The Sith Rule of Two says: One to embody power, one to crave it. It's like a survival of the fittest.
If the apprentice must kill the master to be the master, that usually means the apprentice is stronger than the master. If this chain went on for many years, does this mean Sidious was the strongest Sith ever, just by the transitive property?
I'll start with Legends since these sources provide us with much more information.
You are correct that the Rule of Two is intended to ensure that each succeeding Sith Master is stronger than the previous:
Under [Bane's] leadership the Sith had been reborn. Now they numbered only two—one Master and one apprentice; one to embody the power of the dark side, the other to crave it. Thus would the Sith line always flow from the strongest, the one most worthy. Bane’s Rule of Two ensured that the power of both Master and apprentice would grow from generation to generation until the Sith were finally able to exterminate the Jedi and usher in a new galactic age.
Dynasty of Evil, p. 9
Sidious could thus be considered the strongest Sith by this metric if there is a direct line from Darth Bane to Darth Sidious in which each Sith Master was killed by his apprentice in personal combat. This seems to be the case, but there are complications in this line from Bane to Sidious.
For one, the early Sith (including Bane himself) knew the transfer essense power. If successfully completed, this would allow a Sith Lord to transfer his consciousness to another body and control it (the Sith Lord's original body would be destroyed). However, the knowledge on how to do this was lost when the insane Darth Gravid destroyed as many Sith holocrons and artifacts as he could before he was killed by his apprentice, Darth Gean. Technically, Darth Gean defeated Darth Gravid in personal combat and thus succeeded him properly according to the Rule of Two. However, the loss of knowledge meant that Darth Gean and her successors (including Sidious) were left without a great deal of ancient Sith knowledge. Consequently, Sidious could not necessarily be considered the strongest Sith -- an ancient Sith with the knowledge of transfer essence (such as Bane) might be strong enough to defeat Sidious and take over his body.
In addition to lacking the knowledge of transfer essence, Sidious seems to lack Darth Plagueis' ability to resurrect someone. Darth Plagueis did succeed in repeatedly resurrecting a Bith named Venamis:
On the same day they had allowed Venamis to die.
Then, by manipulating the Bith’s midi-chlorians, which should have been inert and unresponsive, Plagueis had resurrected him. The enormity of the event had stunned Sidious into silence and overwhelmed and addled 11-4D’s processors, but Plagueis had carried on without assistance, again and again allowing Venamis to die and be returned to life, until the Bith’s organs had given out and Plagueis had finally granted him everlasting death.
Darth Plagueis, p. 279
However, Sidious told the newly minted Darth Vader that he did not know how to "cheat death" and he never demonstrated this ability. Sidious managed to cheat death via clones of himself, but this was not the same as Plagueis' resurrection ability. It is much closer to the original transfer essence power, but not as powerful since Sidious only transferred his consciousness to his own clones whereas Bane's transfer essence could be used to transfer one's consciousness to a hostile body and destroy that body's original consciousness. More pertinently to your question, Sidious would not have learned it via the Rule of Two -- he would have discovered it independently (and with a great deal of cloning help).
Since there were earlier Sith who knew powers that Sidious did not, Sidious was not necessarily the strongest Sith. Even if he was, it wasn't because of the Rule of Two since Sith knowledge was lost between the time of Darth Bane and Darth Sidious.
We don't have enough information to answer this with strictly canon sources. There are just too many variables to know for sure.
For example, we don't know if there is a direct line from Darth Bane to Darth Sidious in which each Sith Master was killed by his apprentice in personal combat. Consequently, we can't be sure that Sidious is the strongest, even if the transitive property holds.
It's also unclear from canon whether Darth Plagueis actually succeeded in resurrecting anyone. Sidious claimed that Plagueis did; however, Sidious also claimed that (1) Plagueis taught him "everything he knew"1 but (2) Sidious told Vader that he did not know how to cheat death (and never demonstrated such an ability). So while we know that Sidious did not know how to cheat death, we don't know if Plagueis had the ability and was thus stronger than Sidious in that sense.
Finally, it's worth noting that different Sith Lords had varying strengths and weaknesses. For example, Sidious was probably unmatched as a politician but may have been outmatched by another Sith Lord with a higher midi-chlorian count. If Vader hadn't lost his limbs on Mustafar, for example, Vader would have theoretically been more powerful than Sidious. Vader would have been able to defeat Sidious in personal combat in such a theoretical scenario, and yet Sidious might have been able to avoid such a duel via political machinations (e.g. have Vader overwhelmed and executed by the clone army). How do we decide which Sith is therefore "stronger"? Again, there is too much variability in skills among the different Sith Lords to declare one of them as the "strongest".
1From the Episode III script, Sidious told Anakin:
He became so powerful...the only thing he was afraid of was losing his power, which eventually, of course, he did. Unfortunately, he taught his apprentice everything he knew, then his apprentice killed him in his sleep. (smiles) Plagueis never saw it coming. It's ironic he could save others from death, but not himself.
The films themselves aren't clear that Sidious was Plagueis' apprentice, but starwars.com made that clear.
That appears to be the theory behind the Rule of Two.
However, it seems to me that it would actually end up resulting in a net loss of knowledge, if not necessarily raw power.
With a single master and a single learner, things will get left out or forgotten, holocrons of vital information will be lost, and misunderstandings of the lore will proliferate. Some things considered so absolutely basic as needing no explanation will fail to be explained and the learner will fail to learn.
An impatient apprentice may strike when he feels he is ready, though woefully lacking in training, and through sneakiness, raw combat ability, and/or luck he kills his master.
The probabilities point towards a degenerative spiral rather than steadily increasing power.
The greatest advantage of Society is the ability of the great minds of one generation to build upon the great minds of the previous generations. When you reduce the population of each generation to a single person, the points of failure are too many to maintain an increase in knowledge.
He wasn't, for a very simple reason. The very purpose of the Rule Of Two was to ensure that each Sith generation was stronger than the previous one. That means that it wasn't enough for the apprentice to just kill his master to succeed him. He had to over-power him, which means confronting him directly in mortal combat, at the peak of his power.
As Sidious states, prior to his death Plagueis had lost his power, or at least a significant enough part of it. At this point, even if Sidious had defeated him in combat, the ascend of the Sith Order's power would had already been in question. As if that wasn't enough though, Sidious's method of eliminating his master was by assassinating him in his sleep.
As such, Sidious's power was never even remotely put up against that of his master's and, in extention, that of the rest of the Sith that came before him. Who knows? Maybe he eventually did end up more powerful than his predecessors. Either way, it was never done through the application of the Rule of Two.
Knowledge=power The Banite Sith Lords didn't grow stronger in the Force; if that's what you think. When Sith speak about "power", they mean "knowledge".
