NEW SUPPLEMENT ΤΟ EUCLID'S ELEMENTS OF GEOMETRY. BY THE AUTHOR OF "A NEW INTRODUCTION TO THE MATHEMATICS." LONDON: WHITTAKER & Co. AVE MARIA LANE. 1840. 881. PREFACE. THE author was induced to undertake the following investigations, partly by inferences which were in a manner forced upon him from Euclid's own propositions; secondly, with a view to supply a general proposition wherever Euclid gives only particular ones up to a limited extent; and, finally, to provide full demonstrations for such geometrical propositions as have been assumed as true by mathematicians without demonstration : perhaps because they thought them too evident to require it, or for some other reason not equivalent to a good demonstration; which desultory method of some mathematicians is obstructive of the advance of science; for if some propositions may be received without the usual strict demonstration, why may not others, or why does any proposition require it? |