secant

Etymology

It is borrowed from Latin secāns (“cutting”), stem secant-, the present participle of secō (“to cut”),^{[2][3][4][5][6]} from Proto-Indo-European *sek- (“to cut”).^[5][3] Merriam-Webster Unabridged takes the noun through New Latin.^[7] The Shorter Oxford, Hoad and the Oxford Dictionary of English instead take the word through French, as French sécant, with the feminine noun sécante (with ligne understood).^[8][9][10]

Earliest recorded meaning

A line that cuts another, in geometry: Barnhart and Merriam-Webster Unabridged date the noun to 1593,^[4][7] and the OED's first records, for both adjective and noun, are from 1594, in Blundeville's Exercises.^[2] According to Etymonline, the Latin term was first used by the Danish mathematician Thomas Fincke in “Geometria Rotundi” (1583);^[5] Barnhart notes the Latin form in an English text of 1583.^[4]

Semantic evolution

In trigonometry the word first named a length, a straight line drawn from the centre of an arc through one of its ends until it meets the tangent at the other; it now names the ratio of that line to the radius, that is, the reciprocal of the cosine.^[2][8][7] Johnson (1755) still defined it as the line itself, drawn from the centre of a circle and meeting the tangent.^[11] The general geometric sense, a line cutting a curve at two or more points, is recorded by the OED from 1684.^[2]

Timeline

• 1593 – noun, a line that intersects.^[4][7] The OED's record of the trigonometric sense begins in 1594.^[2]
• 1594 – adjective, of a line or surface, cutting another.^[2]
• 1684 – a line cutting another, especially a straight line cutting a curve.^[2]

Meanings

Noun

1. In trigonometry, the ratio of the hypotenuse of a right-angled triangle to the side next to a given angle; the reciprocal of the cosine, abbreviated sec.^[12][7]
2. A straight line that cuts a curve at two or more points.^[12][7][2]
3. A straight line drawn from the centre of a circle through one end of an arc to a tangent at the other end.^[7][2]

Adjective

1. (rare) Of a line or surface: cutting or intersecting another.^[7][8][2]

Word family

• secantly

Related words

• cosecant
• section
• sector
• saw
• scythe
• sickle

References

1. ^ Wiktionary, the free dictionary, https://en.wiktionary.org
2. ^ a b c d e f g h i j Oxford English Dictionary Online (accessed March 2026), Oxford: Oxford University Press
3. ^ a b The American Heritage Dictionary of the English Language (online 2024), 5th ed., Boston: Houghton Mifflin Harcourt
4. ^ a b c d Barnhart, Robert K. (1988), The Barnhart Dictionary of Etymology
5. ^ a b c Harper, Douglas. Online Etymology Dictionary, https://www.etymonline.com
6. ^ Dictionary.com Unabridged (2016), based on the Random House Unabridged Dictionary, New York: Random House
7. ^ a b c d e f g h Merriam-Webster Unabridged Dictionary (2024), online ed., Springfield, Mass.: Merriam-Webster
8. ^ a b c Shorter Oxford English Dictionary on Historical Principles (2002), 5th ed., ed. William R. Trumble and Angus Stevenson, Oxford: Oxford University Press
9. ^ Hoad, T. F., ed. (1986), The Concise Oxford Dictionary of English Etymology, Oxford: Clarendon Press
10. ^ Stevenson, Angus, ed. (2010), Oxford Dictionary of English, 3rd ed., Oxford: Oxford University Press
11. ^ Johnson, Samuel (1755), A Dictionary of the English Language, London; 4th ed. 1773; Johnson's Dictionary Online, ed. Beth Rapp Young et al.
12. ^ a b Collins English Dictionary (2023), Glasgow: HarperCollins