Areas. Applications of Integral Calculus 



8460 



of spheroidal triangle, sides of which are lines 

 of shortest distance. Puissant, L. Par. 

 Mm. Ac. Sc. 10 (1831) 530-. 



star-polygons. Jacobi, C. G. J. Crelle J. 

 65 (1866) 173-. 



surface of elasticity. Roberts, W. Liouv. 

 J. Mth. 11 (1846) 81-. 



--- ellipsoid, and surface of ellipsoidal 



vault on rectangular base. Plana, G. Crelle 



J. 17 (1837) 345-. 

 -- , expression for. Strebor [Roberts, W.]. 



N. A. Mth. 9 (1850) 310. 

 -- , -- . Faure, H. N. A. Mth. 11 (1852) 



393-. 

 -- , from perimeter, application to volumes. 



Linotte, L. Bologna Opusc. Sc. 2 (1818) 108-. 



surfaces. Essen, E. Grunert Arch. 22 

 (1854) 56-. 



-- , analogies to Viviani's theorem. Crocchi, 



L. G. Mt. 13 (1875) 170-. 

 -- , by coordinates determining direction of 



normal to an element. Schlomilch, 0. 



Z. Mth. Ps. 11 (1866) 505-. 



, and length of curves. Goedseels, . 

 Brux. S. Sc. A. 16 (1892) (Pt. 1) 79-. 



in polar coordinates. Bing, F. (xn) 

 Ts. Mth. 4 (1874) 164-. 



-- , various. Schlomilch, 0. Leip. B. 18 



(1866) 38-. 

 theorem including Holditch's, and analogue in 



3 dimensions. Elliott, E. B. Mess. Mth. 7 



(1878) 150- . 

 of trajectories described in plane motion of figure 



of invariable form. Liguine, V. Bll. Sc. 



Mth. As. 2 (1878) (Pt. 1) 306-. 



2 triangles, problems in maximum. Dippe, 

 M. C. Crelle J. 16 (1837) 65-. 



and volumes. Terquem, 0. N. A. Mth. 5 



(1846) 232-. 

 -- (shallow surfaces) , approximate formulae 



for. Geisenheimer, L. Z. Mth. Ps. 30 (1885) 



325-. 

 volumes, centroids, etc., application of approxi- 



mation formula for definite integrals. Li- 



gowski, W. Ev. Mar. et Col. 51 (1876) 



159-. 

 and volumes of conical wedge. Monteiro, A. S. 



G. Teix. J. Sc. 2 (1880) 68-, 81-, 110-. 



cylindrical ungula. Schell, W. 

 Grunert Arch. 19 (1852) 70-. 



-- , determination. Juel, C. N. Ts. Mth. 8 

 (B) (1897) 49-; Fschr. Mth. (1897) 497. 



-- of ellipsoid, reduction of integrals for. 

 Lobatto, R. ' Amst. Vs. Ak. 13 (1862) 193-. 



-- , fundamental problem. Rausenberger, 0. 

 Mth. A. 43 (1893) 601-. 



generated by motion of curves and 

 surfaces. NehU, C. Arch. Mth. Ps. 13 

 (1895) 225-, 337-. 



-- and lengths related to regular polygons. 



Gelin, E. Mathesis 11 (1891) 160-. 

 -- , measurement. Sang, J. [1836] Edinb. 



N. Ph. J. 22 (1837) 231-. 

 -- of surfaces of equation 



8460 



and volumes of surfaces generated by regular 

 polygon rotating about a diameter. Sohncke, 

 L. A. Arch. Mth. Ps. 48 (1868) 457-. 



tore (anchor ring). Gelin, E. 

 Mathesis 10 (1890) 190- ; 11 (1891) 66-. 



in trilinear and quadriplanar coordinates. 



Slesser, G. M. QJ. Mth. 2 (1858) 357-. 



zone, etc. Stein, J. P. Gergonne A. Mth. 

 16 (1825-26) 257-. 



of zoneof pedal surfacesof quadrics. Schlomilch, 

 O. Leip. B. 14 (1862) 51-. 



Argument 



- of plane curve F (x, y) = 0, 



Spitzer, S. D. Nf. B. (*1877) 111-. 



properties. Roberts, R. A. L. Mth. S. P. 



15 (1883-84) 4-; 16 (1884-85) 238-. 

 Boundary integral. Prym, F. E. [1869] 



Crelle J. 71 (1870) 305-. 

 Closed plane curves, theorem. Risteen, A. D. 



A. Mth. 3 (1887) 104. 

 Conical surfaces, integrals analogous to angle 



and its bisector. Humbert, G. C. B. 105 



(1887) 739-. 

 Conies, pedals and inverses of division of arcs. 



Strebor [Roberts, W.]. N. A. Mth. 11 (1852 



182-. 

 Cono-cuneus of Wallis, problem. Berg, F. J. 



van den. Amst. Arch. Wisk. Gn. 2 (1860-63) 



1-, 10-, 23-. 

 Curves, arc of which is elliptic or hyperelliptic 



integral of 1st kind. Schwering, K. Z. Mth. 



Ps. 25 (1880) 234-. 

 , integral of 1st kind. 



Kiepert, L. [1874-76] Crelle J. Mth. 79 



(1875) 304- ; Freiburg B. 7 (1880) 1-. 

 , equals elliptic arc. Euler, L. 



[1781] St Pet. Ac. Sc. Mm. 11 (1830) 95-. 

 , parabolic arc. Euler, L. 



[1781] St Pet. Ac. Sc. Mm. 11 (1830) 



100-. 

 , arcs of which can be expressed by circular 



arcs. Euler, L. [1781] St Pet. Ac. Sc. 



Mm. 11 (1830) 114-. 

 , . Serret, J. A. 



[1852] Par. EC. Pol. J. 33 e cah. (1853) 



69-. 

 , represent elliptic functions. 



Serret, J. A. Liouv. J. Mth. 10 (1845) 



421-. 

 , Legendre's elliptic functions of 



1st kind. Talbot, W. H. F. Gergonne A. 



Mth. 14 (1823) 380. 



conjugate hyperbolas, perimeters, 

 two theorems. Roberts, W. Liouv. J. Mth. 

 13 (1848) 179-. 



on ellipsoid. Dienger, J. Tortolini A. 2 

 (1851) 104-. 



with equal arcs. Leaute, H. Toul. Ac. Sc. 

 Mm. 6 (1874) 419-. 



quadrable by elliptic or circular functions, 

 Clebsch's two theorems. Marie, M. C. E. 

 84 (1877) 227-. 



Cycloidal arcs. Tortolini, B. A. Mt. 7 (1865) 



211-. 

 Cylinder and sphere, problems. Berg, F. J. 



van den. Amst. Arch. Wisk. Gn. 2 (1860- 



63) 1-, 10-, 23-. 



624 



