 | Euclides - 1821 - 294 páginas
...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 the... | |
 | Euclid - 1822 - 222 páginas
...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 the segment... | |
 | John Playfair - 1829 - 210 páginas
...+ 2(BC.CD). Therefore, in any &c. QED PROPOSITION XIII. THEOREM. 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 contained by either of those sides and the... | |
 | Miles Bland - 1830 - 394 páginas
...sides containing the opposite angle, then will 48. In any quadrilateral figure, the square of one side is less than the sum of the squares of the other sides by twice the sum of the products of these sides taken two and two together, and multiplied by the cosine of the... | |
 | Euclid - 1833 - 216 páginas
...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 the segment... | |
 | Euclid, James Thomson - 1837 - 410 páginas
...PROP. XIII. THEOR. IN any triangle, the square of the side subtending an acute angle, is less than the squares of the other sides, by twice the rectangle contained by either of those sides, and the straight line intercepted between the acute angle and the perpendicular drawn... | |
 | Adrien Marie Legendre - 1838 - 382 páginas
...another place. GEOMETRY. PROPOSITION XII. THEOREM. In every triangle, the square of a side opposite an acute angle is less than the sum of the squares of the other two sides, by twice the rectangle contained by the base and the distance from the acute angle... | |
 | Euclides - 1840 - 82 páginas
...perpendicular let fall on it from the 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 part... | |
 | Euclides - 1840 - 192 páginas
...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 (AB)... | |
 | Euclid, James Thomson - 1845 - 382 páginas
...and twice the rectangle BC.CD. Therefore, in an obtuse-angled triangle, &c. PROP. XIII. THEOR. — In any triangle, the square of a side subtending an acute angle, is less than the squares of the other sides, by twice the rectangle contained by either of those sides, and the straight... | |
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... the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall on it from the opposite angle, and the acute angle. 
