᾶς αὐτοῦ Mt 13:44; cp. Lk 24:41; Ac 12:14. ἀ. τοῦ φόβου κράζειν Mt 14:26, ἀ. φόβου καὶ προσδοκίας with fear and expectation Lk 21:26. Hence verbs of fearing, etc., take ἀ. to show the cause of the fear (s. above 1c) μὴ φοβεῖσθαι ἀ. τ. ἀποκτεννόντων τὸ σῶμα not be afraid of those who kill only the body Mt 10:28; Lk 12:4 (cp. Jdth 5:23; 1 Macc 2:62; 3:22; 8:12; En 106:4).ⓓ to indicate the originator of the action denoted by the verb from (Trag., Hdt. et al.) ἀ. σοῦ σημεῖον ἰδεῖν Mt 12:38. γινώσκειν ἀπό τινος learn fr. someone Mk 15:45. ἀκούειν ἀ. τοῦ στόματός τινος hear fr. someone’s mouth, i.e. fr. him personally Lk 22:71 (Dionys. Hal. 3, 8 ἀ. στόματος ἤκουσεν); cp. Ac 9:13; 1J 1:5. τὴν ἀ. σοῦ ἐπαγγελίαν a promise given by you Ac 23:21 (cp. Ath. 2, 3 ταῖς ἀπὸ τῶν κατηγόρων αἰτίαις ‘the charges made by the accusers’). ἀφʼ ἑνὸς ἐγενήθησαν Hb 11:12. Prob. παραλαμβάνειν ἀ. τοῦ κυρίου 1 Cor 11:23 is to be understood in the same way: Paul is convinced that he is taught by the Lord himself (for direct teaching s. EBröse, Die Präp. ἀπό 1 Cor 11:23: StKr 71, 1898, 351–60; Dssm.; BWeiss; Ltzm.; H-DWendland. But for indirect communication: Zahn et al.). παραλαβὼν ἀπὸ τῶν θυγατέρων Φιλίππου, ὅτι Papias (11:2); opp. παρειληφέναι ὑπὸ τῶν θ. Φ. (2:9).—Of the more remote cause ἀπʼ ἀνθρώπων from human beings (as opposed to transcendent revelation; w. διʼ ἀνθρώπου; cp. Artem. 1, 73 p. 66, 11 ἀπὸ γυναικῶν ἢ διὰ γυναικῶν; 2, 36 p. 135, 26) Gal 1:1. ἀ. κυρίου πνεύματος fr. the Lord, who is the Spirit 2 Cor 3:18. ἔχειν τι ἀπό τινος have (received) someth. fr. someone 1 Cor 6:19; 1 Ti 3:7; 1J 2:20; 4:21.—In salutation formulas εἰρήνη ἀ. θεοῦ πατρός ἡμῶν peace that comes from God, our father Ro 1:7; 1 Cor 1:3; 2 Cor 1:2; Gal 1:3; Eph 1:2; cp. 6:23; Phil 1:2; Col 1:2; 1 Th 1:1 v.l.; 2 Th 1:2; 1 Ti 1:2; 2 Ti 1:2; Tit 1:4; Phlm 3. σοφία ἀ. θεοῦ wisdom that comes fr. God 1 Cor 1:30. ἔπαινος ἀ. θεοῦ praise fr. God 4:5. καὶ τοῦτο ἀ. θεοῦ and that brought about by God Phil 1:28. The expr. εἰρήνη ἀπὸ ‘ὁ ὢν καὶ ὁ ἦν καὶ ὁ ἐρχόμενος’ Rv 1:4 is quite extraordinary. It may be an interpretation of the name Yahweh already current, or an attempt to show reverence for the divine name by preserving it unchanged, or simply one more of the grammatical peculiarities so frequent in Rv (Meyer6-Bousset 1906, 159ff; Mlt. 9, note 1; cp. PParis 51, 33 ἀπὸ ἀπηλιότης; Mussies 93f, 328).ⓔ to indicate responsible agents for someth., from, ofα. the self, st. Gk. usage (Thu. 5, 60, 1; X., Mem. 2, 10, 3; Andoc., Orat. 2, 4 οὗτοι οὐκ ἀφʼ αὑτῶν ταῦτα πράττουσιν; Diod S 17, 56; Num 16:28; 4 Macc 11:3; En 98:4; TestAbr A 15 p. 95, 26 [Stone p. 38]; 18 p. 101, 6 [Stone p. 50]; Just., A I, 43, 8) the expr. ἀφʼ ἑαυτοῦ (pl. ἀφʼ ἑαυτῶν) of himself and ἀπʼ ἐμαυτοῦ of myself are common Lk 12:57; 21:30; 2 Cor 3:5, esp. so in J: 5:19, 30; 8:28; 10:18; 15:4.—7:17f; 11:51; 14:10; 16:13; 18:34. So also ἀπʼ ἐμαυτοῦ οὐκ ἐλήλυθα I did not come of myself (opp. the Father sent me) 7:28; 8:42.β. fr. others. W. verbs in the pass. voice or pass. mng. ὑπό is somet. replaced by ἀπό (in isolated cases in older Gk. e.g. Thu. 1, 17 et al. [Kühner-G. II/1 p. 457f]; freq. in later Gk.: Polyb. 1, 79, 14; Hero I 152, 6; 388, 11; Nicol. Dam.: 90 Fgm. 130, 130 Jac.; IG XII/5, 29, 1; SIG 820, 9; PLond III, 1173, 12 p. 208; BGU 1185, 26; PFlor 150, 6 ἀ. τῶν μυῶν κατεσθιόμενα; PGM 4, 256; Kuhring 36f; 1 Macc 15:17; Sir 16:4; ParJer 1:1 ᾐχμαλωτεύθησαν … ἀπὸ τοῦ βασιλέως; Philo, Leg. All. 3, 62; Just., A I, 68, 6 ἐπιστολὴν … γραφεῖσάν μοι ἀπὸ Σερήνου, D. 121, 3 ἀπὸ παντὸς [γένους] μετάνοιαν πεποιῆσθαι. See B-D-F §210; Rob. 820; GHatzidakis, Einl. in d. neugriech. Gramm. 