. Cottage, lodge, and villa architecture. rate ; but, as before adverted to, in order to attain a complete rig 38<knowledge of the subject, as well as to be able to cope withthe different forms which occur, it is necessary to under-stand correctly their geometrical construction. Problem XXIII. The diameter of an hyperbola, a b (), its abscissa, b c, and double ordinate, d e, being given,it is required to delineate the curve by determining a certainnumber of points which shall be in its course. 1. Through b draw g f parallel to d e, and from the ex-tremities, d and e, of the ordinates,
. Cottage, lodge, and villa architecture. rate ; but, as before adverted to, in order to attain a complete rig 38<knowledge of the subject, as well as to be able to cope withthe different forms which occur, it is necessary to under-stand correctly their geometrical construction. Problem XXIII. The diameter of an hyperbola, a b (), its abscissa, b c, and double ordinate, d e, being given,it is required to delineate the curve by determining a certainnumber of points which shall be in its course. 1. Through b draw g f parallel to d e, and from the ex-tremities, d and e, of the ordinates, draw d g and e f parallelto the abscissa, b c, cutting g f in the points f and g. 2. Divide c d and c e, each into any number of equalparts, as four ; and through the points of division, a b c, oneach side of the point c, draw lines to a. 3. Divide d g and e f into the same number of equalparts, and from the points of division on d g and e f, drawlines to b. A curve drawn through the intersections at a be,that of the hyperbola on each side the Problem XXIV. The transverse and conjugate diameters, a b and c d (fig. 39), being given,it is required to determine a certain number of points in the curve with a view to its the extremity b, of the diameter a b, draw f g parallel to c d, the other diameter ; and make b f and b g equal to the semi-diametersec or e d. Through the points f and g thus deter-mined, draw e h and e j, which will be the symptotesof the figure. From a, as before, draw lines at pleasure towardsthe curve to be described, as a g, a h, a j, a k, cuttingthe asymptotes at the points abed, and efg, and h,&c. Set off the distances a h, h g, a/, a ^respectively,from the points a b c and d on the lines from a ; andthe points g h, j k, will be in the curve required.
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Keywords: ., bookcentury1800, bookdecade1870, bookpublisherlondon, booksubject
