καίω

Matthew 5:15 καίουσιν do they light

Neither do people light a lamp and put it under a basket. Instead, they set it on a stand, and it gives light to everyone in the house.

Here: "They light." The 'they' is general and means 'people' or 'anyone'. The present tense states what people always do, a fact of everyday life, not one event.

Luke 12:35 καιόμενοι, burning,

Be dressed for service and keep your lamps burning.

Here: Present participle: 'burning, and kept burning.' Through the long night the flame has to be tended again and again. A lamp is not lit once and then forgotten.

Luke 24:32 καιομένη burning

They asked each other, “Were not our hearts burning within us as He spoke with us on the road and opened the Scriptures to us?”

Here: A present participle in the middle/passive form: 'being set alight, burning'. Combined with 'was', it pictures a fire that kept burning the whole time he talked, not one flash.

John 5:35 καιόμενος is burning

John was a lamp that burned and gave light, and you were willing for a season to bask in his light.

Here: A present passive participle: 'being lit' or 'burning'. It shows the lamp actually alight and burning its oil. The passive form may hint that someone else lit it, but the word is also ordinary Greek for 'burning'.

John 15:6 καίεται. it is burned.

If anyone does not remain in Me, he is like a branch that is thrown away and withers. Such branches are gathered up, thrown into the fire, and burned.

Here: Present passive, singular, 'it burns' or 'it is burned'. Greek normally uses a singular verb with a neuter plural subject, so 'it' means the heap of branches. The verse ends abruptly on the burning.

Hebrews 12:18 κεκαυμένῳ kindled

For you have not come to a mountain that can be touched and that is burning with fire; to darkness, gloom, and storm;

Here: A perfect passive participle: "set ablaze and still burning." It either describes the touchable thing ("burning with fire", echoing Deut 4:11 "the mountain was burning with fire") or describes the fire itself ("a blazing fire").

Revelation 4:5 καιόμεναι burning

From the throne came flashes of lightning, rumblings, and peals of thunder. Before the throne burned seven torches of fire. These are the seven spirits of God.

Here: Present participle, "burning": they burn on and on and never go out. This recalls the lamp and altar fire in Israel's sanctuary that were never to go out.

Revelation 8:8 καιόμενον burning

Then the second angel sounded his trumpet, and something like a great mountain burning with fire was thrown into the sea. A third of the sea turned to blood,

Here: 'Burning'. The present tense shows the mountain still burning as it falls, ablaze in flight. This matches Jeremiah's 'burnt mountain' and Enoch's 'stars like great burning mountains'.

Revelation 8:10 καιόμενος burning

Then the third angel sounded his trumpet, and a great star burning like a torch fell from heaven and landed on a third of the rivers and on the springs of water.

Here: A present participle: it is burning as it falls, a continuing blaze. The same verb describes the burning mountain in 8:8.

Revelation 19:20 καιομένης is burning

But the beast was captured along with the false prophet, who on its behalf had performed signs deceiving those who had the mark of the beast and worshiped its image. Both the beast and the false prophet were thrown alive into the fiery lake of burning sulfur.

Here: 'That is burning': a present participle, so the burning goes on and does not die down.

Revelation 21:8 καιομένῃ is burning

But to the cowardly and unbelieving and abominable and murderers and sexually immoral and sorcerers and idolaters and all liars, their place will be in the lake that burns with fire and sulfur. This is the second death.”

Here: "Burning." The present participle shows a fire that keeps burning, not one that flares and goes out.