For instance, with Project Origami, it was Microsoft — not Apple — that presaged the coming of a cheap, touch-centric tablet with all-day battery life. But, as we all know, the iPad hails from Cupertino, not Redmond.

With last week’s announcement of iCloud, we may be on the verge of seeing history repeat itself.

For years, Microsoft, under Ray Ozzie, has been on about the opportunity of merging software with the cloud. In particular, Ozzie’s team laid the groundwork for Live Mesh, a software service designed to keep documents in sync, in the cloud and on devices.

But after a quick start out of the gate when it was launched back in 2008, Mesh has been at best running in place for the past several years. It has gone through name changes, feature changes and switched places in the Microsoft organization. Yet, it remains limited by its caveats and complexity.

While Google touted its cloud-only approach with Docs and Microsoft allowed Mesh to stagnate, Apple flew largely under the radar. It took baby steps of its own, mainly with a little-known product called iDisk that allowed documents to be saved to the cloud. Like Mesh, it was limited and cumbersome. But Apple has clearly learned from its mistakes.

Has Microsoft?

To be fair, we don’t totally know the answer to this. There are indications that there will be greater cloud integration in the upcoming Mango version of Windows Phone and little is known of Windows 8, beyond ARM chip support and the new interface shown at D9.

What we do know is what Apple is pledging to deliver this fall: a service that synchronizes all one’s documents, wherever they are saved and on PCs, Macs and mobile devices — at least the mobile ones with an Apple logo. By contrast, Microsoft’s Mesh remains a work in progress, and one where users still have to actively decide which files and folders they want to keep in sync.

Live Mesh, though it takes Ozzie five pages to describe it, is essentially a “software-plus-services” platform that uses the Web to synchronize and share data among devices, applications and people (you’ll find a walk-through here and a good overview here).

“Over the past ten years, the PC era has given way to an era in which the Web is at the center of our experiences–experiences delivered not just through the browser but also through many different devices including PCs, phones, media players, game consoles, set-top boxes and televisions, cars, and more,” Ozzie writes. “It is our mission in this new era to create compelling, seamless experiences that combine the power of the Internet, with the magic of software, across a world of devices. … the Web is the hub of our social mesh and our device mesh.”

“The Web is the hub of our social mesh and our device mesh.“

Wait.

Does Bill Gates know that? Because last year he told CNN’s “American Morning,” “We’re making the PC the place where it all comes together.” Clearly, in the ensuing year, Gates and Microsoft noticed that Google (GOOG) et al. are fast shifting computational relevancy to the Web, away from the desktop and, more importantly, away from Microsoft.

Live Mesh, if it’s successful, will change that. Because, as Joe Wilcox notes over at Microsoft Watch, “Live Mesh is Microsoft’s attempt to turn operating system and proprietary services platforms into hubs that replace the Web. Microsoft is building a services-based operating system that transcends and extends Windows and also the function of Web browsers.” Adds Wilcox, “It’s bold, brilliant and downright scary.”