RM, circular saws were in use in the 18th century. Perhaps not widely in use but still in use.
It’s commonly told that Samuel Miller was awarded
British Patent #1152 in 1777 for what is considered the first circular saw machine. Some assert that the wording in his patent indicates the
circular blade itself was in common use by that time — it was the sawing machine itself that Miller had invented.

A patent drawing for an early table (circular) saw. Being a Shaker, Tabitha Babbitt did not patent (1810) her original version.
As with many inventions, accounts of the circular saw’s early history are conflicting. Some evidence shows that Gervinus of Germany built something similar in 1780, while others claim it was the Dutch who invented the device some hundred or so years earlier.
All that said, I have had a clock or two from 1820-1830 that had the circular saw cut marks in case parts. Not common. And yes, I proceed with great caution anytime I see such marks in "period" pieces as they generally do suggest something is likely wrong!
I have been doing a bit of research on clock making machines used in the USA 1750-1850. The very few clock-related "machines" from those periods support a lot of one-off sorts of clocks and even limited production runs, I.E. Terry and the famous Porter contract clocks as well as the tools from Seth Thomas, etc. The surviving machinery tends to lead us into perhaps incorrect assumptions on early production clockmaking. There is a dearth of information on early machinery before about 1840. Yet, by 1840 cast iron massive machines were being made for just about every purpose. They didn't just remarkably fall off a turnip truck starting in 1840. Their predecessors are the machines that built tens of thousands of clocks in America, machines of which we have no surviving examples. For purposes of understanding the machine sophistication of the period please review this device. Here is an example of a pin making machine circa1838. I suspect equally sophisticated clockmaking machines had been developed and used early in the 19th century. By the introduction of Jeromes' 1839 patent clock, a clock very quickly made in the thousands if not 10's of thousands, machines had to be pretty well developed. Just sayin'
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