13.

  1. Orte und Lagen: places and positions.
  2. [1]
  3. see [1 Note 2].
  4. [2]
  5. gelegen: situated.
  6. [3]
  7. fortschreitende Bewegung: motion of translation.
  8. [4]
  9. die ... Wege: the paths; see [1 Note 10].
  10. [5]
  11. von einem ... begriffenen Körper: of a body engaged; see 1 Note 10.
  12. [6]
  13. see [1 Note 2].
  14. [7]
  15. der ... Weg: the path; see [1 Note 10]
  16. [8]
  17. infolge (in Folge): in consequence.
  18. [9]
  19. einer beliebig: of any desired, of any whatever.
  20. [10]
  21. kommt ... zu stande: comes about, is brought about.
  22. [11]
  23. bei: in the case of (not by.) Bei is of very common occurence with this meaning, which will generally suggest the proper preposition (at, with, in etc.) to use in English.
  24. [12]