 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 490 pages
...harmonically. (301, 302.) * Ex. 1076. The sum of the squares of the four sides of any quadrilateral is equal to the sum of the squares of the diagonals plus four times the square of the line joining the mid-points of the diagonals. (337.) * Ex. 1077. If from a point within the triangle... | |
 | Horace Wilmer Marsh, Annie Griswold Fordyce Marsh - Mathematics - 1914 - 270 pages
...finish the demonstration. V THEOREM 29 The sum of the squares of the sides of any quadrilateral equals the sum of the squares of the diagonals plus four times the square of the line joining the middle points of the diagonals. Draw a very irregular quadrilateral. Connect the middle... | |
 | John Charles Stone, James Franklin Millis - Geometry - 1916 - 298 pages
...D'i If £ falls on D'! 31. In any quadrilateral, the sum of the squares of the four sides is equal to the sum of the squares of the diagonals plus four times ^ the square of the line-segment joining the middle points of the diagonals. SUGGESTION. — ED, EB, and EF are medians... | |
 | John Charles Stone, James Franklin Millis - Geometry - 1916 - 306 pages
...and substitute AD for DB. How does the proof differ if E falls between A and D'l HE falls onD'l 31. In any quadrilateral, the sum of the squares of the four sides is equal to the sum of the squares of the diagonals plus four times the square of the line-segment joining... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1918 - 486 pages
...harmonically. (301, 302.) * Ex. 1076. The sum of the squares of the four sides of any quadrilateral is equal to the sum of the squares of the diagonals plus four times the square of the line joining the mid-points of the diagonals. (337.) * Ex. 1077. If from a point within the triangle... | |
 | Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Plane - 1918 - 360 pages
...of opposite sides are equal. 2. The sum of the squares of the sides of a quadrilateral is equal to the sum of the squares of the diagonals plus four times the square on the line connecting their middle points. Suggestion. AE, CE, EF are medians of & ABD, BCD, and CEA,... | |
 | Herbert Ellsworth Slaught - 1918 - 344 pages
...of opposite sides are equal. 2. The sum of the squares of the sides of a quadrilateral is equal to the sum of the squares of the diagonals plus four times the square on the line connecting their middle points. Suggestion. AE, CE, EF are medians of A ABD, BCD, and CEA,... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 484 pages
...harmonically. (301, 302.) * Ex. 1076. The sum of the squares of the four sides of any quadrilateral is equal to the sum of the squares of the diagonals plus four times the square of the Hue joining the mid-points of the diagonals. (337.) * Ex. 1077. If from a point within the triangle... | |
 | Claudi Alsina, Roger B. Nelsen - Education - 2006 - 202 pages
...quadrilaterals. Theorem. In any convex quadrilateral the sum of the squares of the sides is equal to the sum of the squares of the diagonals plus four times the square of the distance between the midpoints of the diagonals. See Figure 20.4. = e2 +f2 + 4g2 FIGURE 20.4 Proof. Joining the midpoints... | |
 | Military Academy, West Point - 906 pages
...equivalent to the sum of tnesja (Wt. 12.) on the other two sides. No. 8.— Theorem: In n paralldo?ram the sum of the squares of the four sides is equivalent to ihesat (Wt. 10.) the squares of the diagonals. No. H.--(O) Problem: To inscribe a regular dodecagon... | |
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In any quadrilateral the sum of the squares of the four sides is equal to the sum of the squares of the diagonals, plus four times the square of the line joining the middle points of the diagonals. 
