Recreations in Mathematics and Natural Philosophy ...

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Side 306 - From this it is manifest that the side of the hexagon is equal to the radius of the circle.
Side 171 - Three jealous husbands, with their wives, having to cross a river at a ferry, find a boat without a boatman ; but the boat is so small that it can contain no more than two of them at once. How can these six persons cross the river...
Side 144 - ... last, you must take that of the second and last; then add together those which stand in the even places, and form them into a new sum apart; add also those in the odd places, the first excepted, and subtract this sum from the former: the remainder will be the double of the second number ; and if the second number, thus found, be subtracted from the sum of the first and second, you will have the first number ; if it be taken from that of the second and third, it will give the third; and so of...
Side 84 - The hyosciamus, which, of all the known plants produces, perhaps, the greatest number of seeds, would, for this purpose require no more than four years. According to some experiments, it has been found that one stem of the hyosciamus produces...
Side 146 - It may be readily seen that the pieces, instead of being in the two hands of the same person, may be supposed to be in the hands of two persons, one of whom has the even number, or piece of gold, and the other the odd number, or piece of silver. The same operations may then be performed in regard to these two persons as are performed in regard to the two hands of the same person, calling the one privately the right, and the other the left.
Side 173 - The four nuns thea came back ; each with a gallant^ and the abbess on paying them another visit, having again counted 9 persons in each row, entertained no suspicion of what had taken place. But 4 more men were introduced, and the abbess again counting 9 persons in each row, retired in the full persuasion that no one had either gone out, or come in. How was all this possible ? This problem may be easily solved by inspecting the four following figures; the first of which represents the original disposition...
Side 137 - Tell the person to multiply the number thought of by itself; then desire him to add 1 to the number thought of, and to multiply it also by itself; in the last place, ask him to tell the difference of these two products, which will certainly be an odd number, and the least half of it will be the number required. Let the number thought of, for example, be 10; which, multiplied by itself...
Side 145 - A person having in one hand an even number of shillings, and in the other an odd, to tell in which hand he has the even number. Desire the person to multiply the number in the right hand by any even number whatever, such as 2 ; and that in the left by an odd number, as 3 ; then bid him add together the two products, and if the whole sum be odd, the even number of shillings will be in the right hand, and the odd number in the left ; if the sum be even, the contrary will be the case.
Side 143 - ... four, 555; and so on; for the remainder will be composed of figures of which the first on the left will be the first number thought of, the next the second, and so on. Suppose the...
Side 174 - U almost needles« to explain in what manner the illusion of the good abbess arose, It is because the numbers in the angular cells of the square were counted twice ; these cells being common to two rows. The more therefore the angular cells are filled, by emptying those in the middle of each band, these double enumerations become greater ; on which account the number, though diminished, appears always to be the same...