Applications of Calculus to Plane Curves 



8430 



Curvature formulae in trilinear coordinates. 

 Walton, W. QJ. Mth. 8 (1867) 39-. 



at multiple point. Painvin, L. C. B. 68 

 (1869) 131- ; A. Mt. 4 (1870-71) 215-. 



of 3rd order. Dupin, C. C. E. 26 (1848) 

 321-, 393-. 



properties of ellipse and hyperbola. Wright, 

 C. Camb. (M.) Mth. M. 2 (1860) 198-. 



, question in. Cesdro, E. Mathesis 13 (1893) 

 177-. 



relations of pencil of curves at basis point. 

 Weyr, E. Z. Mth. Ps. 15 (1870) 486-. 



Curves. 

 (See also 7610, 7630.) 



algebraic, curvature. Servais, C. Brux. Ac. 



Bll. 21 (1891) 587-; 22 (1891) 512-. 

 , , etc. Ocagne, M. d'. Mathesis 12 



(1892) 100-. 

 , equal to circular arcs [p=r (a-r)]. Fuss, 



N. [1823] St Pet. Ac. Sc. Mm. 11 (1830) 



274-. 

 , hyperbolic arcs. Fuss, N. [1798] 



St Pet. Ac. Sc. N. Acta 14 (1805J 111-. 

 , intersecting orthogonally, and their con- 



focality. Rummer, E. E. N. A. Mth. 11 



(1852) 426-. 

 analogous, intrinsically, to catenary of equal 



resistance. Cifarelli, T. G. Mt. 36 (1898) 



183-. 

 angles with straight lines. Monteiro, A. S. 



G. Teix. J. Sc. 1 (1878) 81-. 

 angularly related, theorems. Holditch, H, 



QJ. Mth. 3 (1860) 271-. 

 apses. Longchamps, G. de. As. Fr. C. E. 



(1891) (Pt. 2) 23-. 



arcs, Graves' and Chasles's theorem, generali- 

 sation. Humbert, G. C. E. 104 (1887) 



1826- ; N. A. Mth. 7 (1888) 5-. 

 with arcs between same radii vec tores equal. 



Fuss, N. [1801] St Pet. Ac. Sc. Mm. 2 



(1810) 29-. 

 asymptotes from polar equation. Nell, A. M. 



Grunert Arch. 15 (1850) 315-. 

 case where curve is its own evolute. Binet, J. 



P. M. Liouv. J. Mth. 6 (1841) 61-. 

 pedal. Haton de la Goupil- 



liere, J. N. Liouv. J. Mth. 11 (1866) 329-. 

 s varies as tan 6. Fuss, N. [1818-26] St 



Pet. Ac. Sc. Mm. 9 (1824) 115- ; 11 (1830) 



314-. 

 cases where p varies as r 2 . Euler, L. St 



Pet. Ac. So. Mm. 9 (1824) 47-. 



normal. Farcy, A. N. A. 

 Mth. 3 (1844) 528-. 



(1) y n ; (2) r; (3) p; (4) s\ 



Hill, T. Am. As. P. 22 (1873) 31-. 

 r is proportional to projection of p upon 



r. Du Chatenet, M. N. A. Mth. 5 (1886) 



233-. 

 s varies as ylx. Velde, A. Arch. Mth. 



Ps. 14 (1896) 200-. 

 characteristic equation 1 , interpretation, cases. 



Brocard, H. P. P. B. (xn) Mathesis 2 (1882) 



25-, 49-. 

 classes, two remarkable. Laisant, C. A. As. 



Fr. C. E. (1890) (Pt. 2) 74-. 



8430 



closed, belonging to same family, criterion. 



Crocchi, L. G. Mt. 10 (1872) 302-. 

 , mean curvature, formulae. Lindelof, L. L. 



[1870] Helsingf. Acta 9 (1871) 361-. 

 , parallels. Hoppe, R. Arch. Mth. Ps. 66 



(1881) 46-. 

 with constant polar tangent. Giard, . N. 



A. Mth. 1 (1862) 70-. 

 continuous development, extension of theorem 



of Bernoulli. Mainardi, G. A. Sc. Lomb. 



Yen. 7 (1837) 29-. 

 convexity and concavity, theorem. Gerono, G. 



C. N. A. Mth. 18 (1859) 397. 

 cubic, curvature. Hoist, E. Arch. Mth. Ntvd. 



7 (1882) 109-, 177-. 

 with several cusps. Laurent, H. N. A. Mth. 



19 (1860) 210-. 

 cutting at given angle. Hoppe, JR. (vi Adds.) 



Berl. Pol. Gs. Vh. 20 (1859) 135-. 



given curve at angle which is given function 

 of point. Franconi, E. G. Mt. 38 (1900) 

 232-. 



cyclic, curvature, and projective geometry. 

 Schwarz, A. Mh. Mth. Ps. 10 (1899) 250- ; 

 11 (1900) 71-. 



, of direction. Humbert, G. Liouv. J. Mth. 

 4 (1888) 129-. 



denned by differential equation, 1st order, be- 

 tween two variables, systems. Dyck, W. 

 Munch. Ak. Sb. 21 (1892) 23-; 22(1893)101-. 



intrinsic relation. Pirondini, G. G. 

 Mt. 30 (1892) 326-; 31 (1893) 51. 



law of rectification. Ocagne, M. d\ 

 N. A. Mth. 10 (1891) 82-, 133. 



property of centre of gravity of area. 



Collignon, E. As. Fr. C. E. (1886) (Pt. 2) 53-. 



relation between ordinate area and sub- 

 tangent. Schlomilch, O. Grunert Arch. 

 10 (1847) 215-. 



"derived." Druckenmiiller, N. Crelle J. 26 

 (1843) 1-. 



" ," algebraic and differential equations. 

 Tortolini, B. A. Mt. 6 (1864) 88-. 



from two plane curves. Laisant, C. A. 

 Par. S. Mth. Bll. 16 (1888) 172-. 



determination, application of method of para- 

 meters. Moseley, H. Thomson A. Ph. 11 

 (1826) 321-. 



by tangential distances from given curves. 

 Ocagne, M. d'. N. A. Mth. 17 (1898) 115-. 



of direction of 3rd class. Laguerre, E. N. A. 

 Mth. 2 (1883) 97-. 



for which 



to - L 



Appell, P. N. A. Mth. 15 (1896) 491-. 

 dividing circular arcs through 2 fixed points 



into n equal parts. Burali-Forti, C. G. 



Mt. 27 (1889) 153-. 

 double tangents. Cayley, A. Phil. Trans. 



(1859) 193-. 

 enveloped, theory. Heilermann, . Grunert 



Arch. 24 (1855) 438-. 

 equidistant, properties. Mahistre, G. A. [1855] 



(xn) Lille S. Mm. 3 (1857) 1-. 

 with evolutes and involutes equal inter se, inte- 

 grals. Aoust, . C. E. 84 (1877) 385-; 



Par. S. Mth. Bll. 7 (1879) 143-. 



600 



