...proceeds entirely from the undeterminate meaning of words, which is corrected by juster definitions. That the square of the hypothenuse is equal to the squares of the other two sides, cannot be known, let the terms be ever so exactly defined, without a train of reasoning...

...is very strong./ That there is such a City as Rome is a Proposition of which we can doubt less than that the Square of the Hypothenuse is equal to the Squares of the two sides when the latter is demonstrated, the highest Degree of testimony leaves less doubt than Demonstration:...

...the same base and between the same parallels are equal. All right angled triangles have this property that the square of the hypothenuse is equal to the squares of the base and perpendicular etc. The general logical type of such proposition is All Zs are Xs of which...

...the power of at once enabling Zerah Colburn to perform his mental calculations. Pythagoras to prove that the square of the hypothenuse is equal to the squares of the other two sides of a right-angled triangle, and Laplace to write " La Mecanique Celeste." Observation...

...accepted or not. I ought to add that Mr. Romesh Chunder Dutt also states :—" The Geometrical theorem that the square of the hypothenuse is equal to the squares of the other two sides of a rectangular triangle is ascribed by the Greeks to Pythagoras; but it was known...

...Indian thinkers had framed out the atomic theory, and had, it is said, found the proof of the theorem that the square of the hypothenuse is equal to the squares of the other two sides of a right-angled triangle. In much later times the decimal system was perfected by...

...creative principle out of matter. This world Pythagoras represented by the Right Angle Triangle, because the Square of the Hypothenuse is equal to the squares of the two other sides, and the world as it is formed, is equal to the formation cause, and matter clothed...