1892, 211; AJannaris, An Histor. Gk. Grammar 1897, §1507). Yet just at this point the textual tradition varies considerably, and the choice of prep. is prob. at times influenced by the wish to express special nuances of mng. Lk 8:29b v.l. (ὑπό text); 43b (ὑπό v.l.); 10:22 D; ἀποδεδειγμένος ἀ. τ. θεοῦ attested by God Ac 2:22. ἐπικληθεὶς Βαρναβᾶς ἀ. (ὑπό v.l.) τ. ἀποστόλων named B. by the apostles 4:36. κατενεχθεὶς ἀ. τοῦ ὕπνου overcome by sleep 20:9. ἀθετούμενος ἀπὸ τῶν παραχαρασσόντων τὰ λόγια αὐτοῦ inasmuch as (Jesus) is being rejected by those who falsify his words AcPlCor 2:3. νεκροῦ βληθέντος ἀπὸ τῶν υἱῶν Ἰσραὴλ ἐπʼ αὐτά when a corpse was cast upon them (the bones of Elisha) 2:32. In such cases ἀπό freq. denotes the one who indirectly originates an action, and can be transl. at the hands of, by command of: πολλὰ παθεῖν ἀ. τ. πρεσβυτέρων suffer much at the hands of the elders Mt 16:21; cp. Lk 9:22; 17:25, where the emphasis is to be placed on παθεῖν, not on ἀποδοκιμασθῆναι. In ἀ. θεοῦ πειράζομαι the thought is that the temptation is caused by God, though not actually carried out by God Js 1:13. ἡτοιμασμένος ἀ. τοῦ θεοῦ prepared by God’s command, not by God in person Rv 12:6.⑥ In a few expr. ἀπό helps to take the place of an adverb. ἀπὸ μέρους, s. μέρος 1c.—ἡμέρᾳ ἀφʼ ἡμέρας day by day GJs 12:3.—ἀπὸ μιᾶς (acc. to Wlh., Einl.2 26, an Aramaism, min ḥădā˒=at once [s. MBlack, An Aramaic Approach3, ’67, 113]; but this does not explain the fem. gender, found also in the formulaic ἐπὶ μιᾶς Maxim. Tyr. 6, 3f En 99:9 [s. SAalen, NTS 13, ’67, 3] and in Mod. Gk. μὲ μιᾶς at once [Thumb §162 note 2]. PSI 286, 22 uses ἀπὸ μιᾶς of a payment made ‘at once’; on the phrase s. New Docs 2, 189. Orig. γνώμης might have been a part of the expr. [Philo, Spec. Leg. 3, 73], or ὁρμῆς [Thu. 7, 71, 6], or γλώσσης [Cass. Dio 44, 36, 2], or φωνῆς [Herodian 1, 4, 8]; cp. ἀπὸ μιᾶς φωνῆς Plut., Mor. 502d of an echo; s. B-D-F §241, 6) unanimously, alike, in concert Lk 14:18. Sim. ἀπὸ τ. καρδιῶν fr. (your) hearts, sincerely Mt 18:35.—Himerius, Or. 39 [=Or. 5], 6 has as a formula διὰ μιᾶς, probably = continuously, uninterruptedly, Or. 44 [=Or. 8], 2 fuller διὰ μιᾶς τῆς σπουδῆς=with one and the same, or with quite similar zeal.—M-M. -
29 Artificial Intelligence
In my opinion, none of [these programs] does even remote justice to the complexity of human mental processes. Unlike men, "artificially intelligent" programs tend to be single minded, undistractable, and unemotional. (Neisser, 1967, p. 9)Future progress in [artificial intelligence] will depend on the development of both practical and theoretical knowledge.... As regards theoretical knowledge, some have sought a unified theory of artificial intelligence. My view is that artificial intelligence is (or soon will be) an engineering discipline since its primary goal is to build things. (Nilsson, 1971, pp. vii-viii)Most workers in AI [artificial intelligence] research and in related fields confess to a pronounced feeling of disappointment in what has been achieved in the last 25 years. Workers entered the field around 1950, and even around 1960, with high hopes that are very far from being realized in 1972. In no part of the field have the discoveries made so far produced the major impact that was then promised.... In the meantime, claims and predictions regarding the potential results of AI research had been publicized which went even farther than the expectations of the majority of workers in the field, whose embarrassments have been added to by the lamentable failure of such inflated predictions....When able and respected scientists write in letters to the present author that AI, the major goal of computing science, represents "another step in the general process of evolution"; that possibilities in the 1980s include an all-purpose intelligence on a human-scale knowledge base; that awe-inspiring possibilities suggest themselves based on machine intelligence exceeding human intelligence by the year 2000 [one has the right to be skeptical]. (Lighthill, 1972, p. 17)4) Just as Astronomy Succeeded Astrology, the Discovery of Intellectual Processes in Machines Should Lead to a Science, EventuallyJust as astronomy succeeded astrology, following Kepler's discovery of planetary regularities, the discoveries of these many principles in empirical explorations on intellectual processes in machines should lead to a science, eventually. (Minsky & Papert, 1973, p. 