## Recreations in mathematics and natural philosophy, recomposed by m. Montucla and tr. by C. Hutton1840 |

### From inside the book

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**polygons**, having a common centre . These are different from the preceding ; for the series of the triangulars of this kind is 1 , 4 , 10 , 19 , 31 , & c . , which are formed by the successive addition of the numbers 1 , 3 , 6 , 9 , 12 ... Page 22

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**polygon**less 2 ; multiply this first product by the proposed number , and to the new product add the square of a num- ber equal to that of the angles of the**polygon**less 4 : if the sum be a perfect square , the given number is a**polygon**... Page 23

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**polygon**of 36 sides , the radix of which is 2 ; for the two first terms of the progression are 1 , 35. The same number 36 is a square ; and lastly it is tri- angular , having 8 for its radix . In the like manner , 21 is a**polygon**of 21 ... Page 24

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**polygon**less 2 ; to the sum add three times the square of the said number of terms , and subtract from it the product of the same number multiplied by that of the angles less 5 : if you divide the remainder by 6 , you will have the sum ... Page 131

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**polygons**in the circle , is given in various books of practical geometry . On the diameter A B ( Fig . 44. ) of the given circle , describe an equilateral triangle ; and divide this diameter into as many equal parts as the required**polygon**...### Contents

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### Other editions - View all

Recreations in Mathematics and Natural Philosophy, Recomposed by M. Montucla ... Jacques Ozanam No preview available - 2018 |

Recreations in Mathematics and Natural Philosophy, Recomposed by M. Montucla ... Jacques Ozanam No preview available - 2015 |

Recreations in Mathematics and Natural Philosophy, Recomposed by M. Montucla ... Jacques Ozanam No preview available - 2019 |

### Common terms and phrases

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### Popular passages

Page 254 - A CENTURY OF THE NAMES AND SCANTLINGS OF SUCH INVENTIONS, as at present I can call to mind to have tried and perfected...

Page 333 - Difference of colour if therefore not a test of difference of refrangibility, and the conclusion deduced by Newton is no longer admissible as a general truth : " That to the same degree of refrangibility ever belongs the same colour, and to the same colour ever belongs the same degree of refrangibility.

Page 138 - From this it is manifest that the side of the hexagon is equal to the radius of the circle.

Page 475 - The rings of Saturn must present a magnificent spectacle from those regions of the planet which lie above their enlightened sides, as vast arches spanning the sky from horizon to horizon, and holding an invariable situation among the stars. On the other hand, in the regions beneath the dark side, a solar eclipse of fifteen years...

Page 254 - An admirable and most forcible way to drive up water by fire, not by drawing or sucking it upwards, for that must be as the philosopher calleth it, infra spheeram activitatis, which is but at such a distance. But this way hath no bounder, if the vessels be strong enough ; for I have taken a piece of a whole cannon, whereof the end was burst, and filled it...

Page 344 - And if he hold out his hand towards the mirror, the hand of the image will come out towards his hand, and coincide with it, of an equal bulk, when his hand is in the centre of concavity; and he will imagine he may shake hands with his image.

Page 450 - But since the mean synodic motion of the moon is at the rate of 30" per minute, it follows that the duration of a total solar eclipse can never exceed four minutes.

Page 254 - One vessel of water rarefied by fire driveth up forty of cold water, and a man that tends the work has but to turn two cocks; that one vessel of water being consumed, another begins to force and refill with cold water, and so successively ; the fire being tended and kept constant, which the selfsame person may likewise abundantly perform in the interim between the necessity of turning the said cocks.

Page 333 - ... very little of the violet. The yellow space, which has not been much absorbed, has increased in breadth. It occupies part of the space formerly covered by the orange on one side, and part of the space formerly covered by the green on the other. Hence it follows, that the blue glass has absorbed the red light, which, when mixed with the yellow light, constituted orange, and has absorbed also the blue light, which, when mixed with the yellow, constituted the part of the green space next to the...

Page 291 - ... each side, make two marks ; then place yourself directly opposite to the paper, and hold the end of your finger before your face in such a manner, that when the right eye is open, it shall conceal the mark on the left, and, when the left eye is open, the mark on the right : if you then look with both eyes to the end of your finger, the paper, which is not at all concealed by it from either of your eyes, will, nevertheless, disappear.