Secant line a circle in the Euclidean plane, a line joining two of them would be a 2-secant (or "bisecant") and a line passing through only one of them would be a 1-secant (or "unisecant"). A unisecant in this example need not be a tangent line to the circle. This terminology is often used in incidence geometry and discrete geometry. For instance, the Sylvester–Gallai theorem of incidence geometry states that if points of Euclidean geometry are not collinear then there must exist a 2-secant of them. And the original orchard-planting problem of discrete geometry asks for a bound on the number of
All that is gold does not glitter and danger. Line seven refers to the sword Narsil. Line eight foreshadows the crownless Aragorn's accession to the throne of both the kingless Gondor and the vanished Arnor. Older editions of "The Lord of the Rings" indexed the poem as "The Riddle of Strider". From the 50th anniversary edition of 2005 on, the new, enlarged index by Wayne G. Hammond and Christina Scull list it as "All that is gold does not glitter". Early versions of the poem are recorded in "The Treason of Isengard", part of "The History of Middle-earth" book series by Christopher Tolkien. The first draft of