The third degree
The classification of the qualities of objects by degree - heat and cold, moisture and dryness etc. - was commonplace in the middle ages. Henry Lyte's translation of Dodoens' Niewe herball or historie of plantes, 1578 includes a description of rue:
"Rue is hoate and dry in the thirde degree."
Shakespeare went on to apply the degree classification to drink, in Twelfth Night, 1602:
"For he s in the third degree of drinke: hee's drown'd: go looke after him."
The present meaning involves more than classification though. 'The third degree' is well-known to all US crime-fiction enthusiasts as 'an intensive, possibly brutal, interrogation'.
In Masonic lodges there are three degrees of membership; the first is called Entered Apprentice, the second Fellowcraft, and the third is master mason. When a candidate receives the third degree in a Masonic lodge, he is subjected to some activities that involve an interrogation and it is more physically challenging than the first two degrees. It is this interrogation that was the source of the name of the US police force's interrogation technique. That is referred to in an 1900 edition of Everybody's Magazine:
"From time to time a prisoner... claims to have had the Third Degree administered to him."