Secant line point a "tangent line" and in no points an "exterior line". A "chord" of a circle is the line segment that joins two distinct points of the circle. A chord is therefore contained in a unique secant line and each secant line determines a unique chord. In rigorous modern treatments of plane geometry, results that seem obvious and were assumed (without statement) by Euclid in his treatment, are usually proved. For instance, "Theorem (Elementary Circular Continuity)": If formula_1 is a circle and formula_2 a line that contains a point that is inside formula_1 and a point that is outside of
Five points determine a conic a polynomial in "d" of degree "n," with leading coefficient formula_21 In the case of plane curves, where formula_22 the formula becomes: whose values for formula_24 are formula_25 – there are no curves of degree 0 (a single point is determines a point, which is codimension 2), 2 points determine a line, 5 points determine a conic, 9 points determine a cubic, 14 points determine a quartic, and so forth. While five points determine a conic, sets of six or more points on a conic are not in general position, that is, they are constrained as is demonstrated in Pascal's