Osculations
A painting from the illuminated Pearl Manuscript, which contains the only surviving manuscript copy of Sir Gawain and the Green Knight.
310, slopes of slopes aligned
Benjamin Williamson, An elementary treatise on the differential calculus: containing the theory of plane curves, with numerous examples, Section 247
The author explains that an osculating circle both intersects and matches the curvature (first derivative) of another; curves with matching higher derivatives have contact of corresponding higher order.
310, a segment superposed
John W. Rutter, Geometry of Curves, Section 9.2.3
The circle of curvature can therefore be regarded as the limiting position of circles passing through three distinct points on the curve as the three points move into coincidence. For this reason the circle of curvature is also called the osculating circle, the unique circle having the highest order of contact with the curve.
310, my mind times three
Thomas Hahn, The Greene Knight
edited and adapted from Sir Gawain and the Green Knight by the unidentified Gawain Poet of the 14th century
The Ladye kissed him times thre …
For I have such a deede to doe,
That I can neyther rest nor roe,
Att an end till itt bee …
In his armes he hent the Knight,
And there he kissed him times thre
310, to prove my points
Thomas Hahn, The Greene Knight
“to prove Gawaines points three,” meaning his three virtues.