## Recreations in Mathematics |

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algebra Analytic Geometry Arabic Archimedes arithmetic base bulls called cattle problem cell circle column computed coördinates cosine cows cube curve curve of pursuit dappled decimal diagonal diameter diaphote differential digits distance divided drawn eight equal equation Euclid expressed fallacy figures formula four fraction Frontinus geometry gives gnomon gravity Gregorian calendar H. E. Licks hence horizontal hyperbolic hyperbolic functions inches inclined integral numbers intersection John Herschel Julian calendar length logarithms loops magic square mathematical mathematicians method midrib moon multiply natural numbers negative notation o'clock parabola plane plate positive prime problem pyramid quadrant quantity radius ratio remainder represent result rhombus right-angled triangle selenium semicircumference shown in Fig sides sine solar solution solve speculum square root straight line student subtract sun dial tangent tion triangular number trigonometry vertical απ

### Popular passages

Page 154 - The heavens themselves, the planets, and this centre, Observe degree, priority, and place, Insisture, course, proportion, season, form, Office, and custom, in all line of order...

Page 154 - Amidst the other; whose medicinable eye Corrects the ill aspects of planets evil, And posts, like the commandment of a king, Sans check to good and bad: but when the planets In evil mixture to disorder wander, What plagues and what portents!

Page 152 - Geheimnisvoll am lichten Tag, Läßt sich Natur des Schleiers nicht berauben, Und was sie deinem Geist nicht offenbaren mag, Das zwingst du ihr nicht ab mit Hebeln und mit Schrauben.

Page 112 - And Isaiah said, This sign shalt thou have of the Lord, that the Lord will do the thing that he hath spoken: shall the shadow go forward ten degrees, or go back ten degrees? And Hezekiah answered, It is a light thing for the shadow to go down ten degrees: nay, but let the shadow return backward ten degrees. And Isaiah the prophet cried unto the Lord : and he brought the shadow ten degrees backward, by which it had gone down in the dial of Ahaz.

Page 138 - That there wasn'ta chance for one to start, For the wheels were just as strong as the thills, And the floor was just as strong as the sills And the panels just as strong as the floor, And the whipple-tree neither less nor more, And the back-crossbar as strong as the fore. And spring and axle and hub encore. And yet, as a whole, it is past a doubt In another hour it will be worn out!

Page 139 - You see, of course, if you're not a dunce, How it went to pieces all at once, — All at once and nothing first, — Just as bubbles do when they burst. End of the wonderful one-hoss shay. Logic is logic. That's all I say.

Page 139 - At half past nine by the meet'n'-house clock,— Just the hour of the Earthquake shock! —What do you think the parson found, When he got up and stared around? The poor old chaise in a heap or mound, As if it had been to the mill and ground! You see, of course, if you're not a dunce, How it went to pieces all at once,— All at once, and nothing first,— Just as bubbles do when they burst.

Page 153 - ... In order to obtain physical ideas without adopting a physical theory we must make ourselves familiar with the existence of physical analogies. By a physical analogy I mean that partial similarity between the laws of one science and those of another which makes each of them illustrate the other. Thus all the mathematical sciences are founded on relations between physical laws and laws of numbers, so that the aim of exact science is to reduce the problems of nature to the determination of quantities...

Page 153 - Then Rory, the rogue, stole his arm round her neck, So soft and so white, without freckle or speck ; And he...

Page 50 - And he made a molten sea, ten cubits from the one brim to the other : it was round all about, and his height was five cubits : and a line of thirty cubits did compass it round about.