A History of Mathematics |
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Page 25
... curve which served to divide an angle not only into three , but into any number of equal parts . This same curve was used later by Deinostratus and others for the quadrature of the circle . On this account it is called the quadratrix ...
... curve which served to divide an angle not only into three , but into any number of equal parts . This same curve was used later by Deinostratus and others for the quadrature of the circle . On this account it is called the quadratrix ...
Page 32
... curves , Menæchmus must have succeeded well in investigating their properties . Another great geometer was Dinostratus , the brother of Menæchmus and pupil of Plato . Celebrated is his mechanical solution of the quadrature of the circle ...
... curves , Menæchmus must have succeeded well in investigating their properties . Another great geometer was Dinostratus , the brother of Menæchmus and pupil of Plato . Celebrated is his mechanical solution of the quadrature of the circle ...
Page 46
... curves were now no longer applicable . Instead of calling the three curves , sections of the acute - angled , ' ' right - angled , ' and ' obtuse - angled ' cone , he called them ellipse , parabola , and hyperbola , respectively . To be ...
... curves were now no longer applicable . Instead of calling the three curves , sections of the acute - angled , ' ' right - angled , ' and ' obtuse - angled ' cone , he called them ellipse , parabola , and hyperbola , respectively . To be ...
Page 47
... curve ; now , through any point whatever of the diameter of the curve , draw at right angles an ordinate : the square of this ordinate , comprehended between the diameter and the curve , will be equal to the rectangle constructed on the ...
... curve ; now , through any point whatever of the diameter of the curve , draw at right angles an ordinate : the square of this ordinate , comprehended between the diameter and the curve , will be equal to the rectangle constructed on the ...
Page 48
... curve and the perpendicular erected at one of its extremities suffice to construct the curve . These are the two elements which the ancients used , with which to establish their theory of conics . The perpendicular in question was ...
... curve and the perpendicular erected at one of its extremities suffice to construct the curve . These are the two elements which the ancients used , with which to establish their theory of conics . The perpendicular in question was ...
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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.