This was a remarkable case in that the fresh proglottids clearly showed the characteristic uterine branching pattern without the need for clearing, mounting, or India ink injection. Instead, you can see all of the lateral branches coming off of the central uterine stem with surprising clarity:
Note that you should only count the primary branch points coming off of the central uterine stem. Also, it is important to count only on one side. As you can see from my line drawing above, there are ~15 branches that can be identified in this specimen, thus making this either Taenia saginata or T. asiatica. Given that this patient was from Africa, we can narrow the differential to T. saginata, the "beef" tapeworm. Upon questioning, the patient admitted to frequently eating undercooked beef, which is the route of human infection.
As a confirmatory measure, the proglottids were manipulated to release eggs like the one shown below, which confirm without a doubt that this is a Taenia proglottid. Note the characteristic morphologic features including internal hooklets (one is clearly seen) and thick outer wall with radial striations.
If one eats undercooked meat in Africa it’s a general rule
It’s likely he will end up with proglottids in his stool!
As deeper into your ID you delve,
Count those branches more than twelve!
You’ll see it’s T. saginata, just like you learned in school!