# Transformations of Applicable Conjugate Nets of Curves on by Eisenhart L.P.

By Eisenhart L.P.

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Extra info for Transformations of Applicable Conjugate Nets of Curves on Surfaces

Example text

9. Given p is false, g is true. Then q p 36. q :. not p 37. P ~ q p~q 39. if 42. notp ~ q :onotq~ p ~ 40. p p ~ q :. p ~ q and q ~ p 38. ~ :. not q p~qorq~p 41. p ~ q "p and g" is false. Then "p and g" is false. Then "p or g" is false. Then "p or g" is false. 10. "p or g" is called a conjunction I 1. If P isf alse, then not -p is true. of p and g. ' 12. " 13. " 14. " 15. The negation "not (p or g)" has the same meaning as "not p or not go" 16. " 17. " 18. If an implication is true, its converse is also true.

5. What What What What What point is the is the is the is the Postulate n. This is called the point plotting postulate. Postulate 12. If AB is a rayon the edge of the half-plane h, thenfor every n be0 and 180 there is exactly one ray AP, with P in h, such that mLP AB = n. This is called the angle construction postulate. Postulate 13. (segment addition postulate). A set of points lying between the endpoints of a line segment divides the segment into a set of consecutive segments the sum of whose lengths equals the length of the given segment.

They represent agreements in truth values of statements that have proved useful to mathematicians and logicians. 4. Disjunction. connective "or" table for the disjunction should have discovered that p and q are true. " It is false when both p and q are false and true in other cases. " = A13 and ,113 U {A, B} = A13. 5. Negation. Statements be made about other statements. " 8. It is not true that 2 plus four equals 6. 9. Two plus 4 equals 8. 10. Perpendicular lines form right angles. I]. All equilateral triangles are equiangular.