 | Euclides - 1864 - 448 pages
...triangles, &c. QED PROPOSITION XIII. THEOREM. In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the...sides, and the straight line intercepted between the acute angle and the perpendicular let fall upon it from the opposite angle, Let ABC be any triangle,... | |
 | Euclides - 1864 - 262 pages
...triangles, &c. QED PROPOSITION XIII. THEOREM. In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the...sides, and the straight line intercepted between the acute angle and the perpendicular let fall upon it from the opposite angle. Let ABC be any triangle,... | |
 | Woolwich roy. military acad - 1864 - 588 pages
...balls standing alternately 1 9. In every triangle the square on the side subtending an acute angle is less than the squares on the sides containing that...line intercepted between the perpendicular let fall on it from the opposite angle and the acute angle. Demonstrate the proposition in the case where the... | |
 | Robert Potts - 1865 - 528 pages
...PROPOSITION Xm. THEOREM. In every triangle, the square on the side subtending eitJter of the acate angles, is less than the squares on the sides containing...sides, and the straight line intercepted between the acute angle and the perpendicular let Jail upon it from the opposite angle. Let ABC be any triangle,... | |
 | Euclides - 1865 - 402 pages
...and the obtuse angle . . . . . n. 12. 2. In every triangle, the square on the side subtending either of the acute angles is less than the squares on the...sides containing that angle, by twice the rectangle under either of these sides, and the straight line intercepted between the acute angle and the perpendicular... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...&c. QED PROPOSITION 13. THEOREM. In every triangle, the square on the side subtending an acute angle, is less than the squares on the sides containing that...line intercepted 'between the perpendicular let fall on it from the opposite angle, and the acute angle. Let ABC be any triangle, and the angle at 5 an... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...&c. QED PROPOSITION 13. THEOREM. In every triangle, the square on the side subtending an acute angle, is less than the squares on the sides containing that...line intercepted between the perpendicular let fall on it from the opposite angle, and the acute angle. Let ABC be any triangle, and the angle at B an... | |
 | James Maurice Wilson - Geometry - 1868 - 132 pages
...on the terminated line GF. THEOREM 30. In any triangle the square on a side opposite an acute angle is less than the squares on the sides containing that...angle by twice the rectangle contained by either of those sides and the projection on it of the other side. Let AB C be a triangle, B an acute angle, BD... | |
 | Robert Potts - 1868 - 434 pages
...triangles, &c. QED PROPOSITION XIII. THEOREM. Jn every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twicp, the rectangle contained by either of these sides, and the straight line intercepted behceen... | |
 | Horatio Nelson Robinson - Geometry - 1868 - 276 pages
...square on a side opposite an acute angle is less than the sum of the squares on the other two sides, by twice the rectangle contained by either of these sides, and the distance from the vertex of the acute angle to the foot of the perpendicular let fall on this side,... | |
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In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the acute... 
