...the unreasonableness of such a desire. What then am I to do ? I need not ask how I am to prove that things which are equal to the same are equal to one another : this truth is one of which I have a clear perception ; I feel sure that I know it by immediate intuition,...

...AB . BE is equal to the figure AE. Hence the rectangle AB . CB is equal to the figure AE. And since things which are equal to the same are equal to one another, the rectangle AC . CB, together with the square, on CB, is equal to the rectangle AB . CB. , Or thus...

...same time be and not be ; (2) that if equals be added to equals the wholes are equal ; and (3) that things which are equal to the same are equal to one another. It so happens that each of these propositions which he has assumed to be true is, if true, much more...

...middle terms is called the minor premiss. The former always comes first. Unless the principle that " things which are equal to the same are equal to one another " were true, it would not follow that " Socrates " and " mortal," which are equal to the same (" man...

...B, at the distance BC, I describe the circle CGH, meeting DF at G, inasmuch as postulate 3 declares that a circle may be described from any centre, at any distance from that centre. I next, from the centre D, at the distance DG, describe the circle GKL, meeting DE at L. Now it follows...

...such that all straight lines drawn from a certain point within the figure are equal to one another ; " and that " A circle may be described from any centre at any distance from that centre." I shall have occasion, in speaking of the application of the principles laid down in this treatise...

...says the trunk lines of railroads unite to raise rates, just as robbers unite to plunder in concert. Things which are equal to the same are equal to one another. If, then, railroad companies unite to raise rates, and workingmen unite to raise rates of wages, and...

...other point. 2. That a Terminated Straight Line may be produced to any length in a straight line. 3. And that a Circle may be described from any centre, at any distance from that centre. 1 ie Elementary Problems whose construction it is to be taken for granted we can effect. AXIOMS.1 1....

...must presuppose the admission of certain postulates on the part of both dramatist and audience. If that a circle may be described from any centre, at any distance from that centre, is matter of opinion, we can prove no mathematical proposition ; and, without some appropriate conceded...

...Mill's " Principles of Pol. Econ.," cap. 21. exports exchange for the same quantity of money. And since things which are equal to the same are equal to one another, the imports and exports which are equal in money price would, if money were not used, precisely exchange...