A cone (or cone section) is a field curve obtained by cutting a cone with a plane through the vertex of the cone. There are three possibilities, depending on the relative position of the cone and field
If there are no lines parallel to the cone, the intersection is a closed curve, called an ellipse. If one line of the cone parallel to the plane, the intersection is an open curve with both ends asymptotic parallel, is called a parabola. Finally, there may be two parallel lines on the cone into the field, the curve in this case has two open, and is called a hyperbola.Conic section between the curves of the oldest, and is the oldest math subjects studied systematically and thoroughly. Conic sections have been discovered by Menaechmus (a, Greece c.375-325 BC), the teacher of Alexander the Great. They are nurtured in an attempt to overcome the three famous problems trisecting angle, duplication of the cube, and squaring the circle.Conic was first defined as the intersection: straight circular cone vertices from different angles, a plane perpendicular to the conical element. (An element of the cone is himpunaniap lines that form a cone) Depending on the angle is less than, equal to, or greater than 90 degrees, respectively obtained ellipse, parabola, or hyperbola.Appollonius (c. 262-190 BC) (known as The Great geometry) extended the previous results and the consolidation of a wedge cone conic section monograph, which consists of eight books with 487 propositions. Euclid's Appollonius' wedge cone Parts and Elements may represent the quintessence of Greek mathematics. Appollonius is the first to third base the theory of conic sections in the part of the circular cone, right or oblique. He also give the names ellipse, parabola, and hyperbola.In Kepler's laws of planetary motion, Descarte and Fermat's coordinate geometry, and the beginning of projective geometry started by Desargues, La Hire, Pascal pushed to high levels of conic sections. Many later mathematicians have also made contributions conic sections, particularly in the development of projective geometry where conic sections are the fundamental objects as circles in Greek geometry. Among the contributors, we may find Newton, Dandelin, Gergonne, Poncelet, Brianchon, Dupin, Chasles, and Steiner. Slice the cone is a classic rich discussion that has prompted many developments in the history of mathematics.
If there are no lines parallel to the cone, the intersection is a closed curve, called an ellipse. If one line of the cone parallel to the plane, the intersection is an open curve with both ends asymptotic parallel, is called a parabola. Finally, there may be two parallel lines on the cone into the field, the curve in this case has two open, and is called a hyperbola.Conic section between the curves of the oldest, and is the oldest math subjects studied systematically and thoroughly. Conic sections have been discovered by Menaechmus (a, Greece c.375-325 BC), the teacher of Alexander the Great. They are nurtured in an attempt to overcome the three famous problems trisecting angle, duplication of the cube, and squaring the circle.Conic was first defined as the intersection: straight circular cone vertices from different angles, a plane perpendicular to the conical element. (An element of the cone is himpunaniap lines that form a cone) Depending on the angle is less than, equal to, or greater than 90 degrees, respectively obtained ellipse, parabola, or hyperbola.Appollonius (c. 262-190 BC) (known as The Great geometry) extended the previous results and the consolidation of a wedge cone conic section monograph, which consists of eight books with 487 propositions. Euclid's Appollonius' wedge cone Parts and Elements may represent the quintessence of Greek mathematics. Appollonius is the first to third base the theory of conic sections in the part of the circular cone, right or oblique. He also give the names ellipse, parabola, and hyperbola.In Kepler's laws of planetary motion, Descarte and Fermat's coordinate geometry, and the beginning of projective geometry started by Desargues, La Hire, Pascal pushed to high levels of conic sections. Many later mathematicians have also made contributions conic sections, particularly in the development of projective geometry where conic sections are the fundamental objects as circles in Greek geometry. Among the contributors, we may find Newton, Dandelin, Gergonne, Poncelet, Brianchon, Dupin, Chasles, and Steiner. Slice the cone is a classic rich discussion that has prompted many developments in the history of mathematics.
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