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TEXT-BOOKS IN ALGEBRA...

193

1.-Elementary

193

II.-Advanced

194

Book Work : Theory and Practice

196

GEOMETRY

197

I.-The Relations and Properties of Similar Rectilinear Figures 198

A New Syllabus of Plane Geometry

199

The Order of Propositions in the Syllabus and their Relation to

Euclid

200

Some Important Theorems and Problems

203

The Sequence of Theorems..

205

The Test of Proportion :.

205

Text-Books in Accordance with Modern Methods

205

Text-Books on the Basis of Euclid..

209

II.—The Elementary Properties of the Plane, including those of

the Angles made by Planes with Right Lines and with each other 211

The Determination of a Plane

212

Pairs of Identical Propositions..

212

Some other Theorems

214

Parallels

214

Perpendiculars and Obliques

215

Dihedral Angles...

215

Polyhedra..

217

Text-Books on the Properties of the Plane

219

III.-The Elementary Properties of the Sphere, including those of

the Great and Small Circles on the Surfaces of Spheres

220

Dernitions and Principles.

220

The Sphere and its Radii

220

The Axis and Poles of a Circle.

221

Great Circles

221

Small Circles

222

Theorems, Deductions, and Problems

223

Text-Books on the Properties of the Sphere

228

IV.—The Mensuration of the Simple Plane and Solid Figures, in-

cluding that of the Circle, the Sphere, the Cylinder, and the Cone.. 229

Useful Rules and Formula..

230

Important Propositions

231

Surfaces, Volumes, Volume of the Sphere

231

Surface of the Sphere, Surface of the Cylinder and the Cone

233

Frustum of a Cone

234

Useful Ratios and Proportions.

234

Text-Books in Mensuration

235

The Use of Symbols and Abbreviations

237

ANALYTICAL OR ALGEBRAICAL GEOMETRY

240

Elements of Co-ordinate Geometry, as far as the Equations and

Properties of the Right Line and Circle

240

Elementary Principles...

241

Outline of the Principal Propositions and Formulæ.

243

The Point, Transformation of Co-ordinates.

243

The Straight Line...

247

The General Equation-Constants and Variables

249

The Straight Line Subject to Conditions

250

The Interpretation of Equations..

261

The Determination of Loci :.

264

THE CIRCLE ..

268

The General Form of Equation..

270

The Circle under Particular Conditions..

273

Tangent and Normal to the Circle

274

The Use of the more General Equation.

280

Polar Equations..

281

Text-Books in Plane Co-ordinate Geometry.

283
297

PAGE

PLANE TRIGONOMETRY..

230

The Different Measurements of Angles..

286

The Trigonometrical Ratios

289

The Trigonometrical Ratios of Two or more Angles..

291

The Use of the Fundamental Formulæ..

293

Relations between the sides and Angles of a Triangle

295

The Solution of Triangles

295

The Determination of the Areas of Triangles.

296

The Determination of Heights and Distances.

Text-Books in Plane Trigonometry.

297

LIST OF OTHER MATREMATICAL WORKS..

300

Arithmetic and Algebra

300

Geometry and Trigonometry

301

Examination-Papers in the Mathematical Subjects..

302-311

CHAPTER IV.-ENGLISH.

ENGLISH LANGUAGE AND LITERATURE

313

Writing out the Substance of a Paragraph previously read by the

Examiner..

313

The Grammatical Structure of the Language.

313

Text-Books on the English Language

314

Composition

315

SPECIAL SUBJECTS

316

The Study of Shakespeare

319

The Study of Chaucer

322

The Study of Spenser

324

The Study of Milton, Dryden, Pope, and other Authors.

326

HISTORY OF ENGLISH LITERATURE

327

Text-Books in English Literature

329

ENGLISH HISTORY

332

Text-Books in English History

334

A LIST OF ADDITIONAL TEXT-BOOKS IN ENGLISH.

339

English Language..

339

English Literature

340

English Classics, Annotated Editions, &c.

341

Other Aids for the Student of English Classics.

343

Etymological Dictionaries..

344

English History

344

Examination-Papers in English

346

CHAPTER V.-THE EXAMINATION.

PROVINCIAL EXAMINATIONS..

356

The Work of the Examiners

357

Their Personal and Joint Responsibility

357

The Number of Marks..

357

The Use of Numbers..

358

Deciding the Results

358

Medium of Communication

Printed Papers

359

ADVICE TO CANDIDATES

360

The Order of Study for the Examination.

360

The Candidate at the Examination

362

Punctuality

362

Answering Questions

363

Guessing

364

Neatness and Method.,

365

Examining the Examiners

365

Essential Features of the Examination-Papers

366

Concerning Failures.....

367

INTRODUCTION.

