*Frontmatter, pg. i*Contents, pg. iv*Introduction, pg. vii*PART I. The Weierstrass integral J, pg. 1*Part II. The Euler Equations, pg. 34*Part III. Minimizing arcs, pg. 92*PART IV. Preparation for Global Theorems, pg. 125*PART V. Global Theorems, pg. 173*Appendices, pg. 217*Bibliography, pg. 244*INDEX OF TERMS, pg. 252