Etymology
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Words related to spiral

aspirin (n.)

coined 1899 in German as a trademark name by German chemist Heinrich Dreser, from Latin Spiraea (ulmaria) "meadow-sweet," the plant in whose flowers or leaves the processed acid in the medicine is naturally found, + common chemical ending -in (see -ine (2)). Spiraea (Tournefort, 1700) is from Latinized form of Greek speiraia "meadow-sweet," so called from the shape of its follicles (see spiral (adj.)). The initial -a- is to acknowledge acetylation; Dreser said the word was a contraction of acetylierte spirsäure, the German name of the acid, which now is obsolete, replaced by salicylic acid.

Die Bezeichnung Aspirin ist abgeleitet aus "Spirsäure" — alter Name der Salicylsäure und A = Acetyl; statt: Acetylirte Spirsäure, kurzweg "Aspirin". [H, Dreser, "Pharmakologisches über Aspirin (Acetylsalicylsäure)," in "Archiv für die Gesammte Physiologie des Menschen und der Thiere," 1899, p.307]

The custom of giving commercial names to medicinal products began in Germany in the late 19th century, when nascent pharmaceutical firms were discovering medical uses for common, easily made chemicals. To discourage competitors they would market the substance under a short trademarked name a doctor could remember, rather than the long chemical compound word. German law required prescriptions to be filled exactly as written.

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Sparta 
capital of Laconia in ancient Greece, famed for severity of its social order, the frugality of its people, the valor of its arms, and the brevity of its speech. Also for dirty boys, men vain of their long hair, boxing girls, iron money, and insufferable black broth. The name is said to be from Greek sparte "cord made from spartos," a type of broom, from PIE *spr-to-, from root *sper- (2) "to turn, twist" (see spiral (adj.)). Perhaps the reference is to the cords laid as foundation markers for the city. Or the whole thing could be folk etymology.
spirillum (n.)
(plural spirilla), 1875, Modern Latin, diminutive of Latin spira (see spiral (adj.)). So called for their structure.
spiro- 
word-forming element meaning "twisted, spiraled, whorled," from combining form of Latin spira "a coil, twist," from Greek speira (see spiral (adj.)).
spirochete (n.)
1877, from Modern Latin Spirochæta, the genus name, from spiro- Modern Latin combining form of Greek speira "a coil" (see spiral (adj.)) + Greek khaite "hair" (see chaeto-).