BOARDING-HOUSE GEOMETRY. A single room is that which has no parts and no magni- tude. The landlady of a boarding-house is a parallelogram, that is, an oblong, angular figure which cannot be described, but which is equal to anything. All the other rooms being - taken, a single room is said to be a double room. The landlady can be reduced to her lowest terms by a series of propositions. A bee line may be made from any boarding-house to any other boarding-house. The clothes of a boarding-house bed though produced ever so far both ways, will not meet. Any two meals at a boarding-house arc together less than one square meal. If from the opposite ends of a boarding-house, a line be drawn, passing through all the rooms in turn, then, the hot water pipe, which warms the boarders, will lie within that line. On the same bill, and on the same side of it, there should not be two charges for the same thing. If there are two boarders on the same floor, and the amount of side of one be equal to the amount of side of the other, each to each, and the wrangle between one boarder and the landlady be equal to the wrangle between the land lady and the other, then shall the weekly bills of the two boarders be equal als,o, each to each. For, if not, let one bill be the greater, then the other bill is less than it might have been, which is absurd, Definitions and Axioms. Postulates and Propositions.