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

...7056. 15. 43081. 22. 3.172181. 29. 207f£. 9. 9801. 16. 47089. 23. 10342656. 30. 34967ft-. 371 578. The square described on the hypothenuse of a rightangled triangle, is equal to the sum of the squares described on the other two sides. (Thomson's Legendre, B. IV. 11, Euc. I. 47.) The truth...

...contains 25 sq. ft. Hence, the square described on the hypothenuse of any right-angled triangle^ is equal to the sum of the squares described on the other two sides. OBS. Since the square of the hypothenuse BC, is 25, it follows that the , or 5, must be the hypothenuse...

...comparative solidity ? Art. 263. We have shown by a diagram in Art. 189, that the square described upon the hypothenuse of a right-angled triangle, is equal to the sum of the squares described upon the base and perpendicular. Hence, when two sides of any right-angled triangle...

...right-angled at B, mid Uio «idu JIC in tin- hypothenuse. B Base. ARTS. 575-580.] SQUARE ROOT. 371 578. The square described on the hypothenuse of a rightangled triangle, is equal to the sum of the squares described on the other two sides. (Thomson's Legendre, B. IV. 11, Euc. I. 47.) The truth...

...the square H to be equal to the number of small squares in the squares I and K. Hence, the square of the hypothenuse of a right-angled triangle is equal to the sum of the squares of both the other sides ; and, therefore, the hypothenuse is equal to the square root of...

...? 26. If you describe a square on the hypotenuse of a right-angled triangle, will it be equivalent to the sum of the squares described on the other two sides ? 27. What is the circumference of a circle? Radius? Arc? Chord? Segment? 28. What is an inscribed...

...PROPOSITION XI. THEOREM. The square described on the hypothenuse of a right angled triangle is equivalent to the sum of the squares described on the other two sides. Let the triangle ABC be right angled at A. Having described squares on the three sides, let fall from...

...that the three angles of a triangle are together equal to two right angles. Such is the truth, that the square described on the hypothenuse of a right-angled triangle, is equal to the sum of the squares described on the two other sides. Such is the law of the Binomial Theorem. Such is the...

...branches of mathematical 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 rera%i#titf »Mes," are facts, the one deduced fiwqa ^fctasrvation or...