 If the square described on one side of a triangle be equal to the sum of the squares described on the other two sides, the angle contained by these two sides is a right angle.  Reports on Elementary schools - Page 810by Her MAjesty' Inspectors of schools - 1850Full view - About this book
 | George Darley - Euclid's Elements - 1836 - 172 pages
...there will remain the complement EGDI ;— hence, these remaining complements are equal. ART. 182. If the square described upon one side of a triangle be equal to the squares described on the other sides of the triangle, taken together, the angle opposite to the first-mentioned... | |
 | Benjamin Peirce - Geometry - 1837 - 216 pages
...parallel. 256. Theorem. The square described upon the hypothenuse of a right triangle is equivalent to the sum of the squares described upon the other two sides. Demonstration. Let squares be constructed upon the three sides of the right triangle ABC (fig. 130),... | |
 | Scotland free church, gen. assembly - 1847 - 554 pages
...straight lines, it makes the alternate angles equal. 2. If the square described on one of the sides of a triangle be equal to the sum of the squares described on the other two sides, these sides contain a right angle. 3. Divide a given line into two parts, so... | |
 | Benjamin Peirce - Geometry - 1847 - 204 pages
...parallel. ' 256. Theorem. The square described upon the hypothenuse of a right triangle is equivalent to the sum of the squares described upon the other two sides. Proof. Let squares be constructed upon the three sides of the right triangle ABC (fig. 130), right-angled... | |
 | Great Britain. Committee on Education - 1850 - 942 pages
...1. '20. Any two sides of a triangle are together greater than the third side. 9. Prove Euc. I. 48. If the square described upon one side of a triangle be equal to the squares described upon the other two sides, the angle contained by those two sides is a right angle.... | |
 | 1851 - 382 pages
...have an angle equal to a given angle, . •I. If the square described upon one of the sides _ 1C 3 of a triangle be equal to the sum of the squares described on the other two sides, the angle contained by those two sides is a right angle, . . 3. If a straight... | |
 | Euclides - 1852 - 48 pages
...from the square of the hypotenuse, and extract the square root of the difference. PEOP. XLVIII. THEOH. If the square described upon one side of a triangle be equal to the squares described upon the other two sides, the angle opposite to that side is a right angle. In the... | |
 | Thomas Lund - Geometry - 1854 - 520 pages
...converse of this proposition is also true, viz. that ' if the square described upon one of the sides of a triangle be equal to the sum of the squares described upon the other two sides of it, the angle between these two sides is a right angle.' Let ABC be a triangle, such that square of AC + square of... | |
 | Thomas Fisher - Mathematics - 1854 - 156 pages
...forty-seventh proposition of the first book of Euclid, viz : that the square described upon the hypothenuse is equal to the sum of the squares described upon the other two sides ja demonstration «>f the highest importance, from the very numerous- applications it finds in every... | |
 | Charles Davies, William Guy Peck - Mathematics - 1855 - 628 pages
...opposite the right angle. In a plane triangle the square described upon the hypothenuse is equivalent to the sum of the squares described upon the other two sides. С In the right angled triangle ВЛС, right angled at B, we have AC' О BA' + CB>. In the right angled... | |
| |
