Preface 1. Introduction 2. Historical note on Landen's transformation and the various scales of moduli and amplitudes 3. On the scale of arithmetico-geometrical means 4. Landen's scale of increasing amplitudes 5. The hyperbolic scale of increasing amplitudes 6. Gauss' scale of increasing amplitudes 7. Landen's scale of decreasing amplitudes 8. The hyperbolic scale of decreasing amplitudes 9. On the numerical computation of the third elliptic integral 10. Note on the calculation of the third elliptic integral in terms of the complementary A. G. M. scale Summary of formulae Appendix. Examples 1-35.
Preface 1. Introduction 2. Historical note on Landen's transformation and the various scales of moduli and amplitudes 3. On the scale of arithmetico-geometrical means 4. Landen's scale of increasing amplitudes 5. The hyperbolic scale of increasing amplitudes 6. Gauss' scale of increasing amplitudes 7. Landen's scale of decreasing amplitudes 8. The hyperbolic scale of decreasing amplitudes 9. On the numerical computation of the third elliptic integral 10. Note on the calculation of the third elliptic integral in terms of the complementary A. G. M. scale Summary of formulae Appendix. Examples 1-35.
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