MENSURATION FOR THE USE OF SCHOOLS. CONTAINING NUMEROUS EXAMPLES, AND (BY THE KIND PERMISSION OF THE OXFORD UNIVERSITY DELEGA'I ES) EMBODYING NEARLY ALL THE QUESTIONS SET IN THEIR LOCAL EXAMINATION PAPERS. BY THE REV. ALFRED HILEY, M.A. ST. JOHN'S COLLEGE, CAMBRIDGE: MATHEMATICAL MASTER AT THORP-ARCH SCHOOL, YORKSHIRE : SIXTH EDITION, WITH A NEW CHAPTER ON LAND-SURVEYING BY THE REV. JOHN HUNTER, M.A. LONDON: LONGMANS, GREEN, AND CO. 1879. PREFACE. SO NUMEROUS are the purposes to which Mensuration is applied, that it would be almost impossible to exaggerate its importance. To many boys also, whose time for instruction is likely to be limited, or who, perhaps, would find Euclid too difficult for them, it is believed that Mensuration would form an excellent substitute. But, important as Mensuration doubtless is, still, in the opinion of many Masters, the works that have recently appeared on this subject are too long to be used as ordinary School Books. Acting on this impression, the Author has endeavoured to supply a work on Mensuration which a boy of ordinary ability could hope to get through within a reasonable time. The Questions, which number about 700, are, for the most part, original; but, by the kind permission of the Oxford University Delegates for Conducting the Local Examinations, nearly all the questions that have appeared in their Examination Papers have been embodied in the present Work. This feature of the Work will doubtless prove most useful, as it will show candidates for these Examinations what is the style of question that they may expectthose that have appeared in the Junior Examination Papers being marked by a single asterisk (*), whilst those that have been set to the Senior Candidates have prefixed to them a double asterisk (**). Whilst framing the Questions with the express intention of impressing the different rules upon the Student's mind, care has been taken to avoid wearying him with unnecessarily long and tedious Arithmetical calculations. But before commencing Mensuration, it is desirable that the Pupil should be well grounded in his Arithmetic, so that his onward course may not be impeded by his ignorance of any particular rule that he may require. The explanations have been made as clear and as simple as possible, and will be sufficient, it is hoped, to enable the Pupil to work nearly all the Questions without much help from his Master. Of course, in a work of this kind, containing so many questions, there will necessarily be some mistakes, but it is hoped that they will be found very few indeed, as the greatest care has been taken to make it as correct as possible. Any corrections, however, or suggestions for its improvement, will be most thankfully received by the Author. THORP-ARCH SCHOOL, YORKSHIRE : June 20, 1871. PREFACE TO THE FIFTH EDITION. WITH THE VIEW of making this New Edition as complete as possible, there is now added a New Chapter on Land Surveying, written expressly for this work by the Rev. John Hunter, M.A., late Vice-Principal of the Battersea Training College. THORP-ARCH SCHOOL, YORKSHIRE. |