11)5) Problems in Machine Intelligence Arise Because Things Obvious to Any Person Are Not Represented in the ProgramMany problems arise in experiments on machine intelligence because things obvious to any person are not represented in any program. One can pull with a string, but one cannot push with one.... Simple facts like these caused serious problems when Charniak attempted to extend Bobrow's "Student" program to more realistic applications, and they have not been faced up to until now. (Minsky & Papert, 1973, p. 77)What do we mean by [a symbolic] "description"? We do not mean to suggest that our descriptions must be made of strings of ordinary language words (although they might be). The simplest kind of description is a structure in which some features of a situation are represented by single ("primitive") symbols, and relations between those features are represented by other symbols-or by other features of the way the description is put together. (Minsky & Papert, 1973, p. 11)[AI is] the use of computer programs and programming techniques to cast light on the principles of intelligence in general and human thought in particular. (Boden, 1977, p. 5)The word you look for and hardly ever see in the early AI literature is the word knowledge. They didn't believe you have to know anything, you could always rework it all.... In fact 1967 is the turning point in my mind when there was enough feeling that the old ideas of general principles had to go.... I came up with an argument for what I called the primacy of expertise, and at the time I called the other guys the generalists. (Moses, quoted in McCorduck, 1979, pp. 228-229)9) Artificial Intelligence Is Psychology in a Particularly Pure and Abstract FormThe basic idea of cognitive science is that intelligent beings are semantic engines-in other words, automatic formal systems with interpretations under which they consistently make sense. We can now see why this includes psychology and artificial intelligence on a more or less equal footing: people and intelligent computers (if and when there are any) turn out to be merely different manifestations of the same underlying phenomenon. Moreover, with universal hardware, any semantic engine can in principle be formally imitated by a computer if only the right program can be found. And that will guarantee semantic imitation as well, since (given the appropriate formal behavior) the semantics is "taking care of itself" anyway. Thus we also see why, from this perspective, artificial intelligence can be regarded as psychology in a particularly pure and abstract form. The same fundamental structures are under investigation, but in AI, all the relevant parameters are under direct experimental control (in the programming), without any messy physiology or ethics to get in the way. (Haugeland, 1981b, p. 31)There are many different kinds of reasoning one might imagine:Formal reasoning involves the syntactic manipulation of data structures to deduce new ones following prespecified rules of inference. Mathematical logic is the archetypical formal representation. Procedural reasoning uses simulation to answer questions and solve problems. When we use a program to answer What is the sum of 3 and 4? it uses, or "runs," a procedural model of arithmetic. Reasoning by analogy seems to be a very natural mode of thought for humans but, so far, difficult to accomplish in AI programs. The idea is that when you ask the question Can robins fly? the system might reason that "robins are like sparrows, and I know that sparrows can fly, so robins probably can fly."Generalization and abstraction are also natural reasoning process for humans that are difficult to pin down well enough to implement in a program. If one knows that Robins have wings, that Sparrows have wings, and that Blue jays have wings, eventually one will believe that All birds have wings. This capability may be at the core of most human learning, but it has not yet become a useful technique in AI.... Meta- level reasoning is demonstrated by the way