A — 1: θεμέλιος
(Strong's #2310 — Adjective — themelios | themelion — them-el'-ee-os )

is properly an adjective denoting "belonging to a foundation" (connected with tithemi, "to place"). It is used (1) as a noun, with lithos, "a stone," understood, in Luke 6:48,49; 14:29; Hebrews 11:10; Revelation 21:14,19; (2) as a neuter noun in Acts 16:26 , and metaphorically, (a) of "the ministry of the Gospel and the doctrines of the faith," Romans 15:20; 1—Corinthians 3:10,11,12; Ephesians 2:20 , where the "of" is not subjective (i.e., consisting of the apostles and prophets), but objective, (i.e., laid by the apostles, etc.); so in 2—Timothy 2:19 , where "the foundation of God" is "the foundation laid by God," -- not the Church (which is not a "foundation"), but Christ Himself, upon whom the saints are built; Hebrews 6:1; (b) "of good works," 1—Timothy 6:19 .

A — 2: καταβολή
(Strong's #2602 — Noun Feminine — katabole — kat-ab-ol-ay' )

lit., "a casting down," is used (a) of "conceiving seed," Hebrews 11:11; (b) of "a foundation," as that which is laid down, or in the sense of founding; metaphorically, of "the foundation of the world;" in this respect two phrases are used, (1) "from the foundation of the world," Matthew 25:34 (in the most authentic mss. in 13:35 there is no phrase representing "of the world"); Luke 11:50; Hebrews 4:3; 9:26; Revelation 13:8; 17:8; (2) "before the foundation of the world," John 17:24; Ephesians 1:4; 1—Peter 1:20 . The latter phrase looks back to the past eternity.

B — 1: θεμελιόω
(Strong's #2311 — Verb — themelioo — them-el-ee-o'-o )

"to lay a foundation, to found" (akin to A, No. 1), is used (a) literally, Matthew 7:25; Luke 6:48; Hebrews 1:10; (b) metaphorically, Ephesians 3:17 , "grounded (in love);" Colossians 1:23 (ditto, "in the faith"); 1—Peter 5:10 , AV, "settle." See GROUND , SETTLE.