...am proving that any two sides of a triangle are greater than the third side ; or that the square of the hypothenuse of a right-angled triangle is equal to the sum of the squares of the two sides, I am engaged in proving a proposition, that no prejudice, no passion,...

...has here. Swedenborgianism, then, is as demonstrably false, as the proposition that the square •of the hypothenuse of a right-angled triangle is equal to the sum of the squares of its two sides, is demonstrably true, and we are no more liable to err, in affirming...

...one of the Methods of Proof. Thus, I may learn at tirstfrom actual measurement, that the square of the hypothenuse of a right-angled triangle is equal to the sum of the squares of the two other sides, and then prove it as a necessary and invariable property of all...

...one of the Methods of Proof. Thus, I may learn at first from actual measurement, that the square of the hypothenuse of a right-angled triangle is equal to the sum of the squares of the two other sides, and then prove it as a necessary and invariable property of all...

...and physical science. That " a whole is greater than any of its parts,"—that " the square described on the hypothenuse of a right-angled triangle is equal to the sum of the squares described on its remaining sides," are facts, the one deduced from observation or simple...

...other as the squares of their radii, diameters or circumferences. FIG. 12. 6. The square described on the hypothenuse of a right-angled triangle is equal to the sum of the squares described on the other two sides. This will be seen by counting the small squares in the...

...propositions as the following? "Things equal to the same things are equal to one another," — " The square of the hypothenuse of a right-angled triangle is equal to the sum of the squares of the two sides," — "6+4=10," — "X=Z,"&c.? The whole science of logic has been constructed...

...practical examples, before the science was established by abstract reasoning. Thus, that the square of the hypothenuse of a right-angled triangle is equal to the sum of the squares of the other two sides, was an experimental discovery, or why did the discoverer sacrifice...

...demonstration. Take an illustration. Euclid came to the conclusion in his own mind — no matter how — that the square on the hypothenuse of a right-angled triangle is equal to the squares on the two sides. To convince others of this truth, he pursues an argument from the beginning,...

...implies ease and instantaneousness of operation. Take the geometrical theorem, that the square described on the hypothenuse of a right-angled triangle is equal to the sum of the squares on the two other sides ; it is proved by a series of propositions, the connection of each...