 | Charles Hutton - Mathematics - 1811
...equal to the squares of AB, BC,. together with twice the rectangle of AB, BD. c^ ED THEOREM XXXVII. IN any Triangle, the Square of the Side subtending an Acute Angle, is Less than the Squares of the Base and the other Side, by Twice the Rectangle of the Base and the Distance of the... | |
 | Charles Hutton - Mathematics - 1812
...the squares of AB, BC, together with twice the rectangle of AB, BD. q. B. i>. THEOREM XXXVII. 0, 4^» IN any Triangle, the Square of the Side subtending an Acute Angle, is Less than the Squares of the Base and the other Side, by Twice the Rectangle of the Base and the Distance of the... | |
 | Charles Hutton - Mathematics - 1822 - 618 pages
...equal to the squares of AB, BC, together with twice the rectangle of AB, BD. u- ED THEOREM XXXVII. IN any Triangle, the Square of the Side subtending an Acute Angle, is Less than the Squares of the Base and the other Side, by Twice the Rectangle of the Base and the Distance of the... | |
 | 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 the segment... | |
 | John Playfair - Geometry - 1829 - 186 pages
...twice the rectangle under the base and the distance between the perpendicular and the obtuse angle. In any triangle the square of the side subtending...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... | |
 | Adrien Marie Legendre - Geometry - 1830 - 344 pages
...another place. THEOREM. 191. In any triangle, the square of the side opposite either of the acute angles, is less than the sum of the squares of the sides containing it, by twice the rectangle contained by either of ilie latter sides and the distance from the acute... | |
 | 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 the segment... | |
 | Euclid - Geometry - 1837 - 410 pages
...of BC, CA, and twice the rectangle BC.CD. Therefore, in an obtuse-angled triangle, &c. 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... | |
 | Adrien Marie Legendre - Geometry - 1838 - 386 pages
...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 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...squares of the sides containing that angle, by twice the rectangle contained by either of those sides and the part of it intercepted between the perpendicular... | |
| |
In any triangle, the square of the side subtending an acute angle is less than the sum of the squares of the... 
