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Synopsis
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. 1817 Excerpt: ...the ellipsis passes through the points A, B: it passes likewise through D (4. cor. 1. 2.), because GD is equal to CA; and through E, because CD is equal toCE. PROP. XXV. Prob. A straight line being given in position and magnitude, and a point without it being given; to describe an ellipsis, of which that straight line shall be one of the axes, and which shall pass through that given point; but the given point must be so situated, that a perpendicular drawn from it may fall between the extremities of the given straight line. Kg. 19. Let AB be the straight line given in position and magnitude, and K the given point, so situated, that a perpendicular drawn from it towards AB may fall between the extremities A, B; it is required to describe an ellipsis which may have AB for one of the axes, and which may pass through K. Draw KL at right angles to AB, and find a straight line DE such, that the square of Find a mean proportional X between AL and LE (13. 6. AB may be to the square of DE, as the rec-Book ii. tangle ALB to the square of KL; and place vv--' DE perpendicular to AB, so that they mutually bisect each other: and by the last prop, with the same AB, DE, as the axes, describe an ellipsis; this ellipsis will pass through (2. cor. 15. 2.) the point K. PROP. XXVI. Prob. To find a diameter, the centre, the axes, and the foci of an ellipsis given in position. Draw two straight lines parallel to each other, and terminated both ways by the ellipsis; the straight line which bisects them is (4. cor. 13. 2.) a diameter; and the point bisecting that diameter is (3. 2.) the centre. Elem.); then to the three straight lines, X, KL, and AB, find a fourth proportional (12. 6. Elem.) which will be the straight line DE wanted. For the square of X, that is, the rectangle ALB ...
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