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Has anyone ever encountered this book before?

It seems to be a very old book of tricks, including some billiard shots.

If the ebay listing can be taken at face-value, I think this book pre-dates Charles Cotton's The Complete Gamester, which (IIRC) was the first work containing rules of billiards and was published in the late 1600s.

Google's translation of the description is:

Ens, Caspar. Thaumaturgus mathematicus, id est, admirabilium effectorum e mathematicarum disciplinarum fontibus profluentium sylloge. Nunc denuo correctior & auctior. Cologne, Munich, 1651. 8°, approximately 15.5 x 10.5 cm. 4 sheets, 304 pp. (with the variant sheet 303-4), 8 sheets, with title woodcut and several woodcuts in the text Newer half-leather with colored paper covers.

- VD17 23:273399R (only has 1 sheet at the end). Rare second Latin edition (first published in 1636) of this curious work about mathematical games, tricks, salon magic, alchemy, etc. This copy includes both versions of the last text sheet, including the one with the bookseller's epilogue, in which the reader is informed that one... presented him here with an adaptation of a French work. These are the "Recréations mathématicques" by the Jesuit Jean Leurechon, which were also translated and adapted or imitated in other countries. The writer Caspar Ens (1570-1656) was apparently particularly interested in remote topics and translated several works from French, including "Guzman de Alfarache" into Latin.
- The woodcuts show various tricks, including a scene on a billiard table on page 146.

- Slightly browned due to the paper, a small trace of worms at the beginning with no loss of text, only the last few sheets a little worn and with damp edges, otherwise very clean. With the rare last leaf in both variants.
 
I haven't, but it's in Google. I don't know much about ancient books, but I wouldn't be surprised if that listing was just someone selling this Google PDF printed on parchment.

Full text is here:

www.google.com

Thaumaturgus mathematicus

www.google.com

Problem LXXXIV is the billiard problem shown in the listing:

1695247475471.png


1695247569725.png
 
Here's a computer translation of the first problem (I was bored). The author is describing the physics of billiards:

"What about? When and how is mathematics used in devices? established, and through [unknown] spread? Possibly, there's hardly any game/practice regulated by mathematical principles more perfectly than this: for every motion is either direct or reflected. From this, just as for the observation of flat and convex mirrors, through straight lines, the production and reflection of light, and the [explanation/manifestation] of forms/species.."...is sung/expressed, in the same manner, the movements of spheres are sufficiently elucidated by lines and geometrical angles. Although the skill of the players, strengthened by frequent practice, might prevail over all others in this respect, following the teachings: however, it pleases [us/the author] to put forth some very important principles; by adhering to which it will certainly and always be easiest to prevail/win."

"I. Whenever a ball is struck by another ball, or by a net, the motion occurs in a straight line from the center of the ball to the point of contact."

"II. In any reflected motion, it is necessary that the angle of incidence is equal to the angle of reflection. The reflected motion, about which I am speaking, occurs, for example, when a ball hits a wall, or a net, or even a drum, and then bounces back. With these established, we then conclude: First: To which point the force directing the ball or sphere should be aimed, so that the ball, when struck regularly, reflects to the intended place. Second: At which point of the stationary ball the pushing force of another will contract, so that it drives the third one at a distance, or itself, through the equality of both angles, rushes into it. Third: By what means can one deflect a stationary ball in any desired direction upon the impact of another."

"However, in this, it is noteworthy that the motion gradually proceeds by decreasing, and by progressing, it diminishes. Hence, the greatest incidences and reflections cannot be observed as precisely as with solar rays. Therefore, this deficiency will be compensated either by discretion or by force."
Click to expand...

For context, Newton published his laws of motion in 1687.
 
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Sooo... There we have ghost ball aiming and mirror-like cushions. The latter is particularly impressive since rubber wasn't used much for cushions until about 1850.
 
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physics and math never change so anything that was true , still is. It seems like a mathematician tried explaining the forces and calculations that were related but he seems to admit it's somewhat impractical.
 
snookered_again said:
physics and math never change so anything that was true , still is. It seems like a mathematician tried explaining the forces and calculations that were related but he seems to admit it's somewhat impractical.
Click to expand...

At least based on the Google database, it might be one of the earliest surviving printed discussions of these basic concepts.
 
I did a little more reading, and it seems like there was a fad in Europe in the 1600s for books of mathematical puzzles. Apparently there was a lot of 'borrowing' of content. I might try to do some investigating and see where billiards first come into the genre, and what people do with it.

If anyone else is interested, we could coordinate here. I would hope at least some of the books would be available in digital form in public archives.
 
The mathematics is exciting.

I believe the competition history is more relevant.

A world championship is a precursor to a global treaty or alliance.

Can you imagine someone saying this game billiards is what we have, now the entire world has to play it?

Whoever was organizing billiards knew government was not the direction to go to build relationships.

Math puzzles are typically intelligence tests. Anyone giving a test is likely an employer.

Back then saying something falling down was a big deal thanks to Newton and his apples. Builders had a practical knowledge, academics had an abstract knowledge.
 
where I sit, math wasn't even invented yet until about 200 or maybe 300? years ago. nor was the invention of the wheel, or metal tools. or written language, or farming. There are no ancient wheels buried here.. It proves how slow worldly knowledge transfer was. The biology of the people was really no different, same amount of brain power, almost identical physical and mental capabilities. some very minor differences in physical features. Evolution was slow! Someone once said we are all of African descent if history and lineage are important.
 
Leonardo Da Vinci was pretty interesting, He definitely had an imagination, aside from paintings he did a lot of diagrams of war machines and showed a lot of early inventiveness. some was pretty impractical but a lot of it was really brilliant too. It would be interesting to see more of his museum artifacts in Italy, I got to see some paintings etc in Florence, would have liked to see the museum based upon him over there.

Leonardo da Vinci Interactive Museum Florence Leonardo Interactive Museum® Florence

Discover in Florence an interactive museum dedicated to Leonardo da Vinci. Come and try the inventions of the great genius and participate in the educational workshops
leonardointeractivemuseum.com
 
Bob Jewett said:
Are you joking? On the face of it, this statement is horribly ignorant.
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I'm not clear what you read into, to arrive at those feelings or what you think is terrible. The point was that human evolution happens very slowly, but knowledge transfer , in the past, was very limited. the topic was how math and physics evolved. I dont see it as insulting. many dont realize how young the wheel is , here. Thats just history.
 
snookered_again said:
I'm not clear what you read into, to arrive at those feelings or what you think is terrible. The point was that human evolution happens very slowly, but knowledge transfer , in the past, was very limited. the topic was how math and physics evolved. I dont see it as insulting. many dont realize how young the wheel is , here. Thats just history.
Click to expand...
Serious math has been around for a few thousand years. Not 200. That's just history.
 
the people that built the pyramids obviously did have pretty advanced math. The part that strikes me is it took that long to arrive Here in BC. Canada There are no artifacts here that show use of math or the wheel that date earlier than sailing ships from europe, when they arrived technology in many of these forms also migrated.

How could a technology as simple as the wheel be lost? one would think it would transfer even without written language. there were no roads here. no old wheels. riding horses wasn't even a method of transportation here.

They were not invented 400 years back. Not here, Yes in Europe they were.

Maybe the ancient Myans had technology in south america that was lost in history? they evidently had technology which was somehow lost over time.. did the myans have the wheel? If so, how was that technology lost?
 
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