This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1888 edition. Excerpt: ...must a ladder be placed so that without moving it at the base it will reach to the top of each tree, the diameter of the garden being 40 feet. Construction.--Let ABC be the circular garden and A C its diameter, fnd let AF and CD be the two trees at the extremities of the diameter. Connect the tops of the trees by the line FD and from the middle point E of FD let fall the the perpendicular EH. Draw EG perpendicular to FD. Then all points of EG are equally distant from FD. At G draw BG perpendicular to A C. Then all points of BG are equally distant from F and D. Hence, B is the required point. 1. A C=2/v=40ft., the diameter of the garden. 2. CD--a=S0 ft., the height of the tree CD, and 3. AF=--b=2G ft, the height of the tree AF. 4. Df=DC--CJ(--=AF) = a--b =-=40 ft.--30 ft.=l0 ft. 5. EH--= ( CZM-AF) = a+b) =4(40 ft.+30 ft.) = 35 ft. By similar triangles, 6. FI.ID:: EH: HG, or 1R: a--b: a+b): HG Whence, II. I. What is the diameter of the largest circular ring that can be put in a cubical box whose edge is 1 foot? Construction.--Let ABCD--jbe the cubical box. Let /, Kr L, M, N, and P, be the middle points of the edge CF, GF, GH% HA, AB, and BC respectively. Connect these points by the lines AT, KL, LM, MN, NP, and PI. Then IKLMNP is a regular hexagon, and the largest ring that can be put in the box will be the inscribed cri- cle of the hexagon. in. 12 feet is the distance from A to where it leaves the I. How many acres are there in a square tract of land containing as many acres as there are boards in the fence inclosing it, if the boards are 11 feet long and the fence is4 boards high? fl. Slf, e) =number of acres in the tract, the side being exlot) pressed in rods. 2. 4Xl6X-'e=number of feet in the perimeter of the field. SECOND SOLUTION..
The Austro-Hungarian Monarchy Revisited
Columbia University Press