one answers the question What is Paul Newman's telephone number? You might reason that "if I knew Paul Newman's number, I would know that I knew it, because it is a notable fact." This involves using "knowledge about what you know," in particular, about the extent of your knowledge and about the importance of certain facts. Recent research in psychology and AI indicates that meta-level reasoning may play a central role in human cognitive processing. (Barr & Feigenbaum, 1981, pp. 146-147)Suffice it to say that programs already exist that can do things-or, at the very least, appear to be beginning to do things-which ill-informed critics have asserted a priori to be impossible. Examples include: perceiving in a holistic as opposed to an atomistic way; using language creatively; translating sensibly from one language to another by way of a language-neutral semantic representation; planning acts in a broad and sketchy fashion, the details being decided only in execution; distinguishing between different species of emotional reaction according to the psychological context of the subject. (Boden, 1981, p. 33)Can the synthesis of Man and Machine ever be stable, or will the purely organic component become such a hindrance that it has to be discarded? If this eventually happens-and I have... good reasons for thinking that it must-we have nothing to regret and certainly nothing to fear. (Clarke, 1984, p. 243)The thesis of GOFAI... is not that the processes underlying intelligence can be described symbolically... but that they are symbolic. (Haugeland, 1985, p. 113)14) Artificial Intelligence Provides a Useful Approach to Psychological and Psychiatric Theory FormationIt is all very well formulating psychological and psychiatric theories verbally but, when using natural language (even technical jargon), it is difficult to recognise when a theory is complete; oversights are all too easily made, gaps too readily left. This is a point which is generally recognised to be true and it is for precisely this reason that the behavioural sciences attempt to follow the natural sciences in using "classical" mathematics as a more rigorous descriptive language. However, it is an unfortunate fact that, with a few notable exceptions, there has been a marked lack of success in this application. It is my belief that a different approach-a different mathematics-is needed, and that AI provides just this approach. (Hand, quoted in Hand, 1985, pp. 6-7)We might distinguish among four kinds of AI.Research of this kind involves building and programming computers to perform tasks which, to paraphrase Marvin Minsky, would require intelligence if they were done by us. Researchers in nonpsychological AI make no claims whatsoever about the psychological realism of their programs or the devices they build, that is, about whether or not computers perform tasks as humans do.Research here is guided by the view that the computer is a useful tool in the study of mind. In particular, we can write computer programs or build devices that simulate alleged psychological processes in humans and then test our predictions about how the alleged processes work. We can weave these programs and devices together with other programs and devices that simulate different alleged mental processes and thereby test the degree to which the AI system as a whole simulates human mentality. According to weak psychological AI, working with computer models is a way of refining and testing hypotheses about processes that are allegedly realized in human minds.... According to this view, our minds are computers and therefore can be duplicated by other computers. Sherry Turkle writes that the "real ambition is of mythic proportions, making a general purpose intelligence, a mind." (Turkle, 1984, p. 240) The authors of a major text announce that "the ultimate goal of AI research is to build a person or, more humbly, an animal." (Charniak & McDermott, 1985, p. 7)Research in this field, like strong psychological AI, takes seriously the functionalist view that