It's all in the title -
It appears that the 35670A communicates using HP's PCL (Printer Command Language) version 5 or 5e based on the release date of the product. There are adaptors available from various online vendors which convert either RS232 (the serial port) or Centronics parallel port to USB. If you simply connected this to your printer, chances are it would not be able to understand the PCL commands natively. It is difficult even to find printers for purchase today which support PCL5. To use an adaptor you would have to find a suitable interpreter driver for your PC to generate a PDF that you could print directly from your computer.
A few people online have attempted this project using a general-purpose microcontroller or dedicated custom PCB to interpret PCL commands. It is a complex task to design your own adaptor and custom parallel/RS232 drivers, but there is a relevant discussion on the EEVblog forum with some ideas. It looks like there are a couple products discussed on that thread which may do this job but I cannot guarantee success since I have not tested them myself.
If you don't have the time to dive so deeply into this task, your best bet might be to look for some old HP printers or HP-GL plotters to buy second-hand. Of course, make sure you can find all the necessary accessories and ink cartridges before committing to a purchase.
Hope this helps.
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