Etymology
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tangent (adj.)

1590s, "meeting at a point without intersecting," from Latin tangentem (nominative tangens), present participle of tangere "to touch," from PIE root *tag- "to touch, handle." First used by Danish mathematician Thomas Fincke in "Geomietria Rotundi" (1583). Extended sense of "slightly connected with a subject" is first recorded 1825. Related: Tangence; tangency.

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tangent (n.)

1590, one of the three fundamental functions of trigonometry, from tangent (adj.). From 1650s as "a tangent line." Figurative use of on a tangent is from 1771.

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arc (n.)

late 14c., "part of a curved line," originally in reference to the sun's apparent motion across the sky, from Old French arc "bow, arch, vault" (12c.), from Latin arcus "a bow, arch," from Proto-Italic *arkwo- "bow."

This has Germanic cognates in Gothic arhvazna, Old English earh, Old Norse ör "arrow," from Proto-Germanic *arkw-o- "belonging to a bow." It also has cognates in Greek arkeuthos, Latvian ercis "juniper," Russian rakita, Czech rokyta, Serbo-Croatian rakita "brittle willow." De Vaan sees an Italo-Germanic word for "bow" which can be connected with Balto-Slavic and Greek words for "willow" and "juniper" "under the well-founded assumption that the flexible twigs of juniper or willow were used as bows." The Balto-Slavic and Greek forms point to *arku-; "as with many plant names, this is likely to be a non-IE loanword."

The electrical sense is attested from 1821.

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arc (v.)

1882, in the electrical sense, from arc (n.). Meaning "to move in an arc" is attested by 1940. Related: Arced; arcing.

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arc-light (n.)

"light produced by an electric arc," 1871, from arc (n.) + light (n.). Related: Arc-lamp.

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cotangent (n.)

in trigonometry, "the tangent of the complement of a given angle," a contraction of co. tangent, abbreviation of complement + tangent (n.).

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tangental (adj.)

1742, from tangent (adj.) + -al (1). Related: Tangentally.

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tangential (adj.)

1620s, see tangent (adj.) + -ial. Figurative sense of "divergent, erratic" is from 1787; that of "slightly connected" is from 1825. Related: Tangentially.

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arcuate (adj.)

"bent like a bow," 1620s, from Latin arcuatus "bow-like, arched," past participle of arcuare "to bend like a bow," from arcus "a bow" (see arc (n.)). Related: Arcuration.

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radian (n.)

"angle subtended at the center of a circle by an arc equal in length to the radius," 1879, from radius.

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