Final answer:
The term for surgical incision of the bladder through the rectum is akin to transrectal cystotomy, which is an atypical procedure in contemporary medicine, with laparoscopy being the preferred minimally invasive technique.
Step-by-step explanation:
The medical term for a surgical incision of the bladder through the rectum is not commonly performed and does not have a standardized term like other more common procedures. However, the description closely matches an approach known in urology as a transrectal cystotomy.
This is a more unconventional approach compared to the typical routes for bladder surgery such as suprapubic or retropubic methods, partly due to the potential risks of infection and complications related to the proximity to the rectum. In modern medical practice, this type of procedure would likely be adapted for minimally invasive techniques such as laparoscopy, where a small camera (such as a duodenoscope) is used to assist the surgeon in visualizing internal structures without the need for large incisions.