...following passage in Dr. Button.s Mathematical Dictionary. In reference to the theorem that the square on the hypothenuse of a right-angled triangle is equal to the sum of the squares on the sides, it is remarked, that " Plutarch even doubts whether such a sacrifice was...

...and joining them by a string, this forms a right-angled triangle. The boys having learned that the sum of the squares of the two sides containing the right angle is equal to the square on the third side, the teacher will tell them, for instance, to draw a line...

...And Apollodorus, the logician, records of him, that he sacrified a hecatomb, when he had discovered that the square of the hypothenuse of a right-angled triangle is equal to the squares of the sides containing the right angle. And there is an epigram which is couched in the...

...And Apollodorus, the logician, records of him, that he sacrified a hecatomh, when he had discovered that the square of the hypothenuse of a right-angled triangle is equal to the squares of the sides containing the right angle. And there is an epigram which is couched in the...

...sets, is a truth ; any two sides of a triangle are together greater than the third side, is a truth ; the square of the hypothenuse of a right-angled triangle is equal to the sum of the squares of the other two sides, is a truth ; but you may be successful in the world, and enter...

...case and iustantaneousness 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...

...place and space, that it 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...

...of any kind. If I 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,...

...which is equally distant from a common point? And when it is fairly demonstrated that the square upon the hypothenuse of a right-angled triangle is equal to the sum of the squares of the other two sides, can any subsequent progressive knowledge prove this theorem false...

...we have treated as 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...