Modern English versions are almost evenly divided as to whether a new paragraph should come at the beginning of verse 8 or verse 9. Revised Standard Version, New Jerusalem Bible, New International Version, New Revised Standard Version, and Bible en français courant make the break at verse 9, but many good English translations (Good News Translation, New English Bible/Revised English Bible, New American Bible, and Anchor Bible) start the new paragraph here. Others, such as New Jerusalem Bible and Traduction œcuménique de la Bible, do not make a break at either place. All things being equal, translators should probably make the break here.
Magnified himself exceedingly: New Revised Standard Version translates simply “grew exceedingly great,” while Revised English Bible says “made a great display of its strength.” The latter seems to capture the idea of arrogance a bit better. The same verbal expression is used of the ram in verse 4, but here an additional word is used to make it stronger. On the word exceedingly, see comments on the corresponding Aramaic word at 6.23; 7.7, 19.
When he was strong: the goat was obviously already strong when it defeated the ram. So this expression is usually taken to mean something like “at the peak of his power” (New Jerusalem Bible), “at the height of his (or its) power” (Good News Translation, New International Version, New American Bible, New Revised Standard Version, and Revised English Bible).
The great horn was broken: this indicates an abrupt change in the political situation, in which power is suddenly relinquished. It is probably a good idea to bring out the abruptness of this event in the translation. Some English versions seek to do this by using the verb “snapped” (New English Bible and New Jerusalem Bible). This almost certainly refers to the untimely death of Alexander the Great in 323 B.C. He was succeeded by four conspicuous horns, a symbolic reference to the kingdoms of Macedonia, Asia Minor, Syria, and Egypt. For comments on the word conspicuous, see verse 5. There is some manuscript evidence that reads “four other horns,” but this is followed by few English versions (New American Bible, for example) and is not recommended to translators.
Toward the four winds of heaven: this expression is used to indicate the four cardinal points of the compass. See comments on 7.2. The same expression is used in 11.4. Compare also Zech 2.6; 6.5; Jer 49.36; Rev 7.1. This may be rendered less literally “toward all directions,” or as in Good News Translation, “each pointing in a different direction.”
Quoted with permission from Péter-Contesse, René & Ellington, John. A Handbook on Daniel. (UBS Helps for Translators). New York: UBS, 1994. For this and other handbooks for translators see here .