Elements of geometry and trigonometry . PROBLEM XVL To construct a rectangle equivalent to a given square, and havingthe sum of its adjacent sides equal to a given line. Let C be the square, and AB equal to the sum of the sidesof the required rectangle. Upon AB as a diame-ter, describe a semicir-cle ; draw the line DEparallel to the diameter,at a distance AD from it,equal to the side of thegiven square C ; from the point E, where the parallel cuts thecircumference, draw EF perpendicular to the diameter ; AFand FB will be the sides of the rectangle required. For their sum is equal to AB ; and t
Elements of geometry and trigonometry . PROBLEM XVL To construct a rectangle equivalent to a given square, and havingthe sum of its adjacent sides equal to a given line. Let C be the square, and AB equal to the sum of the sidesof the required rectangle. Upon AB as a diame-ter, describe a semicir-cle ; draw the line DEparallel to the diameter,at a distance AD from it,equal to the side of thegiven square C ; from the point E, where the parallel cuts thecircumference, draw EF perpendicular to the diameter ; AFand FB will be the sides of the rectangle required. For their sum is equal to AB ; and their rectangle isequivalent to the square of EF, or to the square of AD ; hencethat rectangle is e(^ivalent to the given square C. Scholium. To render the problem possible, the distance ADmust not exceed the radius ; that is, the side of the square Cmust not exceed the half of the line BOOK IV. 1U7 PROBLEM XVII. To construct a rectangle that shall he equivalent to a givensquarey and the difference of whose adjacent sides shall heequal to a given line. Suppose C equal to the given square, and AB the differenceof the sides. Upon the given line AB as a diame-ter, describe a semicircle : at the ex-tremity of the diameter draw the tan-gent AD, equal to the side of the squareC ; through the point D and the centreO draw the secant DF ; then will DEand DF be the adjacent sides of therectangle required. For, first, the difference of these sidesis equal to the diameter EF or AB ;secondly, the rectangle DE, DF, isequal to AD^ (Prop. XXX.) ; hence that rectangle is equivalentto the given square C.
Size: 2412px × 1036px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bo, bookcentury1800, booksubjectgeometry, booksubjecttrigonometry
