...we have treated as 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...

...had been seen in 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...

...the' process of thought (statements and demonstrations) by which we are conducted to the conclusion, that the square of the hypothenuse of a right-angled triangle, is equal to the sum of the squares of its two sides. We affirm that, on account of what is contained in said process, that...

...extraction of the Square Root; but no figure or explanation is given, excepting the following foot-note. " The square of the hypothenuse of a right-angled triangle, is equal to the sum of the squares of the other two sides." It should be represented as on page 92. In a similar manner should...

...such 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...

...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...

...lines, and joining them by a string, this forms a right-angled triangle. The boys have 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...

...had been seen in 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 OF THE PYTHAGOREAN PROPOSITION. ВТ .1ЛМ1.Ч EDWAKD OLIVES. The square described on the hypothenuse of a right-angled triangle is equal to the sum of the squares described on the other ¿wo sides. Drop a perpendicular from the right angle to the hypothenuse,...

...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...