Elliptic Integrals

Original Titles
English Titles

28Example of the construction of equations
52Solution of a problem requiring the rectification of an ellipse
154Observations on the rectification of ellipses
211Problema, ad cuius solutionem geometrae invitantur; theorema, ad cuius demonstrationem geometrae invitantur
251On the integration of the differential equations (m dx)/√(1-x4) = (n dy)/√(1-y4)
252Observations on the comparison of arcs of irrectifiable curves
261Example of another new methods for comparing transcendental quantities; on the comparison of the arcs of ellipses
263An example of a new method for the quadrature and rectification of curves and of comparing other quantities which are transcendentally related to each other
264Proof of a theorem and solution of a theorem proposed in the Acta Eruditorum of Leipzig
273Consideration of formulas, of which the integral can be obtained by sections of arcs of cones
295On the reduction of integral formulas for the rectification of the ellipse and hyperbola
345On integrated equations of the type dx/√(A+Bx+Cx2+Dx3+Ex4) = dy/√(A+By+Cy2+Dy3+Ey4)
347More general development of formulas serving for the comparison of curves
448A new infinite series that expresses the perimeter of an ellipse, and which converges very rapidly
506(Elucidations about a most elegant method, which the illustrious la Grange used in the integration of the differential equation dx/√X = dy/√Y
581A more complete investigation into the relationship between those quantities contained in the integral formula ∫ (\Z dz)/√(1+mzz+nz4), where Z denotes a rational function of zz.
582The fruitful development of a relation which may be established between the arcs of conic sections
590Certain theorems in analysis, of which a demonstration is thus far desired
605On the remarkable properties of the elastic curves under the equation y = ∫ (xx dx)/√(1-x4)
624De superficie coni scaleni, ubi imprimis intentes difficultates, quae in hac investigatione occurrunt, perpenduntur
633De binis curvis algebraicis inveniendis, quarum arcus indefinite inter se sint aequales
638On innumerable algebraic curves, of which the longitude is able to be measured by parabolic arcs
639On innumerable algebraic curves, of which the longitude is able to be measured by elliptical arcs
645On algebraic curves, of which the longitudes are expressed by the integral formula ∫ (vm-1 dv)/√(1-v2n)
676Methodus succinctior comparationes quantitatum transcendentium in forma ∫ (P dz)/√(A + 2Bz + Czz + 2Dz3 + Ez4) contentarum inveniendi
714Exempla quarundam memorabilium aequationum differentialium, quas adeo algebraice integrare licet, etiamsi nulla via pateat variabiles a se invicem separandi
780De infinitis curvis algebraicis, quarum longitudo indefinita arcui elliptico aequatur
781De infinitis curvis algebraicis, quarum longitudo arcui parabolico aequatur
782De binis curvis algebraicis eadem rectificatione gaudentibus
783On algebraic curves, all of whose arcs may be measured by circular arcs
817On curved lines, the rectification of which is measured by given quadratures
818On the comparison of irrectifiable curved arcs
819Continuation of some fragments taken from the Mathematics day book