| Mathematics - 1836 - 488 pages
...which are about the diameter of any parallelogram, are equal to one another. XLVII. In any right angled **triangle, the square which is described upon the side...described upon the sides which contain the right angle.** XLVIII. If the square described upon one of the sides of a triangle, be equal to the squares described... | |
| John Playfair - Geometry - 1836 - 148 pages
...square upon the side BC,. is equal to the squares upon the sides AB, AC. Therefore, in any right angled **triangle, the square which is described upon the side...described upon the sides which contain the right angle.** Which was to be proved. PROP. XVIIL THEOR. If the square described upon one of the sides of a triangle... | |
| Andrew Bell - Euclid's Elements - 1837 - 290 pages
...parallelogram that has one right angle has all its angles right angles. PROPOSITION XL VII. THEOREM. **In any right-angled triangle, the square which is...described upon the sides which contain the right angle.** Let ABC be a right-angled triangle having the right angle BAG ; the square described upon the side... | |
| Euclides - Euclid's Elements - 1837 - 112 pages
...ADE = 2 right Zs, 5. that the fig. is rectangular (and :. a square.) PROPOSITION XLVII. ii Theorem. **In any right-angled triangle, the square which is...described upon the sides which contain the right angle.** In the construction of the figure it is necessary to show that GA is on the same right line with AC... | |
| Edward Tagart - Logic - 1837 - 156 pages
...of the term straight, the less likely they were to enclose a space. If I were asked how I know that **in any rightangled triangle the square which is described...described upon the sides which contain the right angle,** my first answer might be, that I knew it by studying the 47th of the first book of Euclid. But the... | |
| Euclid, James Thomson - Geometry - 1837 - 410 pages
...I. THEOR. IN any right-angled triangle, the square which is described upon the hypotenuse, that is, **the side subtending the right angle, is equal to the...described upon the sides which contain the right angle.** Let ABC be a right-angled triangle, having the right angle BAC; the square described upon the hypotenuse... | |
| Thomas Oswald Blackett - Leveling - 1838 - 136 pages
...between the true and apparent level may also be found according to the (Prop. 47, 1st. Book EuclidJ. **In any rightangled triangle, the square which is described...described upon the sides which contain the right angle,** or, in other words, in all right angled plain triangles, the sum of the squares of the two short sides... | |
| Robert Simson - Geometry - 1838 - 434 pages
...angles right angles. PROP. XLVII. THEOR. IN any right angled triangle, the square which is described ' G **upon the side subtending the right angle, is equal...described upon the sides which contain the right angle.** Let ABC be a right angled triangle, having the right angle BAC ; the square described upon the side... | |
| Euclid - Geometry - 1838 - 478 pages
...parallelogram that has one right angle, has all its angles right angles. THE ELEMENTS OF EUCLID. G **upon the side subtending the right angle, is equal...described upon the sides which contain the right angle.** Let ABC be a right angled triangle, having the right angle BAC ; the square described upon the side... | |
| Euclides - Geometry - 1841 - 378 pages
...Hence every parallelogram that has one right angle has all its angles right angles. PROP. XLVII. THEOR. **In any right-angled triangle, the square which is...described upon the sides which contain the right angle.** Let ABC be a right-angled triangle having the BC shall be equal to the squares described upon BA, AC.... | |
| |