mentality can be realized in many different types of physical devices. Suprapsychological AI, however, accuses strong psychological AI of being chauvinisticof being only interested in human intelligence! Suprapsychological AI claims to be interested in all the conceivable ways intelligence can be realized. (Flanagan, 1991, pp. 241-242)16) Determination of Relevance of Rules in Particular ContextsEven if the [rules] were stored in a context-free form the computer still couldn't use them. To do that the computer requires rules enabling it to draw on just those [ rules] which are relevant in each particular context. Determination of relevance will have to be based on further facts and rules, but the question will again arise as to which facts and rules are relevant for making each particular determination. One could always invoke further facts and rules to answer this question, but of course these must be only the relevant ones. And so it goes. It seems that AI workers will never be able to get started here unless they can settle the problem of relevance beforehand by cataloguing types of context and listing just those facts which are relevant in each. (Dreyfus & Dreyfus, 1986, p. 80)Perhaps the single most important idea to artificial intelligence is that there is no fundamental difference between form and content, that meaning can be captured in a set of symbols such as a semantic net. (G. Johnson, 1986, p. 250)Artificial intelligence is based on the assumption that the mind can be described as some kind of formal system manipulating symbols that stand for things in the world. Thus it doesn't matter what the brain is made of, or what it uses for tokens in the great game of thinking. Using an equivalent set of tokens and rules, we can do thinking with a digital computer, just as we can play chess using cups, salt and pepper shakers, knives, forks, and spoons. Using the right software, one system (the mind) can be mapped into the other (the computer). (G. Johnson, 1986, p. 250)19) A Statement of the Primary and Secondary Purposes of Artificial IntelligenceThe primary goal of Artificial Intelligence is to make machines smarter.The secondary goals of Artificial Intelligence are to understand what intelligence is (the Nobel laureate purpose) and to make machines more useful (the entrepreneurial purpose). (Winston, 1987, p. 1)The theoretical ideas of older branches of engineering are captured in the language of mathematics. We contend that mathematical logic provides the basis for theory in AI. Although many computer scientists already count logic as fundamental to computer science in general, we put forward an even stronger form of the logic-is-important argument....AI deals mainly with the problem of representing and using declarative (as opposed to procedural) knowledge. Declarative knowledge is the kind that is expressed as sentences, and AI needs a language in which to state these sentences. Because the languages in which this knowledge usually is originally captured (natural languages such as English) are not suitable for computer representations, some other language with the appropriate properties must be used. It turns out, we think, that the appropriate properties include at least those that have been uppermost in the minds of logicians in their development of logical languages such as the predicate calculus. Thus, we think that any language for expressing knowledge in AI systems must be at least as expressive as the first-order predicate calculus. (Genesereth & Nilsson, 1987, p. viii)21) Perceptual Structures Can Be Represented as Lists of Elementary PropositionsIn artificial intelligence studies, perceptual structures are represented as assemblages of description lists, the elementary components of which are propositions asserting that certain relations hold among elements. (Chase & Simon, 1988, p. 490)Artificial intelligence (AI) is sometimes defined as the study of how to build and/or program computers to enable them to do the sorts of things that minds can do. Some