Existence, Co-existence, Sequence, Causation, Resemblance: one or other of these is asserted (or denied) in every proposition which is not merely verbal. This five-fold division is an exhaustive classification of matters-of-fact; of all things that can be believed, or tendered for belief; of all questions that can be propounded, and all answers that can be returned to them. Royyyyyyyyyyy! Thats swell. How’s your big girl? Hazel. He put on his worried look again and said: I’m supposed to meet her at five. How long will it be before you’re able to go back to San Francisco? The Wendel girl was prettier than Id thought she’d be from her picture. Medium-sized, quite dark, and apparently not too fond of talking. At least she seemed to spend most of her time either listening or dancing. Lester agreed this was reasonable. I said:Dya think this big amp-tray of yours could find out what the Wendel woman is getting a divorce for? Why her husband can’t see her? How’s that for an angle? What about your friend Kewpie Martin? The theory of chances consists in reducing all events of the same kind to a certain number of cases equally possible, that is, such that we areequally undecided as to their existence; and in determining the number of these cases which are favorable to the event of which the probability is sought. The ratio of that number to the number of all the possible cases is the measure of the probability; which is thus a fraction, having for its numerator the number of cases favorable to the event, and for its denominator the number of all the cases which are possible. Rob Trenton shook his head.Im afraid I can’t tell you any of it. So plausible, so convincing and so charming was Ostranders conversation, that Rob Trenton began to fight against becoming an inanimate chattel, a hundred and thirty-six pounds of weight to be distributed in the right rear of the car, balancing the boxes of cowbells which Ostrander had so painstakingly collected. How about water? Rob asked thickly. The proposition now stated is the text on which the two succeeding chapters will furnish the comment. Curt? she whispered. 108 Ill say it’s a perfect case, Captain Harmon agreed fervently. When was it, Mom? Every theorem in geometry is a law of external nature, and might have been ascertained by generalizing from observation and experiment, which in this case resolve themselves into comparison and measurement. But it was found practicable, and, being practicable, was desirable, to deduce these truths by ratiocination from a small number of general laws of nature, the certainty and universality of which are obvious to the most careless observer, and which compose the first principles and ultimate premises of the science. Among these general laws must be included the same two which we have noticed as ultimate principles of the Science of Number also, and which are applicable to every description of quantity; viz., The sums of equals are equal, and Things which are equal to the same thing are equal to one another; the latter of which may be expressed in a manner more suggestive of the inexhaustible multitude of its consequences, by the following terms: Whatever is equal to any one of a number of equal magnitudes, is equal to any other of them. To these two must be added, in geometry, a third law of equality, namely, that lines, surfaces, or solid spaces, which can be so applied to one another as to coincide, are equal. Some writers have asserted that this law of nature is a mere verbal definition; that the expressionequal magnitudes means nothing but magnitudes which can be so applied to one another as to coincide. But in this opinion I can not agree. The equality of two geometrical magnitudes can not differ fundamentally in its nature from the equality of two weights, two degrees of heat, or two portions of duration, to none of which would this definition of equality be suitable. None of these things can be so applied to one another as to coincide, yet we perfectly understand what we mean when we call them equal. Things are equal in magnitude, as things are equal in weight, when they are felt to be exactly similar in respect of the attribute in which we compare them: and the application of the objects to each other in the one case, like the balancing them with a pair of scales in the other, is but a mode of bringing them into a position in which our senses can recognize deficiencies of exact resemblance that would otherwise escape our notice..