w the whole pack x=the number of spots required. Then the Theorem will be 13 xn-w+r=r, the number of spots required. (4) Suppose a pack of cards be dealt into seven heaps, and then there are 12 cards left out. Query, the number of spots on all the bottom cards? (5) What dimensions must I give to a joiner to make a cubical box that will hold 2000 oranges of 24 inches diameter each, supposing the oranges globular, keeping that form, and laid in rows exactly at the top of each other? Ans. 31,498 inches inside. (6) A master-joiner gives to one of his men a plank that is 10 feet by 2, with orders to make of it a square table, equal in area to the said plank, but not to exceed five segments: the poor man being ignorant of lines (and not willing his master should know it), would be greatly obliged to any one who will draw the plan how the said plank must be cut and applied together. (7) A person being asked what hour of the day it was, answered, it is between 5 and 6, and both the minute hand and hour hand are together. Required the hour of the day? (8) A lady has a dressing-table, each side of which is 27 inches: but she is desirous to know how each side of the same may 36 inches, by having 4 feet of plank, superficial measure, joined to the same. The plan in what manner the plank must be cut and applied to the table is required. (9) A gentleman purchases a piece of land in form of a parallelogram, and encloses one fourth part (as per figure) to build a house and other conveniences upon: now he desires the remainder of this land may be divided into four parts, equal and similar to each other, to be appropriated to such uses as he shall hereafter think proper. sired. (10) Required to divide a given trapezium, of two equal parts, geometrically, by the shortest line possible. The plan is de (11) A person, for a considerable wager, is to travel from a town A. to another B. but he is to call at a place which is somewhere on the line ab. Now his time limited being very short, he is desirous to know (by geometry) the situation of the place on the line ab, the distance from thence to A. and B. being the shortest possible. (12) All the different ways possible in which a gentleman can place his servants, combining them by 1, 2, 3, &c. at a time, are 960799. What number of servants does he keep? APPENDIX; CONTAINING Various Forms of Acquittances, Promissory Notes, Bills of Exchange, Letters of Advice, Letters of Credit, Bills of Parcels, and Bills on Book Debts; all of which are adapted to such circumstances as occur in real Business, to enter a Pupil in the manner and Method of Commerce, and to make him ready at Computation. A general Receipt. RECEIVED, August 9th, 1806, of Mr. Anthony Buskin, the sum of fifty pounds, in full for one quarter's rent, due at Midsummer last, and of all demands, A Receipt or Acquittance for Rent paid. RECEIVED, this 5th day of January, 1806, of Mr. Thomas Field, the sum of thirty-two pounds sixteen shillings, in money, which, with eight pounds four shillings more, disbursed by the said Thomas Field, for taxes and reparations of the messuage and tenements he now occupies, situate in Chiswell-street, London, makes in the whole the sum of forty pounds, and is in full of half a year's rent |