"soapy, resembling soap," 1710, from Latin sapo, sapon (see soap (n.)) + -aceous. In mid-19c. jocular use for "slippery, unctuous" in figurative senses (1837). Related: Saponacity. 

"conversion into soap," 1801, from French saponification, from saponifier, from Modern Latin saponificare, from sapon "soap" (see soap (n.)) + -ficare, combining form of Latin facere "to make" (from PIE root *dhe- "to set, put").

"ooze or percolate gently through pores," 1790, a variant of sipe (c. 1500), which is perhaps ultimately from Old English sipian "to seep," from Proto-Germanic *sip- (source also of Middle High German sifen, Dutch sijpelen "to ooze"), from PIE root *seib- "to pour out, drip, trickle" (see soap (n.)). Related: Seeped; seeping.

"a strainer, simple instrument for separating the finer from the coarser parts of disintegrated matter by shaking it so as to force the former through holes or meshes too small for the latter to pass," Middle English sive, from Old English sife, from Proto-Germanic *sib (source also of Middle Dutch seve, Dutch zeef, Old High German sib, German Sieb), from PIE *seib- "to pour out, sieve, drip, trickle" (see soap (n.)). Related to sift.

The Sieve of Eratosthenes (1803) is an ancient method for finding prime numbers. A sieve is noted as something a witch sails in by 1580s; hence sieve and shears, formerly used in divination.

1838, "act or operation of shampooing;" 1866, "soap for shampooing;" from shampoo (v.).

"viscous substance," 1949, American English, apparently from Gunk, trademark for a thick liquid soap patented 1932 by A.F. Curran Co. of Malden, Mass.

also tooth-paste, 1832, from tooth + paste (n.). Earlier substances were tooth-powder (1540s); tooth-soap (c. 1600).

in chemistry, "convert into soap" (by combining with an alkali), 1821, from French saponifier (see saponification). Related: Saponified; saponifying.

"sebaceous secretion," 1819, from Latin, from Greek smēgma "a detergent, soap, unguent," from smēkhein "to wipe off, wipe clean, cleanse," from PIE root *smeh- "to smear" (source also of Czech smetana "cream," and see smear (v.)). So called from resemblance of the substance to soap; a medical coinage, the word seems not to have been used in its literal Greek sense in English before this. Related: Smegmatic.

Old English leaþr "foam, soap, washing soda," from Proto-Germanic *lauthran (source also of Old Norse lauðr "washing soap, foam"), from PIE *loutro- (source also of Gaulish lautron, Old Irish loathar "bathing tub," Greek louein "to bathe," Latin lavere "to wash"), which is from root *leue- "to wash" + instrumentative suffix *-tro-.

The modern noun might be a 16c. redevelopment from the verb. Meaning "violent perspiration" (especially of horses) is from 1650s; hence the transferred sense "state of agitation" (such as induces sweating), attested from 1839.