Download Affine Geometries of Paths Possessing an Invariant Integral by Eisenhart L. P. PDF

By Eisenhart L. P.

Show description

Read Online or Download Affine Geometries of Paths Possessing an Invariant Integral PDF

Similar geometry and topology books

Symplectic Geometry & Mirror Symmetry

Complaints of the 4th KIAS Annual overseas convention, held in August 14-18, 2000, Seoul, South Korea. major specialists within the box discover the newer advancements with regards to homological replicate symmetry, Floer thought, D-branes and Gromov-Witten invariants.

General topology and applications: proceedings of the 1988 Northeast conference

Lawsuits of the Northeast convention at the topic at Wesleyan college, Connecticut, in June 1988. the 2 dozen papers, by way of mathematicians from the united states, Canada, and the Netherlands, file on fresh advances in topology for study mathematicians and graduate scholars. They specialize in the theor

Additional resources for Affine Geometries of Paths Possessing an Invariant Integral

Example text

W e shall see that the data of mathematics are not without their premises; they are not, as the Germans say, voraussetzungslos; and though math­ ematics is built up from nothing, the mathematician does not start w i t h nothing. H e uses mental i m ­ plements, and i t is they that give character to his science. Obviously the theorem of parallel lines is one instance only of a difficulty that betrays itself every­ where i n various forms; i t is not the disease of geometry, but a symptom of the disease.

53 kind of argument, and its statements are practically tautologies. The case is different w i t h causation. The class of abstract notions of which causation is an instance is much more complicated. keenest thinkers was in deep earnest when he doubted the possibility of p r o v i n g this obvious state­ ment. A n d K a n t , seeing its kinship w i t h geometry and algebra, accepted i t as a priori and treated i t as being on equal terms w i t h mathematical axioms. Yet there is an additional element i n the formula of causation which somehow disguises its a priori origin, and the reason is that it is not as r i g i d l y a priori as are the norms of pure logic.

M a x i m u m intensity. Each of these rays, thus ide­ ally constructed, is a representation of the straight line which being the shortest path between the start­ ing-point A and any other point, is the climax of directness: i t is the upper limit of effectiveness and its final boundary, a 11011 plus ultra. I t is a m a x i ­ m u m because there is no loss of efficacy. , the greatest intensity on the shortest path that is reached among infinite possibilities of progression by u n i f o r m l y following up all.

Download PDF sample

Rated 4.33 of 5 – based on 22 votes