strength

Distinctions

koach (כח)

Rabbi Pappenheim: the most general term, plain ability to do or withstand. Rabbi Soloveitchik (Catharsis): in Tanach, physical strength, shared with the animals; hence "who gives koach to the weary". Rabbi Mecklenburg: the power to hold a state against what would break it; or mental fortitude, so Targum renders koach (Devarim 8:18) as eitzah, and "with all his koach" (Shabbos 119b) means full focus, not volume (Rashi, against Tosafos).

gevurah (גבורה)

Avos 4:1: the gibbor conquers his yetzer. Rabbi Soloveitchik: given to man alone, the power to rise above the survival instinct, best "heroism"; a gibbor is not always the victor but always enters the fight with all his might; Hashem is Gibbor because He holds back His anger (Yoma 69b; Yirmiyahu 32:18). Rabbi Pappenheim: the act that actualizes potential koach, lent even to the Flood waters (Bereishis 7:18-19). Rabbi Mecklenburg: not withstanding opposition but defeating it. Rabbi Shapira-Frankfurter (Bereishis 25:23) alone makes it physical.

chozek (חזק) and ometz (אמץ)

Bedersi and Rabbi Wertheimer: chozek is normal strength (a sick man restored is chazak); ometz is strength beyond the normal. Vilna Gaon (Yehoshua 1:7; Mishlei 24:5) and Malbim (Yair Ohr): chozek outer and physical, ometz of the heart; Malbim elsewhere (Yeshayahu 28:2): chozek fades, ometz renews itself. Rabbi Shapira-Frankfurter reverses part of this: chozek is strength of will (courage to enter battle), ometz strength of heart (courage to stay). Berachos 32b reads חזק ואמץ to Yehoshua as Torah and good deeds; Rabbi Wertheimer: the greater the scholar, the more than ordinary strength he needs to keep doing, hence ometz. Rabbi Pappenheim: ometz from מ-צ, squeezing out the last drop (Zechariah 6:3); chozek withstands being overpowered, tokef overpowers.

otzem (עצם), oz (עז), kabir (כביר)

Rabbi Dr. Asher Weiser: otzem is ometz by aleph/ayin and metathesis. Rabbi Edel: strength through numbers (Shemos 1:8, 1:20; Devarim 7:1; Yoel 2:2), then inherent strength; or from etzem, bone. Rabbi Moshe Shapiro: every ע-צ word holds potential inside, so otzem is pent-up, unexpressed strength. Rabbi Pappenheim: otzem is quantitative strength from unequal parts, kabir from equal parts (Rashi to Berachos 8a). Rabbi Wertheimer: oz and az are undeterrable strength of spirit, seen in the face (Koheles 8:1); the spies were sent to test chazak (Bamidbar 13:18) and reported az (13:28), resolve, not muscle. Rabbi Wessely, cited by Rabbi Edel: oz is primarily Divine, supernatural power, against gevurah within nature; "Hashem gives oz to His people" (Tehillim 29:11, printed 28:11 in the article) lifts them above nature; "give oz to Hashem" (68:35) is figurative (Eichah Rabbah 1:33; Rabbi Yerucham Levovitz). Rabbi Marcus: oz, eitz, otzem are one root (tzadi/zayin).

eitan (איתן), adir (אדיר), takif (תקיף)

Eitan: Rashi (Devarim 21:4) strong, hard; Rambam (Hilchos Rotzeach 9:2) strong-flowing; Rabbi Edel reconciles them as the river bank that holds the water back, and holding back takes strength: Yosef (Bereishis 49:24), Yisro's rock (Bamidbar 24:21), the Avos as eitanim born in Tishrei (Melachim I 8:2; Rosh Hashanah 11a; Metzudas David). Rav Hirsch (Shemos 14:27): durable, like bedrock. Adir: Rabbi Pappenheim, chazak is stronger than another, adir the strongest of a whole group, fit for Hashem (Shemos 15:6; Tehillim 8:2, 93:4); Rabbi Edel: kin to hadar. Takif: Targum's word for chozek and oz, also Biblical (Esther 9:29; Koheles 4:12; Daniel 4:27); Rabbi Pappenheim, root ק-פ, a full circle, strength that surrounds and overpowers; Rabbi Edel: of Hashem, all-encompassing sovereignty (Talmudic matkif, one sage overpowering another's position).

Rendering guidance

• koach "strength"; gevurah "might" ("heroism" for self-mastery), so the morning berachos read "who girds Yisrael with might" and "who gives strength to the weary" (Rabbi Soloveitchik); chozek "strength", chazak "strong"; ometz "fortitude", "resolve"; oz "might", az "bold"; eitan "steadfast"; adir "mighty"; kabir "mighty in number"; takif "overpowering"; otzem "vastness" (number) or "innate strength".
• חזק ואמץ: "be strong and resolute" (Bedersi, Wertheimer, Gra), the greater word second; "strong and courageous" only if "courageous" is held for ometz throughout. Rabbi Shapira-Frankfurter's reversal is a minority reading.
• Trap: "strength" absorbs every word here, "power" absorbs koach, oz and takif. When several sit together (Rabbi Shlomo of Urbino counts 36 in Ohel Moed), assign each its English before drafting and hold it throughout.

Sources

Rabbi Reuven Chaim Klein, "The Power to Hold Back," What's in a Word?, Ohr Somayach, 8 Tishrei 5781 (2020-09-26), raw text in sources/whats-in-a-word/raw/8868-the-power-to-hold-back.md; and "The Strong Ones," 23 Elul 5780 (2020-09-12), raw text in sources/whats-in-a-word/raw/8857-the-strong-ones.md. Primary loci: Melachim I 8:2 with Rosh Hashanah 11a; Devarim 21:4 with Rashi and Rambam, Hilchos Rotzeach 9:2; Avos 4:1; Yoma 69b; Rabbi Soloveitchik, Catharsis; Shabbos 119b; Devarim 31:7, 31:23; Yehoshua 1:6-18; Vilna Gaon to Yehoshua 1:7 and Mishlei 24:5; Malbim, Yair Ohr and to Yeshayahu 28:2; HaRechasim LeVikah to Bereishis 25:23; Berachos 32b; Bamidbar 13:18, 13:28; Tehillim 29:11, 68:35; Ohel Moed.