| Euclides - 1821 - 294 pages
...rectangles under the whole produced line and, side. PROP. 13. THEOR, In any triangle the square of **the side subtending an acute angle, is less than the sum of the squares** of the sides containing that angle, by twice the rectunyle under either of them and the segment between... | |
| Euclid - 1822 - 179 pages
...rectangle under DC and CB. PROP. XIII. THEOR. In any triangle (ABC) the square of the side (AB) Fi^. 25. **subtending an acute angle is less than the sum of the squares** of the sides(AC and CB), containing that angle by twice the rectangle under either of them (AC), and... | |
| John Playfair - Geometry - 1829 - 186 pages
...base and the distance between the perpendicular and the obtuse angle. In any triangle the square of **the side subtending an acute angle is less than the sum of the squares** of the two sides containing that angle by twice the rectangle under either of these sides and the distance... | |
| Euclid - Euclid's Elements - 1833 - 183 pages
...rectangle under DC and CB. PROP. XIII. THEOPv. In any triangle {ABC) tie square of the side (AB), Fig. 25. **subtending an acute angle, is less than the sum of the squares** of the sides (AC and CB) containing that angle, by twice the rectangle under either of them (AC) and... | |
| Euclides - 1840 - 82 pages
...opposite angle and the vertex of the obtuse angle. PROP. XIII. THEOR. In any triangle, the square of a **side subtending an acute angle is less than the sum of the squares** of the sides containing that angle, by twice the rectangle contained by either of those sides and the... | |
| Euclides - 1840 - 194 pages
...AB and its external segment BD. PROP. XIII. THEOR. In any triangle (ABC) the square of a side (CB) **subtending an acute angle, is less than the sum of the squares** of the sides (CA, AB) containing that angle, by twice the rectangle contained by either of those sides... | |
| George Roberts Perkins - Geometry - 1847 - 308 pages
...illustrated by aid of the annexed diagram : n"=9' PROPOSITION XI. THEOREM. In any triangle, the square of **the side subtending an acute angle is less than the sum of the squares** of the base and the other side, by twice the rectangle of the base and the distance of the perpendicular... | |
| George Roberts Perkins - Geometry - 1850 - 332 pages
...the annexed diagram : 17 2 =9 2 +10 2+ 2.9X6. PROPOSITION XI. THEOREM. In any triangle, the square of **the side subtending an acute angle is less than the sum of the squares** of the base and the other side, by twice the rectangle of the base and the distance of the perpendicular... | |
| Euclid - Geometry - 1853 - 176 pages
...to the rectangle under the other side and its produced part. The square on the side subtending that **acute angle is less than the sum of the squares on the sides** which contain that angle, by double the rectangle under the side to which the perpendicular is drawn,... | |
| Robert Potts - 1855 - 1050 pages
...same base and on the same side of it, are between the same parallels. 4. In any triangle the square of **the side, subtending an acute angle, is less than the sum of the squares** of the sides containing that angle, by twice the rectangle contained by either of them and the segment... | |
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