Theories of Parallelism An Historical Critique
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S, where J. is a con- stant over the plane. But A 4= A'; and therefore S must be zero, and A infinite ; and the geometry of the plane is parabolic.
Wallis' proof of the Fifth Postulate was effected thus : Let MA, NB be two straight lines making with MN the angle.s AMN, BNM together less than two right angles. Suppose the angle AMN to slide along MN until M reaches N. Then because the angle AMN is less than the supplement of the angle BNM, AM in its final position will be outside BNM.
Therefore ...at some position of MA before M reaches N, say ma, MA will intersect NB, say at p. Now by the principle of similitude, it is possible to draw on MN a triangle similar to the triangle mNp. Therefore corresponding to the point p there exists a point P wherein MA and NB intersect. Q.e.d.
Theories of Parallelism 19 LEIBNIZ Characteristica Geometrica, 1679 ; In Euclidis IIPOTA ; etc.
Leibniz's geometrical tracts have been gathered together in the first volume of his collected mathematical writings (Ger- hardt's edition, Halle, 1858).
What to read after Theories of Parallelism An Historical Critique?
You can find similar books in the "Read Also" column, or choose other free books by William Barrett Frankland to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
S, where J. is a con- stant over the plane. But A 4= A'; and therefore S must be zero, and A infinite ; and the geometry of the plane is parabolic.
Wallis' proof of the Fifth Postulate was effected thus : Let MA, NB be two straight lines making with MN the angle.s AMN, BNM together less than two right angles. Suppose the angle AMN to slide along MN until M reaches N. Then because the angle AMN is less than the supplement of the angle BNM, AM in its final position will be outside BNM.
Therefore ...at some position of MA before M reaches N, say ma, MA will intersect NB, say at p. Now by the principle of similitude, it is possible to draw on MN a triangle similar to the triangle mNp. Therefore corresponding to the point p there exists a point P wherein MA and NB intersect. Q.e.d.
Theories of Parallelism 19 LEIBNIZ Characteristica Geometrica, 1679 ; In Euclidis IIPOTA ; etc.
Leibniz's geometrical tracts have been gathered together in the first volume of his collected mathematical writings (Ger- hardt's edition, Halle, 1858).
What to read after Theories of Parallelism An Historical Critique?
You can find similar books in the "Read Also" column, or choose other free books by William Barrett Frankland to read onlineMoreLess
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