...between the definition of a straight line and the celebrated Pythagorean demonstration that the square of the hypothenuse of a rightangled triangle is equal to the sum of the squares of the two sides, so we may be able to trace but little resemblance between the great law...

...right-angled at B, and the side AC is the hypothenuse. 356. It is an established principle in geometry, that 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. (Leg. IV. 11. Euc. I. 47.) Thus if the base of the triangle...

...right-angled at B, and the side AC is the hypothenuse. 356. It is an established principle in geometry, that the square described on the hypothenuse of a right-angled triangle, is equal to the sum of the squares described on the other too sides. (Leg. IV. 11. Euc. I. 47.) Thus if the base of the triangle...

...right-angled at B, and the side AC is the hypotheimse. 356. It is an established principle in geometry, that the square described on the hypothenuse of a right-angled triangle, is equal to the sumo? the squares described on the other two sides. (Leg. IV. 11., Euc. I. 47.) Thus, if the base...

...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...

...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...

...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...