FromH. J. Cooke, Esq., The Academy, Banbridge.
FromH. J. Cooke, Esq., The Academy, Banbridge.
”In the clearness, neatness, and variety of demonstrations, it is far superior to any text-book yetpublished, whilst the exercises are all that could be desired.”
FromJamesA. Poole, M.A., 29, Harcourt-street, Dublin.
FromJamesA. Poole, M.A., 29, Harcourt-street, Dublin.
”This work proves that Irish Scholars can produce Class-books which even the Head Masters ofEnglish Schools will feel it a duty to introduce into their establishments.”
FromProfessorLeebody, Magee College, Londonderry.
FromProfessorLeebody, Magee College, Londonderry.
”So far as I have had time to examine it, it seems to me a very valuable addition to ourtext-books of Elementary Geometry, and a most suitable introduction to the ‘Sequel to Euclid,’which I have found an admirable book for class teaching.”
FromMrs. Bryant, F.C.P., Principal of the North London Collegiate School for Girls.
FromMrs. Bryant, F.C.P., Principal of the North London Collegiate School for Girls.
”I am heartily glad to welcome this work as a substitute for the much less elegant text-books invogue here. I have begun to use it already with some of my classes, and find that the arrangement ofexercises after each proposition works admirably.”
From theRev. J. E. Reffé, French College, Blackrock.
From theRev. J. E. Reffé, French College, Blackrock.
”I am sure you will soon be obliged to prepare a Second Edition. I have ordered fifty copiesmore of the Euclid (this makes 250 copies for the French College). They all like the bookhere.”
From theNottinghamGuardian.
From theNottinghamGuardian.
”The edition of the First Six Books of Euclid by Dr. John Casey is a particularly useful andable work.…The illustrative exercises and problems are exceedingly numerous, and havebeen selected with great care. Dr. Casey has done an undoubted service to teachers inpreparing an edition of Euclid adapted to the development of the Geometry of the presentday.”
From theLeedsMercury.
From theLeedsMercury.
”There is a simplicity and neatness of style in the solution of the problems which will be of greatassistance to the students in mastering them.…At the end of each proposition there is anexamination paper upon it, with deductions and other propositions, by means of which the studentis at once enabled to test himself whether he has fully grasped the principles involved.…Dr. Caseybrings at once the student face to face with the difficulties to be encountered, and trains him, stageby stage, to solve them.”
From thePracticalTeacher.
From thePracticalTeacher.
”The preface states that this book ‘is intended to supply a want much felt by Teachers at thepresent day–the production of a work which, while giving the unrivalled original in all its integrity,would also contain the modern conceptions and developments of the portion of Geometry over whichthe elements extend.’
”The book is all, and more than all, it professes to be.…The propositions suggested are such aswill be found to have most important applications, and the methods of proof are both simple andelegant. We know no book which, within so moderate a compass, puts the student in possession ofsuch valuable results.
”The exercises left for solution are such as will repay patient study, and those whose solution aregiven in the book itself will suggest the methods by which the others are to be demonstrated. Werecommend everyone who wants good exercises in Geometry to get the book, and study it forthemselves.”
From theEducationalTimes.
From theEducationalTimes.
”The editor has been very happy in some of the changes he has made. The combination of thegeneral and particular enunciations of each proposition into one is good; and the shortening of theproofs, by omitting the repetitions so common in Euclid, is another improvement. The use of thecontra-positive of a proved theorem is introduced with advantage, in place of thereductio adabsurdum; while the alternative (or, in some cases, substituted) proofs are numerous, many of thembeing not only elegant but eminently suggestive. The notes at the end of the book are of greatinterest, and much of the matter is not easily accessible. The collection of exercises, ‘of which thereare nearly eight hundred,’ is another feature which will commend the book to teachers. To sum up,we think that this work ought to be read by every teacher of Geometry; and we make bold to saythat no one can study it without gaining valuable information, and still more valuablesuggestions.”
From theJournalofEducation, Sept. 1, 1883.
From theJournalofEducation, Sept. 1, 1883.
