| 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... | |
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