Secant Origin: How Did the Word Get its Name?

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I know that cotangent is thus named because its the compliment of tangent, but where did Secant get its name?
 

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According to this dictionary:

"secant
..from L. secantem (nom. secans) "cutting," prp. of secare "to cut" (see section). First used by Dan. mathematician Thomas Fincke in Geometria Rotundi (1583)."