Sorry, no online dictionaries contain the exact phrase orthogonal axis.
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Reverse dictionary results:
1. quadrant
 2. revolving door
3. cartesian
4. luminance
5. radiance
6. curvilinear
7. ell
8. orthographic
9. perpendicularity
10. strain
 11. stress
12. stressed
13. trajectory
14. abscissa
15. amplitude
16. back
17. bak
18. core
19. crane
20. cross section
 21. direction
22. elevation
23. fimbriate
24. globe
25. gnomon
26. inclination
27. inclinometer
28. kingpin
29. lap
30. lapped
 31. level
32. median
33. nack
34. occipital
35. ordinate
36. orthotropic
37. pitch
38. plagiotropic
39. point
40. pole

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You can look up the words in the phrase individually using these links:   orthogonal ?   axis ?
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