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The design of the University of L ndon, according to the Royal Charter which founded it, is “to hold forth to all classes and denominations, without any distinction whatsoever, an encouragement for pursuing a regular and liberal course of education ; and considering that many persons do prosecute and complete their studies both in the United Kingdom and elsewhere, to whom it is expedient to offer.” certain “facilities," it is thought "just" to confer on them “such distinctions and rewards as may incline them to persevere in these their laudable pursuits." Unlike other and older institutions, this University does not require residence at particular colleges, or tuition by any favoured staff of professors. It does not prescribe times and modes of study, or inquire into a candidate's religious views. There is no respecting of persons, no desire to learn where or when the student acquired his knowledge. Every one is judged solely by his work at the time of examination, by examiners who show no one any favour, and whose strict impartiality cannot for a moment be questioned.

The Bachelor of Arts Degree of the University is deservedly held in high esteem. It is at once a sign of native genius, of solid learning and literary skill. It is never given without merit and the strictest scrutiny of every candidate's powers and personal work. No one can hold it who is not well versed in all the subjects of examination. To fail in one is to fail in all. The University never seeks popularity by conferring honorary degrees, which are as hollow as they are ‘honorary.' It opens one door only, and through that door of test must go alike the rich patron and his protégé, the trained collegian and the struggling private student. The only consolation is that the door is open to all without distinction; if they are willing to meet its ordeal and prove their competency to pass to the incomparable honours beyond.

There can be no question that to ministers of religion, to teachers, and to those who wish to lay a solid basis for future studies or pursue a literary life, a degree at the University of London is of particular value. Especially should schoolmasters aspire to it if they wish to rise in their rank and be in honourable possession of a diploma which not even “ My Lords” at the Education Department can touch. It will gift them with self-reliance in their work, and inspire others with confidence in their abilities; it will furnish them with the educational status from which, and by means of which, they may legitimately hope to advance to the higher honours and rewards of their profession. With a view to guide and encourage those students who, having matriculated, will wish at once to proceed to the First B.A. Examination, we propose to set before them a few hints as to the best means and text-books for self-preparation, together with a few suggestions as to plans of study, the more important features of the curriculum, and the management of an examination-paper. Our object is not to teach the subjects of study, but to show their range and peculiar difficulties, how they may be dealt with, and where adequate knowledge and help of various kinds may be found. We address ourselves mainly to those many private students who have no other means of acquiring information. We do not profess to be infallible ; we simply offer them the results of patient inquiry and of sure experience gleaned from many quarters. Those students who can, will, doubtless, avail themselves of the valuable aid which collegiate professors and private tutors afford. We would advise them to do so, especially when the course of instruction is adapted to the requirements of the University. But even pupils like these, who may have peculiar difficulties and a desire for further sources of help, will probably find a reference to these pages very serviceable and suggestive. • Some persons may object to the large number of books enumerated. We may say that we have endeavoured to guide the reader by pointing out the value and range of some of the books and by indicating the kind of aid they will render. It is not implied that any candidate will need all the works referred to. Some candidates are deficient in one thing, some in another; some wish for further light on one difficulty, some on another ; some have access to public libraries; others may already have books which cover only a part of the groundwork of study required. Haply they may here find directions to what they are still in want of. Each must select for himself according to his personal need, the extent of his knowledge, and the specified authors of his year of examination. Of these authors we have given a long and comprehensive list, including textbooks, translations, and other valuable helps, suited to the wants of every class of students in any particular year.

It would be a great mistake for the candidate to imagine that because he has the necessary appliances a mere cursory and casual use of them will suffice. The test of the examination is not what he has read but what he has mastered and made his own; not what is diffused among many text-books, but what he has remembered, classified, and put into shape for ready production at a moment's notice. The examiners cannot possibly take account of what he intended to do or might have done under more favourable circumstances. Their simple and absolute duty is to judge each one by the proof of his skill and knowledge left on his paper.

Many of the books herein described are prepared by the present examiners to the University. As a rule these books are the best to use ; but as some of the examiners are occasionally changed, the candidate should consult the list given in the Calendar of the University, published early in each year by Messrs. Taylor and Francis, Fleet Street, London, price 4s. In this calendar much useful information is afforded. The “Regulations Relating to Degrees in Arts,” and those also “Relating to the Examinations for Women,” may be had free, at any time, on application to “The Registrar of the University of London, London, W.” In reference to the latter examinations, a notice has been appended to the Regulations to which lady candidates should pay attention. It is as follows : “The Senate desire to make it known that the standard of attainment expected at the General Examination is the same as that expected at the Matriculation Examination; and that the standard of attainment expected at the Special Examinations is the same as that expected at those Examinations for the B.A. and B.Sc. Degrees, of which the programmes correspond.” To preserve our unity of purpose we shall make distinct reference in the following pages to the First B. A. Examination only ; but the above notice will show the wisdom of ladies' comparing together the two sets of programmes and examination-papers, not forgetting, of course, the special requirements which are laid down in the regulations with regard to some of the subjects.

Our personal acquaintance, for many years, with all the main features of the First B.A. Examination has enabled us to set them before our readers with more fulness of detail and comprehensiveness than has ever, we believe, been attempted before. We have taken considerable pains to be accurate, so that in all respects we might be a safe and complete guide. But as errors may have crept in, we shall be glad to receive needful corrections, or any suggestions which our readers may think will be useful to candidates.

J. G. January, 1878.

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