Etymology
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horoscope (n.)

"observation or diagram of the heavens, showing the positions of planets, on any given day, used by astrologers," mid-16c., from French horoscope, from Latin horoscopum/horoscopus, from Greek hōroskopos "nativity, horoscope," also "one who casts a horoscope, one who observes the hour of a birth," from hōra "hour; season; period of time" (see hour) + skopos "watcher; what is watched" (from PIE root *spek- "to observe").

The notion is of "observing the hour" (of someone's birth, etc.). The word was in late Old English and Middle English as horoscopum, from Latin, but the modern form is considered to be a reborrowing. Old English glossed Latin horoscopus with tidsceawere ("time-shower"). Related: Horoscopic; horiscopal. Horoscopy "the casting of a nativity" is attested from 1650s, from Latin horoscopium, from Greek hōroskopeion, from hōroskopia.

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scope (n.2)

[instrument for viewing] 1872, shortened from telescope, microscope, etc., in which the element (Latinized) is from Greek skopein "to look" (from PIE root *spek- "to observe"). Earlier used as a shortening of horoscope (c. 1600). Extended to radar screens, etc., by 1945 as a shortening of oscilloscope.

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calculation (n.)

late 14c., "art, manner, or practice of computing by numbers," also "the process of making a horoscope," from Late Latin calculationem (nominative calculatio) "a computation, calculation, reckoning," noun of action from past-participle stem of calculare "to reckon, compute," from Latin calculus "reckoning, account," originally "pebble used in counting," diminutive of calx (genitive calcis) "limestone" (see chalk (n.)). From early 15c. as "the result of reckoning, the solution for a problem."

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ascendant (adj.)

late 14c., ascendent, in astrology, "rising over the horizon," from Latin ascendentem (nominative ascendans), present participle of ascendere "to mount, ascend, go up" (see ascend). The sense "moving upward, rising" is recorded from 1590s.

As a noun in astrology, "point of the ecliptic or sign of the zodiac which is on the eastern horizon at the moment of birth." The planet that rules the ascendant is believed to have predominant influence on the horoscope. Hence in the ascendant "ruling, dominant" (not, as is often thought, "rising"), 1670s, and the adjective meaning "superior, dominant," 1806.

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