Search help: the root meaning of Trust in Ps37:3

Maybe we should set our watches for David Paul's arrival with his recommendation for Barr (and indeed needed in Logos).

Your closest is probably going to be TWOT.  But TLOT (you'd have to purchase separately) goes over the discussed arabic usage to include the one you mention, as well as non-ripe fruit and pregnant mare. HALOT is good but doesn't have the lengthy discussion as in TLOT. Note the standard principle that  context establishes the approximation of meaning, with 'root' being a major stretch.

David P. Moore said:

In a devotion I read recently on Psalm 37:3, the author made the statement: 

This word “trust” is an interesting word. Its root is from the word that means “to lie face down on the ground.” 

I was curious and went to my library to see which resources made this observation, especially lexicons, but none of my lexicons did. The John MacArthur Sermon Archive did, as well as the NIVAC and the Ryrie Study Bible, but MacArthur and Ryrie were commenting on Prov. 3:5 when they made that observation. And the NIVAC was commenting on a verse in Joshua. So my question is, starting at Ps37:3, how can I use my L6 Platinum Plus library to come to this observation so I could share it with my class? As you can guess I have no formal training in the Biblical languages. Is that what I need in order to come to these observations? If so then I'll have to rely on MacArthur and Ryrie for help!

I don't know who your source happens to be, but he's wrong.  The phrase שְׁכָן־אֶ֝֗רֶץ is "abide in the land"  whereas the phrase בְּטַ֣ח בַּֽ֭יהוָה which begins the verse is what encourages "trust in YHWH."  This is one of the reasons I dislike devotionals—they attempt to derive significance from the roots of words when most of the time they're wrong.  Barr, indeed.  He's much needed.

PS:  שׁכן means to settle or reside but בטח means to trust or be confident.

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The power of Logos:

בָּטַח S⁹⁸² TWOT²³³ GK^{1052, 1053, 1054}vb. trust (cf. Arabic بَطَحَ (baṭaḥa) to throw one down upon his face Thes, اِنْبَطَحَ (ʾinbaṭaḥa) lie extended on the ground, ‘se reposer sur quelqu’un’ Fl MV)—Qal Pf. בָּטַח ψ 28:7 + 35 times; Impf. יִבְטַח Jb 40:23 + 27 times; Imv. בְּטַח ψ 37:3 + 8 times; Inf. abs. בָּטוֹחַ Is 59:4, cstr. בְּטֹחַ ψ 118:8 + 2 times; Pt. בֹּטֵחַ ψ 21:8 + 35 times; pass. בָּטוּחַ ψ 112:7 Is 26:3. I. trust. 1. abs. Is 12:2. 2. with cogn. acc. מה הבטחון הזה אשׁר בטחת what is this trust that thou dost trust? 2 K 18:19 = Is 36:4. 3. with בְּ trust in—a. God 2 K 18:5; 19:10 1 Ch 5:20 ψ 9:11; 21:8; 22:5, 6; 25:2; 26:1; 28:7; 32:10; 37:3; 40:4; 55:24; 56:5, 12; 62:9; 84:13; 91:2; 112:7; 115:9, 10, 11; 125:1; 143:8 Pr 16:20; 29:25 Is 26:3, 4; 37:10 Je 17:7; 39:18 Zp 3:2. b. persons Ju 9:26 ψ 41:10; 118:8, 9; 146:3 Pr 31:11 Je 17:5; 46:25 Mi 7:5. c. things Dt 28:52 Jb 39:11 ψ 27:3; 44:7; 52:9; 62:11; 115:8; 135:18 Pr 11:28; 28:26 Is 30:12; 42:17; 47:10 Je 5:17; 7:14; 12:5; 13:25; 48:7; 49:4 Ez 16:15 Ho 10:13 Am 6:1. d. in the name of God ψ 33:21 Is 50:10; mercy of God ψ 13:6; 52:10; word of God ψ 119:42; salvation of God ψ 78:22. 4. with עַל, trust or rely upon—a. God ψ 31:15; 37:5 Pr 28:25 Je 49:11. b. persons 2 K 18:20, 21, 24 = Is 36:5, 6, 9, Je 9:3. c. things 2 K 18:21 = Is 36:6 2 Ch 32:10, ψ 49:7 Is 31:1; 59:4 Ez 33:13 Hb 2:18. 5. with אֶל trust to—a. God 2 K 18:22 ( = Is 36:7) ψ 4:6; 31:7; 56:4; 86:2 Pr 3:5. b. persons Ju 20:36. c. things Je 7:4 ( = על דבר 7:8). II. be confident Jb 6:20; 40:23 Pr 14:16; צַדִּיקִים כִּכְפִיר יִבְטַח the righteous are bold as a lion Pr 28:1; secure Jb 11:18 Pr 11:15; עַם בֹּטֵחַ a people secure Ju 18:7, 10, 27; בָּנוֹת בֹּטְחוֹת careless daughters, (women) Is 32:9 cf. v 10, 11. Hiph. Pf. הִבְטַחְתָּ Je 28:15; Impf. יַבְטַח Is 36:15 + 2 times; Pt. מַבְטִיחִי ψ 22:10; cause to trust, make secure, abs. ψ 22:10; with עַל Je 28:15; 29:31; with אֶל 2 K 18:30 = Is 36:15.

