Life of Sir William Rowan Hamilton

This historic book may have numerous typos, missing text, images, or index. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. 1889. Not illustrated. Excerpt: ... complaining, in the name of that respectable member of society, of geometers having made it appear as if the ellipse took more than its share of a certain property. Both in the ellipse and hyperbola the locus of the perpendicular on the tangent from the focus is the circle--an ellipse. The ellipse has the lion's share of this property. Now what is the property in which the hyperbola takes both P You will not be long in finding it. 'I shall draw up a small Paper to show how the modern geometry may be worked without ambiguity on the system of signs which I gave in the Cambridge and Dub/in Journal. I have been looking at Salmon's book lately, and regret much that his general propositions are worked on a case of the diagram, their generality being secured by trusting in algebra for the other oases. 'As to people ridiculing quaternions, let them do it; but do not let them succeed in making you feel it. They exist and act-- as Newton said of gravitation. You take care of your "contents," and never mind the " non-contents." 'If Mac Cullagh imagined that the property of the ellipse he had assigned had anything to do with any system of v'-i except the old one--or could suggest anything--he was strangely deceived. The property, so far as appears, has a shade more of connexion with the couplets of the Pure Time than with quaternions. In devising the question, he first established x* + x* = constant, &c, and then constructed his equation. 'I object much to the phrase of six points in involution. * If the ratio compounded of AB to BC, and CD to DA give a ratio of equality, we say AC is harmonically divided in B and D. Say, AB, CD are harmonics. 'Then if AB to BC, CD to DE, EF to FA, compounded, also give a ratio of equality, why not say A B C D E i^1 are harmonics? ...