How we cite our quotes: (Book.Chapter)
Quote #1
It follows that the longest and the shortest lives are brought to the same state. The present moment is equal for all; so what is passing is equal also; the loss therefore turns out to be the merest fragment of time. No one can lose either the past or the future—how could anyone be deprived of what he does not possess? (2.14.1)
Marcus is able to keep away from emotional drama and existential angst by observing that all life is the same—no matter how long or short it is in duration. He also emphasizes the importance of the present for all human beings, since it's the only place in time that we can influence or own. Everything else is swallowed by the gulf of time, on either side.
Quote #2
Remind yourself too that each of us lives only in the present moment, a mere fragment of time: the rest is life past or uncertain future. (3.10)
Marcus is sounding more and more like a modern motivational speaker here: Live in the present! Seize the day! Kidding aside, Marcus has a point: we can only control and affect the present moment. No one is guaranteed a tomorrow, and we have no real access to the past.
Quote #3
One who is all in a flutter over his subsequent fame fails to imagine that all those who remember him will very soon be dead—and he too. Then the same will be true of all successors, until the whole memory of him will be extinguished in a sequence of lamps lit and snuffed out. But suppose immortality in those who will remember you, and everlasting memory. Even so, what is that to you? (4.19)
Marcus's purpose here is to kill the desire for fame or to have a good and lasting reputation. He speaks elsewhere of how concern for these things often turn men away from their humanity. By using the image of extinguishing lamps, Marcus faces up to reality: everyone is going to die, including the person seeking fame—and all that person's friends and admirers. Memory itself is fragile and transient.