”In the text of the propositions, the author has adhered, in all but a few instances, to thesubstance of Euclid’s demonstrations, without, however, giving way to a slavish following of hisoccasional verbiage and redundance. The use of letters in brackets in the enunciations eludes thenecessity of giving a second or particular enunciation, and can do no harm. Hints of other proofs areoften given in small type at the end of a proposition, and, where necessary, short explanations. Thedefinitions are also carefully annotated. The theory of proportion, Book V., is given in an algebraicalform. This book has always appeared to us an exquisitely subtle example of Greek mathematicallogic, but the subject can be made infinitely simpler and shorter by a little algebra, andnaturally the more difficult method has yielded place to the less. It is not studied in schools,it is not asked for even in the Cambridge Tripos; a few years ago, it still survived inone of the College Examinations at St. John’s, but whether the reforming spirit whichis dominant there has left it, we do not know. The book contains a very large body ofriders and independent geometrical problems. The simpler of these are given in immediateconnexion with the propositions to which they naturally attach; the more difficult aregiven in collections at the end of each book. Some of these are solved in the book, andthese include many well-known theorems, properties of orthocentre, of nine-point circle,&c. In every way this edition of Euclid is deserving of commendation. We would alsoexpress a hope that everyone who uses this book will afterwards read the same author’s‘Sequel to Euclid,’ where he will find an excellent account of more modern Geometry.”
________________NOW READY, Price 6s.,A KEY to the EXERCISES in the ELEMENTS of EUCLID.
________________
NOW READY, Price 6s.,
A KEY to the EXERCISES in the ELEMENTS of EUCLID.
TypographicalErrorscorrectedinProjectGutenbergedition
TypographicalErrorscorrectedinProjectGutenbergedition
p.??. “Def.viii.—When a right line intersects …” in original, amended to “Def.vii” in sequence.
p.??. 12 “bisects the parallellogram” in original, amended to match every other occurrence as “parallelogram”.
p.??. “△ACHis half the rectangleAC.AH(I.Cor.1)” in original. The reference is to Prop. I. of the current book and misnumbered, it should be (i.Cor.2).
p.??. “The parallelogramCMis equal toDE[I.xliii.,Cor.3];” in original, amended to “Cor.2” following MS. correction: there is noCor.3.
p.??. “OnCBdescribe the squareCBEFI. [xlvi.].” in original, clearly meant to read [I.xlvi.].
p.??. “The remainiug parts of the line” in original, obvious error amended to “remaining”.
p.??. “that which is nearest to the line throuyh the centre” in original, obvious error amended to “through”.
p.??. “Then this line [I.,Cor.1]” in original. The reference is to Prop. I. of the current book, so it should be [i.,Cor.1].
p.??. “OAis equal toOC[I., Def.xxii.]” in original. The reference should be [I., Def.xxxii.].
p.??. “the four pointsA,C,D,Bare concylic” in original, evidently intended is “concyclic”.
p.??. as p.??.
p.??. “Through tho pointE” in original, obvious error amended to “the”.
p.??., p.??. “the pointsA,B,C,Dare concylic” in original, as p.??.
p.??. “(Ex. 2.) …or touchlng a given file and a given circle.” in original, obvious error amended to “touching”.
p.??. “21. What is the locus of the middle points …” in original, amended to “31.” in sequence.
p.??. In (21) “the if then lineDEintersect the chords …” in original, garbled phrase amended to “then if the”.
p.??. In (44) “these circle sintersect” in original, misplaced space amended to “these circles intersect”.
p.??. “4. The point of bisection (1) of the line (OP)” in original, from the diagram and following discussion this should be (I).
p.??. Prop. IX. “About a given circle (ABCD) to describe a circle.” in original, clearly this is nonsense and must mean “About a given square”.
p.??. “Then the trainglesABO,CBO” in original, obvious error amended to “triangles”.
p.??. In (52) “and also en equilateral circumscribed polygon” in original, wrong letter amended to “an”.
p.??. Heading “PROP.XXV.—Problem.” in original, the preamble to this book says that every Proposition in it is aTheoremand this one seems to be no exception, so amended.
p.??. Reference “[I.]” is to Proposition I. of current book, amended to “[i.]” (4 times).
p.??sqq. Reference “[II.]” is to Proposition II. of current book, amended to “[ii.]” (4 times).
p.??. Prop V. header “subtended bg the homologous sides” in original, obvious error amended to “by”.
p.??. Reference “[XVI.]” corrected to “[xvi.]”.
p.??. “From the construction is is evident …” in original, obvious error amended to “it is”.
p.??. “20. Find a poiatO” in original, obvious error amended to “point”.
p.??. “the linesGH,GKeach perpendiclar toEF” in original, obvious error amended to “perpendicular”.
p.??. “O” when associated with a lower case letter was wrongly printed aso, which is not defined. These have been corrected (3 times).
p.??. Reference “[VI.,Cor.6]” corrected to “[vi.,Cor.6]”.