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Note, on the contrary, that in the solution of an equation the sign of equality is only put between the two members of the equation, and not at the beginning of each line. The importance of equations is worth insisting on, indeed if any question has to be omitted in working a paper, it certainly should not be that containing the equations. Factors always prove the great difficulty in elementary Algebra, and it is most important to grasp how formulae are used to discover them. The Algebra paper usually ends with two, or, mostly three, problems, for which somewhat higher marks are assigned than for the other questions. Accordingly it is worth while to spend time and trouble on them, so as to make certain of solving at least one in the examination. It is indeed possible to pass in the subject without solving any problem, but it requires great correctness of work in the whole of the rest of the paper.
Geometry. The present Regulations have been in force about two years. Consequently the papers actually set have been supplemented in this volume by some of those set in former years for the Further Examination in Mathematics. The propositions of Euclid set have not been printed, but the numbers of the questions, which have been left unaltered, will show exactly where they lie. In the Responsions papers it will be noticed at once what a small proportion these propositions bear to the deductions and other questions. The principle which the examiners seem to have before them in marking the subject, is that no man should be allowed to pass if he has only worked the propositions correctly, but that he should be required to show some further knowledge of the subject, by solving at least one or two of the deductions.
First then the actual propositions of Euclid must not be neglected, but learnt even more carefully than under the old system, for a candidate who is able to write them all out correctly will have left as little as possible to chance. Since Euclid's proofs are no longer required, they may be studied in any textbook and on any method. Most of Book II may be treated Algebraically.
The rest of the paper may be conveniently grouped under four heads :
(1) Particular cases of propositions of Euclid.
(2) Supplementary propositions, which will be found in any textbook. One which has been used at school will probably be a safe guide, but those who have studied on Euclid's lines are recommended to use Hall & Stevens' School Geometry, which is perhaps the most conservative of the books on the new geometry. In the notes at the end of this volume it has been systematically referred to.
(3) Loci. For the study of these, the four or five simplest cases (of those in which the locus is a straight line or a circle) should be carefully learnt, and their most important applications noted.
(4) Deductions from other propositions. Of all those which have been so far set ample solutions have been appended. Other examples can be taken from Hall & Stevens. In solving these it is well to bear in mind those propositions of Euclid, the results of which are valuable and may have to be used. For instance the important propositions in Book III are 3, 11, 12, 14, 16, 20, 21, 22, 31, 32, 35, 36.
Latin Prose. The candidate is recommended to translate a considerable number of the proses which have been actually set so as to familiarize himself, not only
with the standard, but also with the styles of the typical passages. Few things are more upsetting than to be confronted with a piece of English of unaccustomed difficulty. Add to this, that there is an unfortunate law of nature, which causes a man, when he feels that a passage is above his strength, to make mistakes upon points which he would, under happier circumstances, bave rendered correctly. The knowledge of the standard cannot be thoroughly obtained from one or two passages, but must be collected from several.
Nor is a knowledge of the various styles, which may occur, of less importance. For now and then a passage will appear harder than it really is, because the language in which it is written seems modern. As an instance of this the passage set in Trinity Term, 1905 may be referred to, which is from Bunyan, and describes the fight between Christian and Apollyon. To many men this will prove difficult, whereas, if the style were slightly altered, and the fight described as between a Roman and a Gaul, it would probably be considered a good deal easier.
The difficulties of Latin Prose may be grouped under the heads of syntax, vocabulary, and idiom. With regard to the first it is better for those who feel shaky to stick to the simpler constructions, and not to attempt to vary them. If really idiomatic Latin can be written, it is an excellent thing, and may cover a multitude of mistakes, but the primary requisite is correctness, and a simple construction that is known is much better than one which is more elaborate but imperfectly understood. In fact it may be emphasized that the great object to aim at is to avoid making bad grammatical mistakes.
The vocabulary is likely to prove the great difficulty. To gain facility it is absolutely necessary to translate several passages without the help of a dictionary. Nothing
strengthens the memory so much. It is a good rule never to leave a word untranslated. At the worst there will be some equivalent or cognate English word, formed from a Latin root, which will suggest a translation. It may not indeed be the best word to use, but it will be far better than none at all, and it is by hunting for words in this way that a vocabulary is acquired. Baldness and oddity in the words used should indeed be avoided if possible, but leaving words untranslated is a much worse fault. It must also be remembered that Latin idiom is often much simpler than English, so that it is not always necessary to produce an exact equivalent for a difficult word, for a paraphrase of the English may suggest a much simpler English word, which will give better Latin than if a literal translation had been aimed at.
This leads to almost the only remark which it seems advisable to make about idiom. As a rule the passages set are plain narratives, which can be translated literally. But occasionally there will occur idiomatic or metaphorical expressions in the English, which are not at all likely to correspond with the Latin idiom. In such cases the sense of the expression should be given in Latin as simply as possible. The ability to notice such expressions should be carefully cultivated, for if translated literally they will involve canine, and sometimes very absurd, Latin. The rules for the order of words should be followed with care as far as possible, for a badly arranged sentence will often not read like Latin at all.
Grammar. The Latin and Greek Grammar papers are at present, as we have already stated, set separately, one hour being allowed for each, and with the arrangement that grammar and translation papers in each language should be set on the same morning, the Latin on one day, the Greek on another. Previously to the change, which was made a year and a half ago, the grammar of both languages was combined in one paper. In order, however, to increase the practical value of this book, the Latin and Greek questions have been separated in all the papers here printed.
Little advice of practical value can be given. In Greek Grammar, it is hardly necessary to say, the main difficulty will be with the irregular verbs. Next in importance are the irregularities of nouns, and the government of prepositions. If the parsing of words detached from their contexts should prove a difficulty, it is best to gain practice by parsing some of the words occurring in the Greek book which is being read. Sentences for translation into Greek are not set so much as formerly, nor are they regarded as of importance, except where they illustrate the construction of some preposition, or some equally simple point.
In Latin Grammar the hardest parts are the sentences for translation into Latin, which often involve fairly hard points of syntax and idiom; and the passages for turning from Oratio Recta into Oratio Obliqua, and vice versa, the second process being by far the hardest. Those who are reading Caesar will be in no lack of examples for practice.
The working of papers in grammar must not be regarded as a sufficient substitute for the unwelcome but necessary grind at the textbooks; but it gives a most valuable test of the progress made, and directs the attention to important points. Further it may be added that the truest way of gaining a knowledge of grammar is to make its study parallel with, and based on, the classical authors read.