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Recreations in mathematics and natural philosophy ...
Jacques Ozanam,Jean Etienne Montucla
Vista completa - 1814
added angle arithmetical progression arranged axis band BLEM cards cells centre chances chord circular sector circumference combinations consequently construction contained cube demonstrated diagonal diameter dice divided dodecagon double doublet draw drawn easily ellipsis employed equal evident example faces figure four fourth geometrical progression geometricians give given circle gonal greater half hexagon Hippocrates of Chios hypothenuse inscribed intersect last place latter less lunule magic square manner means method Montucla multiply natural numbers necessary number of terms number thought parallel parallelogram Parcieux pentagon perimeter perpendicular person pints polygon prime numbers PROB probability problem proportion proposed quadrature quotient radius radix ratio readily seen rectangle rectilineal remainder rightangled triangle semicircle sides sine solution squarable square number straight line subtract third throwing tion trapezium unity whole number
Página 66 - ... for the value of the twenty-fourth nail in his shoes, reckoning one farthing for the first nail, two for the second, four for the third, and so on to the twenty-fourth. The gentleman, thinking...
Página 147 - It is almost needless to explain in what manner the illusion of the good abbot 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...
Página 123 - 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.
Página 113 - Desire the person, who has thought of- a number, to triple it, and to take the exact half of that triple if it be even, or the greater half if it be odd. Then desire him to triple that half, and ask him how many times it contains 9 ; for the number thought, if even, will contain twice as many units as it does nines, and one more if -it be odd.
Página 54 - It is clear that to pick up the first stone and put it into the basket, the person must walk two yards, one in going...
Página 123 - ... following method : — Some value, represented by an even number, such as 8, must be assigned to the gold, and a value represented by an odd number, such as 3, must be assigned to the silver; after which, desire the person to multiply...
Página 53 - Multiply one half the sum of the first and last terms by the number of terms. Thus, the sum of eight terms of the series whose first term is 3 and last term 38 is 8 x * (3 + 38) = 164.
Página 114 - METHOD. Bid the person 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.