By Robert E. Stong

These notes comprise the 1st entire remedy of cobordism, a subject matter that has turn into more and more very important some time past ten years. the topic is totally built and the newest theories are treated.

Originally released in 1968.

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For our next example we pass to the thirteenth century and consider the contributions of Nasiraddin (1101-1174), Persian astron- omer and mathematician, who compiled an Arabic version of Euclid and wrote a treatise on the Euclidean postulates. He seems to have first to direct attention to the importance, in the study of the Fifth Postulate, of the theorem on the sum of the angles of a triangle. In his attempt to prove the Postulate one finds the germs been the of important ideas Nasiraddin first which were asserted, F to be developed later.

Of the substitutes for the Fifth some to examine we wish present Postulate. 1 1 . Substitutes (or the Fifth Postulate. When, in the preceding chapter, attention was directed to the importance of the Fifth Postulate in elementary geometry and in what is to follow here, the reader may have been disturbed by an inability to recall any previous encounter with the Postulate. Such a situation is due to the fact that most writers of textbooks on geometry use some substitute postulate, essentially equivalent to the Fifth, but simpler in statement.

The angle (A, k) 5. (/>", The III. last A"), *h* two **tl* ( h '> *') spectively, angle also to angle (h" , k"*). line point of a. A not lying on a, then there exists, in the plane and A but not any of Continuity. Given any two segments . ) AB and CD, sequence of points A\, A%, As, An . of Parallels. (Playfair's A\Ai, AzAz, re- the ' A'B'C congruent to angle a and a point V. The Postulate segments and the congruence of angles. and A'B'C, AB, AC and angle BAC are, congruent to A'B', A'C and angle B'A'C, then ABC is The Postulate Given a VI.

### Notes on cobordism theory, by Robert E. Stong

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