| Euclides - 1852
...equals 48, which is less than 64, or the square of 8.] OF EUCLID. PROP. XII. THEOR. In obtuse angled **triangles, if a perpendicular be drawn from either...angles to the opposite side produced, the square of the** sides subtending the obtuse angle is greater than the squares of the sides containing the obtuse angle,... | |
| Euclides - 1853
...kd PEOPOSITION XII. — THEOREM. In obtuse-angled triangles, if a perpendicular be drawn froni any **of the acute angles to the opposite side produced,...of the side subtending the obtuse angle is greater** tJian the squares of the sides containing the obtuse angle, by twice the rectangle contained by the... | |
| Euclides - 1853
...divided in K, as was required. Which was to be done. PEOP. XII. THEOE. In any obtuse-angled triangle, **the square of the side subtending the obtuse angle is greater than the squares of the sides** including the obtuse angle, by twice the rectangle contained by either of those sides, and the straight... | |
| Thomas Lund - Geometry - 1854 - 362 pages
...obtuse-angled triangle if a perpendicular be drawn from the vertex of either of the acute angles upon **the opposite side produced, the square of the side subtending the obtuse angle is greater than the** sum of the squares of the sides forming the obtuse angle by twice the rectangle contained by the side... | |
| William Somerville Orr - Science - 1854
...to be done. PROPOSITION XII.— THEOEEM. In an obtuse-angled triangle (ABC), if a perpendicular (AD) **be drawn from either of the acute angles to the opposite side** prolonged, the square of the side (AB) subtending thf ebtuse angle is greater than the squares of the... | |
| John Playfair - Geometry - 1855 - 318 pages
...the square of AH. PROP. XII. THEOR. In obtuse angled triangles, if a perpendicular be drawn from any **of the acute angles to the opposite side produced,...obtuse angle is greater than the squares, of the sides** contammg the obtuse angle, by twice the rectangle contained by the side upon which, when produced,... | |
| Euclides - 1855
...by catting off from it a part equal to their difference, and so on continually. PROP. XIL THEOREM. **In obtuse-angled triangles, if a perpendicular be...the opposite side produced, the square of the side** tubtending the obtuse angle, ii greater than the squares of the sides containing the obtuse angle,... | |
| W. Davis Haskoll - Technology & Engineering - 1858 - 324 pages
...the square of the straight line, which is made up of the whole line and that part. In obtuse angled **triangles, if a perpendicular be drawn from either...of the acute angles to the opposite side produced,** tho square of the side subtending the obtuse angle is greater than GEOMETRICAL MEMORANDA. — PERPEls-DICULARS.... | |
| Euclides - 1858
...perpendicular It drawn from cither of tlte acute ¿s to the opposite sidt produced, the square of the fide **subtending the obtuse angle is greater than the squares of the sides containing the** rib'use angle by tiriee the rect. contained by the side upon which when produced the perp. falh, and... | |
| Sandhurst roy. military coll - 1859 - 1869 pages
...condition in italics is not fulfilled, where would the construction for this proposition fail ? 3. **In obtuse-angled triangles, if a perpendicular be drawn from either of the acute** nngles to the opposite side produced, the square of the side subtending the obtuse angle is greater... | |
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