## A Long Way from EuclidMathematics has come a long way indeed in the last 2,000 years, and this guide to modern mathematics traces the fascinating path from Euclid's |

## A Long Way from EuclidMathematics has come a long way indeed in the last 2,000 years, and this guide to modern mathematics traces the fascinating path from Euclid's |

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3-dimensional analytic geometry angle arithmetic assumptions axioms bers called Cantor cardinal number century circle circumference complex numbers congruent construction coordinate cube decimal deﬁned deﬁnition denumerable inﬁnity Desargues determine distance divide Elements equal Euclid Euclidean geometry ﬁfth ﬁgure ﬁnd ﬁnite number ﬁrst ﬁve Gauss Georg Cantor given Greeks Hilbert hypotenuse inﬁnite inﬁnite class inﬁnite number inﬁnity of points integers irrational numbers logical mathe mathematicians mathematics matics ment method multiplied natural numbers negative numbers never non-denumerable inﬁnity non-Euclidean geometry number line one-to-one correspondence original parallel lines placed in one-to-one plane point sets positive integers possible postulate problem projective geometry proof proved Pythagoras Pythagorean Quadratic Reciprocity rational numbers reader real numbers rectangles represented right triangle rotation segment sentence sentential calculus sides simple closed curve solve speciﬁc sphere square root Square Theorem statement straight line straightedge and compass surface symbol tetrahedron theory tion topology trisect true truth tables whole numbers