-- Enhanced Brown-Driver-Briggs Hebrew and English Lexicon (p. 105)

Some observations:
1. BDB makes the suggestion (not a statement) that Arabic بَطَحَ could have some etymological link to the Hebrew. BDB is a good lexicon for researching such associations but in many cases it can go too far.

2. NIDOTTE says:

בָּטַח (bāṭaḥ II), q. fall to the ground (#1054).

OT Two passages have been suggested as illustrating this root, but both fail to confirm it with certainty. In Jer 12:5 it makes good sense to translate the verb בָּטַח as “fall” or “stumble”: “If you stumble in safe country, how will you manage in the thickets by the Jordan?” However, it is also possible to take בּוֹטֵחַ here in the sense of “feeling secure,” as in Judg 18:10, Isa 32:9–11, and Amos 6:1. Similarly in Prov 14:16 בּוֹטֵחַ probably means that the fool is self-assured rather than that he is reckless and falls (cf. W. McKane, Proverbs: A New Approach, OTL, 1970, 465).

3. HALOT lists several alternatives:

I בטח: MHb. Can. ba-ti-i-ti EA 147:56 I am confident; JArm.^tb, otherwise not attested in Arm. (Kraeling Arm. Pap. 187); Arb. bāṭeḥ pregnant mare (Musil Arabia 3:273): baṭaḥa בטח to be taut, firm (→ אֲבַטִּיחַ) > to be reliable.

II בטח: Arb. baṭaḥa to fall prostrate Driver Fschr. Robinson 59f; Gemser Spr. 112 :: Loewenstamm-B: basic meaning of I. qal: pt. בּוֹטֵחַ: to fall on the ground Jr 125 Pr 1416.

4. TLOT comments:

Only a few, isolated instances of bṭḥ “to trust” have been identified so far outside the OT in Can.; it is absent in Aram. (apart from a few borrowings from the Hebr.) and is represented by the roots rḥṣ/rahúāṣu and tkl/takālu in Akk. Etymologies that attempt to trace bṭḥ to a physical-concrete root meaning have not yet produced universally accepted results.

A Can. gloss in EA 147:56 offers ba-ti-i-ti (baṭīti) “I am confident” (cf. CAD B:177a; DISO 33).

bṭḥ appears in a 6th-cent. Phoen. letter (KAI no. 50.5) in a damaged, not entirely lucid context (“security, guarantee”?).

On the PN mbṭḥyh, “Yahweh is the object of (my) trust,” with the by-form mpṭḥyh and the abbreviated forms mb/pṭḥ in the Aram. Elephantine Papyri (Cowley 295a, 297b; BMAP 187), cf. J. J. Stamm, FS Baumgartner 314. Hebr. mbṭḥyhw occurs in Lachish Letter 1:4 (cf. TGI  no. 34).

On the basis of Arab. bṭḥ “to throw down” (VII “to lie on one’s belly”), the meaning “to fall to the ground” has been postulated for Jer 12:5 and Prov 14:16, whether this may be taken as the basic meaning (“to lie there” > “to depend on” >) “to trust” (G. R. Driver, FS Robinson 59f.; J. Blau, VT 6 [1956]: 244; L. Kopf, VT 8 [1958]: 165–68), or a root bṭḥ II is assumed (HAL 116a: qal Jer 12:5; Prov 14:16; baṭṭūḥâ “inhabited valley” Job 12:6; denied e.g., by Rudolph, HAT 12, 84; Fohrer, KAT 16, 237), which presumes a different etymology for bṭḥ I (L. Köhler, ZAW 55 [1937]: 172f.; id., OTS 8 [1950]: 144f.; and KBL 118b: following Arab. bāṭeḥ “pregnant mare” and Hebr. ʾabaṭṭīḥîm “watermelons,” he suggests bṭḥ “to be taut, firm” > “to be trustworthy, trust, be certain”; otherwise, Ch. Rabin, FS Baumgartner 225–28: Arab. btʿ with the basic meaning “to be strong” and a semantic shift from “strength, greatness” > “self-confidence”).

5. Even if there is such a root, exegetically and devotionally we can attach too much meaning to them. Scripture uses the vehicle of accepted canons of human communication, and usually the old roots have long disappeared from the minds of speakers and hearers. For example, it is interesting that the etymology of "interest" can be traced to Latin -- to be between, make a difference, concern, from inter- + esse to be -- but that is just interesting and nobody thinks about or relies on those "root meanings" in normal communication. For more on this issue, Semantics of Biblical Language by Barr is a classic treatise.