Everything in the entire material universe, is circles, squares, lines and arcs.
If you can rotate one piece and hold another piece completely still against it to cut it or grind it, you can make anything perfectly round and concentric.
Once you get a set of four pieces perfectly round, concentric, and identical, you can find perfect level.
Once you can make four pieces perfectly round, concentric, and level, you can take a piece and make one surface perfectly flat.
Once you can make one surface perfectly flat and level, you can make a second surface perfectly perpendicular to it, and perfectly flat and level.
Once you can make two surfaces perfectly flat, level, and perpendicular to each other you can always find 90 degrees.
Once you can make things perfectly round and concentric, and make two surfaces perfectly flat and perpendicular to each other, you can make anything flat and square on all sides.
Once you know one exact measurement... all you need to do is hold it up to something else you know the size of... and can make something flat, square, perpendicular, and level on all sides, then you can always find a 45 degree angle.
Once you can make something flat and square on all sides, and you can always find a 45 degree angle, you can make anything flat, square, and true on all sides.
Once you can find an exact measurement, and exact 90 and 45 degree angles, you can always find the center of any measurement, and you can always double any measurement.
Once you can halve and double any measurement, find 90 and 45 degrees, and find the center of any measurement, you can find any measurement at all.
Once you can find 90 degrees, 45 degrees, and any measurement at all, you can find any angle at all.
Once you can make something round, concentric, flat, square and true, and can find any measurement and any angle, you can make any spiral or helix you want, and thus, cut any screw thread or gear you want.
Once you cut four threads and four gears to act against each other, you can double the precision of your threads and gears.
Once you can find any measurement, and the center of any measurement, and can find 90 degrees, and 45 degrees, and any angle at all... and can halve and double them... you can double the precision of your measurements... and redouble them to any degree of precision.
Once you can double the precision of your measurements, and the precision of your threads and gears, you can make anything round, concentric, flat, square, and true at double precision.
Once you can make four flat, square, and true objects at double precision, and four round and concentric flat and shafts at double precision, you can double it again...
Then you can double the precision of your threads and gears again, and redouble, and redouble, to any degree of precision.
...and by doubling, redoubling, and halving, and quartering, over and over, you can find any measurement, of any line, at any degree of precision, and make anything round, concentric, flat, and square to any degree of precision.
Once you can find any measurement, at any degree of precision, and can always find the center, 90 and 45 degrees, you can find any angle, to any degree of precision.
Once you can find always find endpoints, and center points of any line, any measurement, and any angle, at any degree of precision, you can describe any arc, at any degree of precision.
... and cut any screw or gear, at any degree of precision.
Once you can make anything round, concentric, flat, square, true, and level, find any measurement and any angle, cut any screw and any gear, and describe any arc, at any precision...
... you can make anything at all...
This is how the entire industrial world developed, and how everything is still made today...
Everything... everything manufactured piece, every machine, everything in this modern world... begins with the lathe.
