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TABLE OF CONTENTS.
28 - 30
30 - 35
Definitions and Axiom
208 - 211
III. Principles of Construction :
211 - 212
212 - 215 IV. Principles for accurately calculating Distances, Magnitudes,
and Areas :-
216 SECTION 3. Magnitudes or Areas
217 - 218
I. Geometrical Synthesis and Analysis
219 - 223 223 – 225 226 - 233
SERIES 1°. Problems in Book I. 1-62
226 Theorems in Book I. 1-17
228 Problems in Book II. 1-14
229 Theorems in Book II. 1-6
230 SERIES 2°. Propositions not fully proved, or not inserted in
the Gradations :Problems.-Book I. 1-13..
230 Theorems.- Book I. 1-15..
231 Problems.Book II. 1-10
232 Theorems.-Book II. 1-15.
“Even the Sleeping Geometrician," says old RALPH CUDWORTH, p. 160, "hath at that time, all his Geometrical Theorems and Knowledges some way on him : as also the Sleeping Musician, all his Musical Skill and Songs : and therefore why may it not be possible for the Soul to have likewise some Actual Energie on it, which it is not Expressly Conscious of ?”
John Heywood, Printer, 141 and 143, Deansgate, Manchester.
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CRITICAL NOTICES. “Mr. Green's 'Gradations' is a valuable work, though it takes in only the first two books of Euclid. Without endorsing all the detail, which we have not had time to examine, we may unhesitatingly speak in praise of the method, which we have examined with care. No introductory Euclid which has fallen in our way contains anything like the help, in the shape of notes and arrangement, that this does." “The whole of the propositions are arranged after the manner recommended by Professor De Morgan, in his
Treatise on the Study and Difficulties of Mathematics. To many of the propositions is appended an account of the practical uses to which the proposition may be applied. An Appendix is added, which contains much that is useful in the way of notes and exercises. We feel sure that schoolmasters will largely patronise Mr. Green's 'Gradations in Euclid,' as a very complete apparatus for teaching the First and Second Books.”—Papers for the Schoolmaster, July, 1858, p. 112.
“We commend the work to the consideration of Teachers.”—Athenaun, July 17, 1858.
“ By printing the distinct parts of the propositions separately a very great help is gained, and the principles more thoroughly learned.”—The Bookseller, July 24, 1858.
“This is a useful book ; in fact, the best introduction to Euclid with which we are acquainted, and we heartily recommend it to the favourable notice of our readers. Its main object is to combine theory with practice, and so soon as a geometrical truth has been established, to point out its use and application.”—The School and the Teacher, August, 1858.
"Mr. Henry Green, A.M., has published the first and second books of Euclid, for pupil. teachers and others. We recommend this as a very useful work introductory to plain geometry, and one which may be put into the hands of either schoolboys or adult mechanics with great advantage.”—Manchester Guardian, Dec. 2, 1858.
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