 ... squares on the diagonals are together equal to twice the sum of the squares on the straight lines joining the middle points of opposite sides. 150. If a circle be described round the point of intersection of the diameters of a parallelogram as a centre,...  Elements of Quaternions - Page 232by Arthur Sherburne Hardy - 1881 - 230 pagesFull view - About this book
 | 1809 - 596 pages
...lines drawn from any point in it, to all the given points, must be always of the game magnitude. Now, the sum of the squares of the lines drawn from any point to all the given points, may be shewn by plane geometry to be equal to the s.iuare of the line drawn... | |
 | John Playfait - 1822 - 516 pages
...lines drawn from any point in it, to all the given points, must be always of the same magnitude. Now, the sum of the squares of the lines drawn from any point to all the given points, may be shown by plane geometry to be equal to the square of the line drawn... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...intersection of the diameters of a parallelogram as a centre, shew that the sum of the squares on the straight lines drawn from any point in its circumference to...four angular points of the parallelogram is constant. 151. The squares on the sides of a quadrilateral are together greater than the squares on its diagonals... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...intersection of the diameters of a parallelogram as a centre, shew that the sum of the squares on the straight lines drawn from any point in its circumference to...four angular points of the parallelogram is constant. 151. The squares on the sides of a quadrilateral are together greater than the squares on its diagonals... | |
 | 1876 - 400 pages
...intersection of the diameters of a parallelogram ai a centre, show that the snm of the squares on the straight lines drawn from any point in its circumference to |the four angular poiats of the parallelogram i» constant.— GIOKQE G. SWAN. 32. A certain sum of money'put out at... | |
 | Mathematics - 1878 - 410 pages
...perpendiculars, and also Ct perpendicular to AO produced. It is well known that AO'+CO2 = DO2 1 + BO*, ie, the sum of the squares of the lines drawn from any point to the opposite I angles of a square or rectangle = the sum of I the squares of the two lines drawn... | |
 | Isaac Todhunter - Euclid's Elements - 1880 - 426 pages
...intersection of the diameters of a parallelogram as a centre, shew that the sum of the squares on the straight lines drawn from any point in its circumference to...four angular points of the parallelogram is constant. 151. The squares on the sides of a quadrilateral are together greater than the squares on its diagonals... | |
 | John Casey - Geometry - 1882 - 186 pages
...side. Cor. 1. — If the point P be in the circumference of the O, we have the following theorem : — The sum of the squares of the lines drawn from any point in the circumference of a circle to the angular points of an inscribed polygon is equal to 2»E 2 . Dem.... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...intersection of the diameters of a parallelogram as a centre, shew that the sum of the squares on the straight lines drawn from any point in its circumference to...four angular points of the parallelogram is constant. 151. The squares on the sides of a quadrilateral are together greater than the squares on its diagonals... | |
 | John Casey - Geometry - 1888 - 279 pages
...proved. Cor. 1. — If the point P be in the circumference of the O, we have the following theorem : — The sum of the squares of the lines drawn from any point in the circumference of a circle to the angular points of an inscribed polygon is equal to 2^R2. The following... | |
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