8460 Quadrature 



methods, Simpson's formula, elementary de- 

 monstration. Steen, A. N. A. Mth. 10 

 (1871) 301-. 



, generalisation. Peano, G. Tor. 

 Ac. Sc. At. 27 (1892) 608-. 



, Stirling's and Wallis's formulae, demonstra- 

 tion. Mansion, . Brux. S. Sc. A. 23 

 (1899) (Pt. 1) 1-. 



of parabola. Voller, . Grunert Arch. 32 

 (1859) 420-. 



, cycloid, and logarithmic spiral. Stain- 



ville, de. Par. EC. Pol. Cor. 2 (1809-13) 

 434-. 



parabolas of 3rd degree. Parmentier, T. 

 As. Fr. C. R. (1879) 150-. 



parabolic curves. Catalan, E. C. [1880] 

 Brux. Ac. Sc. Mm. 43 (1882) (No. 8) 9 pp. 



segments cut off by focal chords. 

 Grunert, J. A. Grunert Arch. 26 (1856) 

 351-. 



parallel surfaces. Roberts, W. Tortolini 

 A. 1 (1850) 143-. 



plane curves. Carvallo, J. N. A. Mth. 1 

 (1842) 370-. 



polygons. Tessari, D. A. G^n. Civ. 3 

 (1864) 239-. 



problems reducible to, approximate solution. 



Monteiro da Rocha, J. Lisb. Ac. Sc. Mm. 



1 (1797) 218-. 

 of quadrics. Jellett, J. H. Camb. and Dubl. 



Mth. J. 1 (1846) 57-; Liouv. J. Mth. 12 



(1847) 92-. 

 . Azzarelli, M. Rm. N. Line. At. 29 



(1876) 337-. 

 , central. Schlomilch, 0. Liouv. J. Mth. 



8 (1863) 89-. 

 and rectification. Carmichael, R. Camb. and 



Dubl. Mth. J. 9 (1854) 266-. 



, reduction to "cubature" and quadra- 

 ture respectively. Denzler, W. Ziir. Mt. 3 

 (1853-55) 75-. 



reduction to rectification. Plana, G. Palomba 



Rac. 2 (1846) 276-. 

 of simple curves, synthetic demonstration of 



rule. Young, M. [1786] Ir. Ac. T. 1 (1787) 



31. 



spherical curves, application of elliptic 

 functions. Tortolini, B. [1849] Mod. S. It. 

 Mm. 24 (1850) 337-. 



surface of cone. Sucksdorff, C. G. Helsingf. 

 Acta 4 (1856) 121-. 



, ellipsoidal, and volume of surface of 8th 



degree, similarity of expressions for. Torto- 

 lini, B. Tortolini A. 3 (1852) 530-. 



, reduction to rectification of curve, 

 Euler's and Legendre's formulae compared. 

 Plana, G. Palomba Rac. 2 (1846) 169-, 

 254-. 



surfaces. Schubert, F. T. St Pe"t. Ac. Sc. 

 Mm. 9 (1824) 277-. 



. Dirksen, E. H. Berl. Ab. (1833) 123-. 



. Bedetti, G. Bologna N. Cm. 6 (1844) 



341-. 

 . Carmichael, R. Camb. and Dubl. Mth. 



J. 9 (1854) 266-. 



. Stem, A. (xn) Ts. Mth. 1 (1865) 38-. 



, formula. Roberts, W. Tortolini A. 1 



(1850) 318-. 



Rectification 8460 



of surfaces parallel to ellipsoid. Tortolini, B. 

 G. Arcad. 119 (1849-50) 3-. 



surface of elasticity. Tortolini, B. 



Tortolini A. 7 (1856) 373-. 



resulting from intersection of cylinders. 



Lanciani, F. A. Mt. 7 (1865) 169-. 



, ruled, cases, and volumes of solids en- 

 closed. Saladini, G. [1804] Bologna Mm. 

 I. It. 1 (1806) 69-. 



, theorem. Jellett, J. H. Camb and 

 Dubl. Mth. J. 5 (1850) 176-. 



, and volumes of solids. Tortolini, B. 

 Palomba Rac. 1 (1845) 96-; Crelle J. 31 

 (1846) 12-; 34 (1847) 101-. 



vaults and lunes. Riccati, G. Verona S. 

 It. Mm. 5 (1790) 48-. 



and volumes. Carvallo, J. N. A. Mth. 1 



(1842) 370-. 

 , approximate. Mansion, P. C. R. 95 



(1882) 384-. 



, equations being given implicitly in 

 Cartesian coordinates. Azzarelli, M. Rm. 

 N. Line. At. 28 (1875) 134-. 



by infinite series. Trowbridge, D. Des 



Moines Anal. 7 (1880) 47-. 



of surface of elasticity. Roberts, W. 

 Liouv. J. Mth. 11 (1846) 124. 



of y* = s - x*. Bonnet, O. N. A. Mth. 3 (1844) 

 75. 



/*\ 2 



- - + 



\a/ 

 Mth. Ps. 6 



:1. Spitzer, S. Arch. 



61 (1877) 329-. 



Ratio of triangle to sector of conic. Fabritius, 



W. As. Nr. 129 (1892) 49-. 

 . Ball, L. de. As. Nr. 



129 (1892) 283-. 

 Rectifiable algebraic curves. Humbert, G. 



C. R. 104 (1887) 1051-. 



arcs of ellipse. Ocagne, M. d'. G. Teix. 

 J. Sc. 7 (1886) 178-. 



curves. Schlomilch, 0. Z. Mth. Ps. 15 

 (1870) 124-. 



. Koenigsberger, .L. Mth. A. 32 (1887) 



589-. 



, finding. Doppler, C. Grunert Arch. 

 19 (1852) 236-. 



on surfaces of revolution. Fuss, N. 

 [1818] St Pdt. Ac. Sc. Mm. 8 (1822) 198-. 



plane algebraic curves. Humbert, G. Liouv. 

 J. Mth. 4 (1888) 133-. 



Rectification. 



of algebraic curves. Kobb, G. Stockh. 6fv. 



(1887) 713- ; Fschr. Mth. (1887) 504. 

 approximate. Pellet, A. E. Par. S. Mth. Bll. 



19 (1891) 5-. 

 , of circular arcs. Rankine, W. J. M. 



Ph. Mg. 34 (1867) 381-. 

 , , case. Berg, F. J. van den. N. 



Arch. Wisk. 4 (*1878) 200- ; 10 (1884) 186-. 

 , circumference of circle. Barrachina, 



E. S. Fschr. Mth. (1897) 447. 

 , curves. Somoff, J. [5omov, O. I.] 



[1870] St Pet. Ac. Sc. Bll. 15 (1871) 257-; 



St Pet. Ac. Sc. Mm. (Rs.) 18 (*1871) 25-. 



627 



KR2 



