A History of Mathematics |
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Page 33
... third of a prism , and a cone one - third of a cylinder , having equal base and altitude . The proof that spheres are to each other as the cubes of their radii is probably due to him . He made frequent and skilful use of the method of ...
... third of a prism , and a cone one - third of a cylinder , having equal base and altitude . The proof that spheres are to each other as the cubes of their radii is probably due to him . He made frequent and skilful use of the method of ...
Page 48
... third book treats of the equality or proportionality of triangles , rectangles , or squares , of which the component parts are determined by portions of transversals , chords , asymptotes , or tangents , which are frequently subject to ...
... third book treats of the equality or proportionality of triangles , rectangles , or squares , of which the component parts are determined by portions of transversals , chords , asymptotes , or tangents , which are frequently subject to ...
Page 50
... third degree . About the time of Nicomedes , flourished also Diocles , the inventor of the cissoid ( " ivy - like " ) . This curve he used for finding two mean proportionals between two given straight lines . About the life of Perseus ...
... third degree . About the time of Nicomedes , flourished also Diocles , the inventor of the cissoid ( " ivy - like " ) . This curve he used for finding two mean proportionals between two given straight lines . About the life of Perseus ...
Page 63
... third hundreds , and so on . Later , frames came into use , in which strings or wires took the place of lines . According to tra- dition , Pythagoras , who travelled in Egypt and , perhaps , in India , first introduced this valuable ...
... third hundreds , and so on . Later , frames came into use , in which strings or wires took the place of lines . According to tra- dition , Pythagoras , who travelled in Egypt and , perhaps , in India , first introduced this valuable ...
Page 69
... third . Thus , take for one side an odd number ( 2n + 1 ) 2 - 12 n2 + 2n = the other side , and ( 2n + 1 ) ; then 2 ( 2n2 + 2 n + 1 ) = hypotenuse . If 2n + 1 = 9 , then the other two numbers are 40 and 41. But this rule only applies to ...
... third . Thus , take for one side an odd number ( 2n + 1 ) 2 - 12 n2 + 2n = the other side , and ( 2n + 1 ) ; then 2 ( 2n2 + 2 n + 1 ) = hypotenuse . If 2n + 1 = 9 , then the other two numbers are 40 and 41. But this rule only applies to ...
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Popular passages
Page 202 - I was so persecuted with discussions arising out of my theory of light, that I blamed my own imprudence for parting with so substantial a blessing as my quiet, to run after a shadow.
Page 298 - THEOREM If a straight line falling on two other straight lines, make the alternate angles equal to one another, the two straight lines shall be parallel to one another.
Page 21 - The formula states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the base and altitude.