Sprint Nextel (NYSE:S) reported third-quarter results this morning, completing the trifecta of major American telecoms with reporting duties. That means it's time to do a little bit of deductive reasoning: Taken together with Verizon (NYSE:VZ) and AT&T's (NYSE:T) reports over the past week, we'll get a read on what Apple (NASDAQ:AAPL) might tell us tonight.

First, let's look at Sprint's news. The third-largest wireless network reported a net loss of $0.26 per share on $8.8 billion in sales. The top-line figure hit analyst expectations right on the nose and the net loss was only about half as bad as the Street had feared. The company faced $1.6 billion of subsidy expenses this quarter, up from $1.2 billion a year ago.

iPhones and other high-speed smartphones come with large subsidy discounts up front, and Sprint is selling a lot of these things nowadays. 81% of Sprint's contract-bound handset sales this quarter were smartphones.

So let's get back to the iPhone tally. Sprint handed out 1.5 million iPhones to its customers, and 40% of these were new accounts for the company. These figures are about the same as the second quarter's, and have been comparable ever since Sprint started selling iPhones in the fourth quarter of 2011.

So what happens when you throw Ma Bell and Big Red into the mix? This is what we get: Verizon sold 3.1 million iPhones in its just-reported quarter and AT&T led the pack with 4.7 million. Ignoring smaller iPhone vendors such as Alaska Communications Systems (NASDAQ:ALSK) and Appalachian Wireless, whose total sales amount to a rounding error in these calculations, the Big Three sold about 9.3 million iPhones.

To put that figure into perspective, Verizon sold 2 million iPhones a year ago and AT&T shipped 2.7 million units. All told, that's 4.7 million handsets, so American iPhone sales just about doubled year over year.

Granted, the iPhone 4S was released too late to count against the year-ago quarter's results and many fans were holding out for the new model. But the telecoms' reporting periods align perfectly with Apple's, so these numbers should be a pretty good proxy for Cupertino's iPhone sales.

In 2011, Apple sold a grand total of 17 million iPhones in the September quarter, worth $11 billion in revenue. If the network math points in the right direction, we should see at least 34 million units and $22 billion of iPhone revenue tonight -- and probably a bit more since Apple is growing sales faster abroad. Analysts currently expect about 27 million activations, so the carrier reports sure look like a good omen.