All 13 Uses of

utmost
in
The Iliad by Homer - (translated by: Butler)

Do your very utmost; dally not about your armour, but loose the horses at once—or else kill the men yourself, while I see to the horses.†
Book 10 *

As a lion fastens on the fawns of a hind and crushes them in his great jaws, robbing them of their tender life while he on his way back to his lair—the hind can do nothing for them even though she be close by, for she is in an agony of fear, and flies through the thick forest, sweating, and at her utmost speed before the mighty monster—so, no man of the Trojans could help Isus and Antiphus, for they were themselves flying panic before the Argives.†
Book 11

They could neither jump it nor cross it, for it had overhanging banks all round upon either side, above which there were the sharp stakes that the sons of the Achaeans had planted so close and strong as a defence against all who would assail it; a horse, therefore, could not get into it and draw his chariot after him, but those who were on foot kept trying their very utmost.†
Book 12

None are held back neither by fear nor slackness, but it seems to be the will of almighty Jove that the Achaeans should perish ingloriously here far from Argos: you, Thoas, have been always staunch, and you keep others in heart if you see any fail in duty; be not then remiss now, but exhort all to do their utmost.†
Book 13

Ajax son of Oileus, never for a moment left the side of Ajax, son of Telamon, but as two swart oxen both strain their utmost at the plough which they are drawing in a fallow field, and the sweat steams upwards from about the roots of their horns—nothing but the yoke divides them as they break up the ground till they reach the end of the field—even so did the two Ajaxes stand shoulder to shoulder by one another.†
Book 13

Fool; Hector and his fleet horses were ever straining their utmost to defend them.†
Book 16

Fear fell upon Hector as he beheld him, and he dared not stay longer where he was but fled in dismay from before the gates, while Achilles darted after him at his utmost speed.†
Book 22

It was when they were doing the last part of the course on their way back towards the sea that their pace was strained to the utmost and it was seen what each could do.†
Book 23

Fly after them at your utmost speed; I will hit on a plan for passing them in a narrow part of the way, and it shall not fail me.†
Book 23

There was little trace of wheel-marks in the fine dust, and the horses came flying in at their utmost speed.†
Book 23

The Achaeans all shouted applause as they saw him straining his utmost, and cheered him as he shot past them; but when they were now nearing the end of the course Ulysses prayed inwardly to Minerva.†
Book 23

Definition:

greatest