Alright. Mace feels Anakin in the Force:
Feeling for its shatterpoint.
He found a knot of fault lines in the shadow's future; he chose the largest fracture and followed it back to the here and the now... And it led him, astonishingly, to a man standing frozen in the slashed-open doorway. Mace had no need to look; the presence in the Force was familiar, and was as uplifting as sunlight breaking through a thunderhead.
The chosen one was here.
Mace feels the shadow's (Palpatine's) shatterpoint and acts on it:
He could feel the end of this battle approaching, and so could the blur of Sith he faced; in the Force, the shadow had become a pulsar of fear. Easily, almost effortlessly, he turned the shadow's fear into a weapon: he angled the battle to bring them both out onto the window ledge.
Out in the wind. Out with the lightning. Out on a rain-slicked ledge above a half-kilometer drop.
Out where the shadow's fear made it hesitate. Out where the shadow's fear turned some of its Force-powered speed into a Force-powered grip on the slippery permacrete.
Out where Mace could flick his blade in one precise arc and slash the shadow's lightsaber in half.
Mace says that Palpatine was defeated by his own fear:
Now the shadow was only Palpatine: old and shrunken, thinning hair bleached white by time and care, face lined with exhaustion.
"For all your power, you are no Jedi. All you are, my lord," Mace said evenly, staring past his blade, "is under arrest."
"Do you see, Anakin? Do you?" Palpatine's voice once again had the broken cadence of a frightened old man's. "Didn't I warn you of the Jedi and their treason?"
"Save your twisted words, my lord. There are no politicians here. The Sith will never regain control of the Republic. It's over. You've lost." Mace leveled his blade. "You lost for the same reason the Sith always lose: defeated by your own fear."
Palpatine says it wasn't his own fear:
"Fool," he said.
He lifted his arms, his robes of office spreading wide into raptor's wings, his hands hooking into talons.
"Fool!" His voice was a shout of thunder. "Do you think the fear you feel is mine?"
Mace feels that it wasn't Palpatine's fear at all, but Anakin's:
He felt Anakin's leap from the office floor to the ledge, felt his approach behind-And Palpatine was not afraid. Mace could feel it: he wasn't worried at all.
That should be sufficient.