A Treatise on the Conic Sections; In Five Books (Paperback)

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1794 edition. Excerpt: ...the squares of the segments of the touching parallels, or the square of, the segment of the touching parallel and the rectangle under the segments of the parallel which cuts, or the rectangles under the segments of the cutting parallels, shall be in the fame proportion as the rectangles under the segments of the cutting line j understanding the segments to be as in the preceding.. ).;. This is inserred in the fame manner as the preceding Cor. 74, 75-Cor. 3. If two right lines meeting each others, do both touch, or the one touch and the other cut, or both cut the fame section or opposite sections, and two other right Jincs parallel, to the former pair fall upon the section or sections in like manner; the squares of the first pair if they both touch, or the square of the one which touches and the rectangle under the segment of the one which cuts, or the rectangles under the segments of each if both cut, shall be in the fame proportion as the like squares or rectangles of the other Pair... I-: . s.. " .. ..".-. For the magnitudes of the one pair and the magnitudes' of the other pair are proportional to the fame focal lines. Cor. 4. The focal lines or focal ordinates parallel to two diameters of the ellipse or hyperbola, are in the duplicate proportion of the semidiameters, or of the diameters. This in the case of the ellipse is the Prop, itself in other words; for the diameters mutually bisecting each other in the centre, the rectangle under the segments of each 'diameter becomes the square of the semidiameter, and therefore the focal parallels are as the F I G..squares1 of the semidiameters, or of the diameters. But in the case of the hyperbola, the Cor. is thus illustrated. 86. Let ED, MN, parallel to any two diameters of the hpperbola be...