in altering for the purpose of disguising the source of their information, were really differences from the original sources altered by the plaintiffs' author for the purpose of disguising the sources to which he was indebted for his book. “After going through every passage challenged in Court, and dealing more at length with those specially assailed by plaintiffs, particularly setting forth that the plaintiffs' author, in relation to the influence of lime on carbonic acid gas, did not appear to understand the difference between 'quick lime' and slaked lime, the learned counsel (Mr. Fry), having spoken for a good part of three days, submitted that the plaintiffs had failed to sustain their charge, and he appealed to his Honour to dismiss the Bill.” Mr. Millar (for defendant) said: “In their ‘Bill,' in the present cause, they (plaintiffs) claimed, as their own exclusive speciality,' the right to 'make phenomena the handmaid of science, and not science the handmaid of phenomena.' What that might mean was not so plain, as the plaintiffs had not told the Court how many phenomena' it takes to make a handmaid !' Now, abandoning their own 'Bill,' they found their claim to the interference of the Court on the Questions, and contend that Questions once answered in their book, however imperfectly, are never to be asked in any subsequent book, though the answers to be given are wholly different. Again, the Court had been told that the Questions are everything; that these once asked suggest the Answers; and that, then, the Answers are easily supplied; but it was very singular that the plaintiffs' author, in his Preface to the 'Guide,' actually says that the Questions in his book ' were often more easily asked than answered!' . Attempts had been made in the Bill,' and again by his learned friend (Mr. Westlake) to prove the existence of common errors in the two books; but in every case, without one single" exception, the attempt had signally failed. The plaintiffs had found errors in their own book, and these they had attempted to foist into defendant's book ; but in every case an examination of the passages proved that the plaintiffs' book was the sole source of those errors. There were, however, a great number of errors in the plaintiffs' book which they had not even tried to parallel in the defendant's book. He would read just one, which, after all their alleged care and 'expense' in revising and correcting, to make their book ‘keep pace with the progress of science, they had allowed to appear, at least as late as the 21st edition of their book. On page 274 of the plaintiffs' book it is taught that ' Forty-seven and a half pounds of carbonic acid gas weigh just as much as one hundred pounds of common air.' (Laughter). Amongst other things commented upon as errors in plaintiffs' book, was the statement, p. 355, that “. Rain' purifies the air, by setting in motion the stagnant contents of sewers and ditches," '-an odd method, it was remarked, of “purifying the air.” The Vice-Chancellor reserved his judgment. [Throughout the Trial, Dr. Brewer, plaintiffs' author, and the two authors of the defendant were present in court, the latter incessantly engaged--as appeared-in selecting suitable citations and parallel passages for the use of defendant's counsel, from their “small scientific library."] [Continued at end of book. BOOK-KEEPING. Two Shillings, in Pour Books. BLANK BOOKS TO ACCOMPANY IRISH BOOK-KEEPING. One Shilling and Sixpence. KEEPING: Use of Schools. CONSISTING OF Credit Day Book. Debit Day Book. Three Shillings and Sixpence, in Three Parts. 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AN INTRODUCTION TO PLANE GEOMETRY, ITS USE AND APPLICATION; WITH Ar Explanatory Preface ; REMARKS ON GEOMETRICAL REASONING, AND ON ARITHMETIC AND ALGEBRA APPLIED TO GEOMETRY; “GEOMETRY IS, PERHAPS, OF ALL THE PARTS OF MATHEMATICS, THAT WHICH OUGHT TO BE TAUGHT FIRST: IT APPEARS TO ME VERY PROPER TO INTEREST CHILDREN, PROVIDED IT IS PRESENTED TO THEM PRINCIPALLY IN RELATION TO ITS APPLICATIONS, WHETHER ON PAPER OR ON LAND,” Lacroix, p. 306. MANCHESTER : LONDON: PREFACE, RESPECTING THE GRADATIONS IN EUCLID'S PLANE GEOMETRY, SKELETON PROPOSITIONS, ETC. The chief aim of the Author or Compiler of the Gradations in Euclid, with Skeleton Propositions, &c., for Written Examinations, has been to furnish a useful book to those who have not much time for the pursuit of Geometrical Studies, and to whom, therefore, the Practical Application of whatever they learn is of great importance. He is, however, persuaded that those who have both time and full opportunity, either in Public Schools or in Colleges, for attaining proficiency in the Higher Mathematics, will find an Introduction, such as is given in this work, very suitable to prepare them more thoroughly to appreciate Geometrical Truths, and to take an interest in them as the ground-work of accurate science. The INTRODUCTION is of general use to all Students of Geometry : it contains—a brief account of the Gradual Growth of Geometry and of the Elements of Euclid ; the Signs and Contractions that may be employed ; and some Remarks on the Nature of Geometrical Reasoning-on the Application of Arithmetic and Algebra to Geometry-on Incommensurable Quantities—and on Written and Oral Examinations. Several of the subjects treated of pre-suppose, indeed, that the Learner has a clear under. standing of Fractions, common and decimal — of the extraction of the Square Root-and of the introductory principles of Algebra : but this knowledge is indispensable for those who would really master the Elements of Geometry. The Editions of Euclid by Potts and BLAKELOCK have shown the advantages of printing separately and distinctly the parts of a Proposition and of its Demonstration : it is a plan which undoubtedly gives very valuable help to Learners in attaining a more exact acquaintance with the Principles on which Geometry, as a science, is founded. No argument is here needed to prove the importance of being able to estimate the force |