...kinds, to wit relations of ideas and matters of fact. Of the first kind are the sciences of geornetry, algebra and arithmetic, and in short every affirmation...is either intuitively or demonstratively certain. — Propositions of this kind are discoverable by the mere Operation of thought, without dependence...

...human reason or enquiry may naturally be divided into two kinds, to wit relations of ideas and matters of fact. Of the first kind are the sciences of geometry,...is either intuitively or demonstratively certain. — Propositions of this kind are discoverable by the mere operation of thought, without dependence...

...that geometry had long ago demonstrated the truth of the problem, that in every right angle triangle, the square of the hypothenuse is equal to the square of the other two sides. The world is excited and feverish ; it has stood " on tip-toe " these many years. We, in this goodly...

...that geometry had long ago demonstrated the truth of the problem, that in every right angle triangle, the square of the hypothenuse is equal to the square of the other two sides. It is a matter of some importance to know, at the present time, whether the minds of men can be brought...

...reason or inquiry may natr urally be divided into two kinds, to wit, Relations of Ideas, and Mailers of Fact. Of the first kind are the sciences of Geometry,...or demonstratively certain. That the square of the liypotliemise is equal to the square of the two sides, is a proposition which expresses a relation...

...Arithmetic, and, in. short, Ql^IX^&^^ti011 which, is eitker, ..... intmtively or demonstrati velj^certain. That the square of the hypothenuse is equal to the square of the two sides, is a proposition which expresses a relation between these figures. That three times five...

...of the forty-seventh proposition of the First Book of Euclid, viz., That in a rightangled triangle, + ֋{ s U G? \ΟGGϾ 7 ? >lE >u wJ| +N n] V . 5| 4W z2> From the word hecatomb, was probably derived the name of the Greek month Hecatomlxson, which commenced...

...example, we have said, in speaking of reciprocal properties, that it was one of rectangled triangles, that the square of the hypothenuse is equal to the square of the sides. This is clear and certain to those who understand it, and those who do not understand it may...

...or inquiry may naturally be divided into two kinds, to wit, Relations of Ideas, and Matters of Fart. Of the first kind are the sciences of Geometry, Algebra,...That the square of the hypothenuse is equal to the squares of the two sides, is a proposition which expresses a relation between these figures. That three...

...reason or inquiry may naturally be divided into two kinds, to wit, Relations of Ideas, and Matters of Fact Of the first kind are the sciences of Geometry,...or demonstratively certain. That the square of the hyjwthenuse is equal to the squares of the two sides, is a proposition which expresses a relation between...