of these things are commonly regarded as requiring intelligence: offering a medical diagnosis and/or prescription, giving legal or scientific advice, proving theorems in logic or mathematics. Others are not, because they can be done by all normal adults irrespective of educational background (and sometimes by non-human animals too), and typically involve no conscious control: seeing things in sunlight and shadows, finding a path through cluttered terrain, fitting pegs into holes, speaking one's own native tongue, and using one's common sense. Because it covers AI research dealing with both these classes of mental capacity, this definition is preferable to one describing AI as making computers do "things that would require intelligence if done by people." However, it presupposes that computers could do what minds can do, that they might really diagnose, advise, infer, and understand. One could avoid this problematic assumption (and also side-step questions about whether computers do things in the same way as we do) by defining AI instead as "the development of computers whose observable performance has features which in humans we would attribute to mental processes." This bland characterization would be acceptable to some AI workers, especially amongst those focusing on the production of technological tools for commercial purposes. But many others would favour a more controversial definition, seeing AI as the science of intelligence in general-or, more accurately, as the intellectual core of cognitive science. As such, its goal is to provide a systematic theory that can explain (and perhaps enable us to replicate) both the general categories of intentionality and the diverse psychological capacities grounded in them. (Boden, 1990b, pp. 1-2)Because the ability to store data somewhat corresponds to what we call memory in human beings, and because the ability to follow logical procedures somewhat corresponds to what we call reasoning in human beings, many members of the cult have concluded that what computers do somewhat corresponds to what we call thinking. It is no great difficulty to persuade the general public of that conclusion since computers process data very fast in small spaces well below the level of visibility; they do not look like other machines when they are at work. They seem to be running along as smoothly and silently as the brain does when it remembers and reasons and thinks. On the other hand, those who design and build computers know exactly how the machines are working down in the hidden depths of their semiconductors. Computers can be taken apart, scrutinized, and put back together. Their activities can be tracked, analyzed, measured, and thus clearly understood-which is far from possible with the brain. This gives rise to the tempting assumption on the part of the builders and designers that computers can tell us something about brains, indeed, that the computer can serve as a model of the mind, which then comes to be seen as some manner of information processing machine, and possibly not as good at the job as the machine. (Roszak, 1994, pp. xiv-xv)The inner workings of the human mind are far more intricate than the most complicated systems of modern technology. Researchers in the field of artificial intelligence have been attempting to develop programs that will enable computers to display intelligent behavior. Although this field has been an active one for more than thirty-five years and has had many notable successes, AI researchers still do not know how to create a program that matches human intelligence. No existing program can recall facts, solve problems, reason, learn, and process language with human facility. This lack of success has occurred not because computers are inferior to human brains but rather because we do not yet know in sufficient detail how intelligence is organized in the brain. (Anderson, 1995, p. 2)Historical dictionary of quotations in cognitive science > Artificial Intelligence
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