 ... does. From the general expression for the subtangent, just given, it follows that that is, as in the ellipse, the rectangle of the subtangent and abscissa of the point of contact is equal to the rectangle of the sum and difference of the same abscissa...  The Elements of Analytical Geometry ... - Page 153by John Radford Young - 1835 - 288 pagesFull view - About this book
 | Charles Hutton - Mathematics - 1807 - 464 pages
...first theorem. Demonstr. By theor. 35, Geom. the rectangle of the -sum and difference of the two sides, is equal to the rectangle of the sum and difference of the two segments. Therefore, by forming the sides of these rectangles into a proportion by theor. 16, Geometry,... | |
 | Charles Hutton - Mathematics - 1811 - 442 pages
...first theorem. Dermnstr. By theor. 35, Geom. the rectangle of the sum and difference of the two sides, is equal to the rectangle of the sum and difference of the two segments. Therefore, by forming the sides of these rectangles into a proportion by theor. 76, Geometry,... | |
 | Charles Hutton - Mathematics - 1822 - 616 pages
...square CD= ^. g. D. Carol. The rectangle of the sum and difference of the two sides of any triangle, is equal to the rectangle of the sum and difference of the distances between the perpendicular and the two extremes of the h:ise. or eqn;il to the. rectangle... | |
 | John Radford Young - Conic sections - 1830 - 342 pages
...subtangent must vary if x' does. From the general expression for the subtangent, just given, it follows that that is, as in the ellipse, the rectangle of the subtangent...of the same abscissa and semi-transverse axis. Thus OM-MR = A'M-MB' (91.) If we compare the expression for the normal with that for the product of the... | |
 | John Radford Young - Conic sections - 1830 - 390 pages
...subtangent must vary if / does. From the general expression for the subtangent, just given, it follows that that is, as in the ellipse, the rectangle of the subtangent...of the same abscissa and semi-transverse axis. Thus OM-MR = A'M-MB' (91.) If we compare the expression for the normal with that for the product of the... | |
 | John Radford Young - Conic sections - 1830 - 360 pages
...expression for the subtangent by x' we have " which shows that the rectangle of the subtangent aud abscissa of the point of contact is equal to the rectangle of the parts into which the diameter is divided by the ordinate. Thus, in the annexed diagram, OM • MR =... | |
 | John Radford Young - Conic sections - 1833 - 310 pages
...general expression for the subtangent by a;' we have T, x' = (A' -\-xr) (A' — x'), which shows that the rectangle of the subtangent and abscissa of the...point of contact is equal to the rectangle of the parts into which the diameter is divided by the ordinate. Thus, in the annexed diagram, OM • MR =... | |
 | Great Britain. Admiralty - Geometry - 1846 - 128 pages
...triangle from the opposite angle; the rectangle of the sum and difference of the segments of that side, is equal to the rectangle of the sum and difference of the other sides. 42. The sides of a triangle are 3, 5, and 7 ; determine the numerical values of the perpendicular... | |
 | Charles William Hackley - Geometry - 1847 - 248 pages
...equal to their difference. But the rectangle of the sum and difference of the two sides of a triangle is equal to the rectangle of the sum and difference of the segments of the base (cor., th. 27) ; therefore the rectangle of FE, EG is equal to the rectangle of... | |
 | George Roberts Perkins - Geometry - 1847 - 326 pages
...AC' - BC' = AD' - BD'. Cor. The rectangle of the sum and difference of the two sides of any triangle, is equal to the rectangle of the sum and difference of the distances between the perpendicular and the two extremes of the base, or equal to the rectangle of... | |
| |
