...friend. If we know extensively, we shall operate extensively. Being cultivated mentally is important. The equality of the three angles of a triangle to two right angles is a previous assumption. Of the same nature with the indulgence of domestic affections, and equally...

...contradicted by immortal, — life by death — existence at a given time by existence at another lime — the equality of the three angles of a triangle to two right angles, by their (alleged) inequality — less or more. (a) In the former kind there is nothing positive. When...

...operation ; and that operation on individuals is successive in time. But the ' necessity' which connects the equality of the three angles of a triangle to two right angles with the data of deduction is in the geometrician's understanding, and not in the things under1 EP....

...was inquiring into the question dealt with in the thirty-second proposition of Euclid's first book : the equality of the three angles of a triangle to two right angles. The story is remarkable enough without the air of miracle with which it is sometimes surrounded, as...

...the mathematical triangle from our conception of it ; he simply asserts the mind's firm persuasion of the equality of the three angles of a triangle to two right angles, from the fact that this equality is necessarily comprised in the idea of it. Nor are we greatly helped,...

...be horrorstruck at the heresy which suggests any doubt as to the sanctions by which they believe in the equality of the three angles of a triangle to two right angles. Let them know now that this proposition has never been proved, and never can be proved, except by the...

...of any other thing, he means only needfulness as a sine qua non. In this sense he might have added, the equality of the three angles of a triangle to two right angles is needful for the equidistance of all the parts of the circumference of a circle from the centre,...

...altogether unfounded; for as Harris, the author of Hermes, has very well observed, the finding out the equality of the three angles of a triangle to two right ones, would, upon the principles here stated, be a sally of wit, instead of an act of the understanding,...

...which inhere universally in the constitution of external things. But it is obvious that a fact such as the equality of the three angles of a triangle to two right angles is not embodied only in molecular particles which are in contact, and the little sporadic aggregates...

...which inhere universally in the constitution of external things. But it is obvious that a fact such as the equality of the three angles of a triangle to two right angles is not embodied only in molecular particles which are in contact, and the little sporadic aggregates...