 | Sir John Leslie - Geometry, Plane - 1809 - 522 pages
...perpendicular, ; . PROP. XXX. THEOR. In any triangle the sum of the squares of the sides, is equivalent to twice the square of half the base and twice the square of the straight line which joins the point of bisection with the vertex. For let fall the perpendicular... | |
 | Sir John Leslie - Geometry - 1817 - 456 pages
...proposition. PROP. XXII. THEOR. In any triangle, the sum of the squares of the sides, is equivalent to twice the square of half the base and twice the square of the straight line which joins the point of its bisection with the vertex. Let BD be drawn from the... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...to A. The square described on EH, therefore, is the required square. PROP. A. THEOR. THE squares of two sides of a triangle are together equal to twice the square of half the remaining side, and twice the square of the straight line drawn from its point of bisection to the... | |
 | Jacques Ozanam - 1840 - 850 pages
...Alexandrinus. THEOREM xr. If the bate of a triangle be bisected, the squares of the other two sides are equal to twice the square of half the base, and twice the square of the line joining the middle point of the base to the vertical angle. Fig. 31. For let D (Fig. 31.)... | |
 | Euclides - Geometry - 1841 - 378 pages
...quadrilateral figure, form a parallelogram. 9. In any triangle, the sum of the squares of the sides is equal to twice the square of half the base, and twice the square of the straight line, which joins the point of bisection with the vertex. 10. Four times the sum of the... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...A. The square described on EH, therefore, is the required square. PROP. A. THEOR. — The squares of two sides of a triangle are together equal to twice the square of half the remaining side, and twice the square of the straight line drawn from its point of bisection to the... | |
 | Alpheus Crosby - Geometry - 1847 - 190 pages
...squares, in both cases, what square is taken twice ? AB2 + AC2 «a 2BD2 + 2AD«? § 207. THEOR. V. The squares of any two sides of a triangle are together equal to twice the squares of half the third side, and of the straight line drawn from the middle of this side to the... | |
 | Euclides - Geometry - 1853 - 176 pages
...hypotenuse. 9. If the base of a triangle be bisected, the sum of the squares of the other two sides is equal to twice the square of half the base and twice the square of the line drawn from the point of bisection to the vertical angle. 10. If the middle points of the opposite... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...to the rectangle under BD and DC, iince BE is equal to EC. QED PROP. B. — THEOREM. The squares on two sides of a triangle are together equal to twice the square on half the remaining side, and twice the square on the straight line drawn from its point of bisection... | |
 | Canada. Department of the Interior - 1888 - 756 pages
...latitude of place of observation ? PLANK GIOMKTRY AND MENSURATION^ Time, 3 hours. 1. The squares on two sides of a triangle are together equal to twice the square on half the third side and twice the square on the line joining the middle point of the third side... | |
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To describe a square that shall be equal to a given rectilineal figure. To describe an isosceles triangle having each of the angles at the base double of the third angle. To inscribe a regular pentagon in a given circle. The squares on two sides of a... 
