 | Jacob William Albert Young - Mathematics - 1911 - 434 pages
...numbers which define analytically the desired geometric elements can be derived from those defining the given elements by a finite number of rational operations...located by means of points either initially given or obtainal as the intersections of two straight lines, a straight line and a circle, or two circles.... | |
 | ELEMENTARY THEORY OF EQUATIONS - 1914 - 212 pages
...the construction, and therefore also the length ± xi of the segment joining two of them, are found by a finite number of rational operations and extractions of real square roots, performed upon rational numbers and numbers obtained by earlier ones of these operations. If xi is... | |
 | Leonard Eugene Dickson - Equations, Theory of - 1914 - 200 pages
...the construction, and therefore also the length ± Xi of the segment joining two of them, are found by a finite number of rational operations and extractions of real square roots, performed upon rational numbers and numbers obtained by earlier ones of these operations. If xi is... | |
 | Leonard Eugene Dickson - Equations, Theory of - 1922 - 194 pages
...numbers which define analytically the desired geometric elements can be derived from those defining the given elements by a finite number of rational operations and extractions of real square roots. In § 29 we were given the numbers a and 6, and constructed lines of lengths Proof. First, we grant... | |
 | Leonard Eugene Dickson - Equations, Theory of - 1922 - 188 pages
...criterion in § 30, since the given numbers in this problem are a, ft, 7, all rational, xi can be obtained by a finite number of rational operations and extractions of real square roots, performed upon rational numbers or numbers derived from them by such operations. Thus xi involves one... | |
 | Benjamin Bold - Science - 1982 - 148 pages
...the Greek mathematicians were able to construct any desired geometric element that could be derived by a finite number of rational operations and extractions of real square roots from the given elements. To illustrate : Suppose we are given the elements^, b, and the unit element.... | |
| |
A proposed construction is possible by ruler and compasses if, and only if, the numbers which define analytically the desired geometric elements can be derived from those defining the given elements by a finite number of rational operations and extractions... 