6810 



Planimetry ; Circles 



6810 



Calculation to 200 decimal places (Dase). 



Schulz van Strasznitzki, L. C. Crelle J. 



27 (1844) 198. 

 250 . Clausen, T. As. Nr. 25 



(1847) 207-. 

 350 . Rutherford, W. N. A. Mth. 



14 (1855) 209-. 



400 . Eichter, (Prof.) . Grunert 



Arch. 22 (1854) 473. 

 . Strehlke, F. Grunert Arch. 



23 (1854) 475-; 24 (1855) 472. 

 500 . Eichter, (Prof.) . Grunert 



Arch. 25 (1855) 471-. 

 707 . Shanks, W. E. S. P. 21 



(1873) 318-. 

 , elementary. Grunert, J. A. Arch. Mth. 



Ps. 46 (1866) 345-. 

 , , description. Matzka, W. Grunert 



Arch. 9 (1847) 74-. 



by logarithms. Chevillier, I. N. A. Mth. 



15 (1856) 261-. 



Determination by equivalent surfaces. Jube, E. 



N. A. Mth. 7 (1848) 366-. 

 , experimental. Hall, A. [1872] Mess. Mth. 



2 (1873) 113-. 



by isoperimeters. Jube, E. N. A. Mth. 5 

 (1846) 42-. 



. Andre, J). N. A. Mth. 13 (1874) 128-. 



, numerical. Girault, . Eouen Tr. Ac. 

 (1850-51) 63-. 



by perimeters. Huet, . N. A. Mth. 4 

 (1845) 156-. 



. Fouche, M. Par. S. Mth. Bll. 18 



(1890) 135-. 

 , Ptolemy's method. Terquem, O. N. A. 



Mth. 13 (1854) 253-. 

 Dirichlet's formula, proof, etc. Lebesgue, V. A. 



Liouv. J. Mth. 11 (1846) 76-. 

 Discrepancies in published value of IT. Shanks, 



W. [1873] E. S. P. 22 (1873-74) 45-. 

 Expression by rapidly convergent series. Lucas, 



F. C. E. 112 (1891) 1050-. 

 Numerical values of first 12 powers and their 



reciprocals, etc. Glaisher, J. W. L. L. Mth. 



S. P. 8 (1876-77) 140-. 

 Powers of w. Broch, 0. J. Sk. Nf . F. 8 (1860) 



571-. 

 Eeciprocal of w, calculation to 208 decimal 



places. Rutherford, W. Phil. Trans. (1841) 



281-. 

 Series for w, and general theorem. Gasparis, 



A.de. Nap. Ed. 7 (1848) 269-. 

 , new. Thomson, (Prof.) James. [1836- 



38] E. S. P. 3 (1836) 417- ; Edinb. E. S. T. 



14 (1840) 217-. 

 Theorem, of which Wallis's theorem is a case. 



Grunert, J. A . Grunert Arch. 38 (1862) 466-. 

 Van Ceulen's 35-decimal value and some of his 



works. Elevens de Haan, D. [1873] (vn) 



Mess. Mth. 3 (1874) 24-. 



Wallis's and Brouncker's expressions, ana- 

 lytical investigation. Plana, G. Crelle J. 



17 (1837) 1-, 163-, 338-. 



formula. Collignon, E. Par. EC. Pol. J. 

 47 cah. (1880) 103-. 



for 71- , and the area of the curve y = sin k x. 



Mansion, P. Mathesis 20 (1900) 183-. 



Wallis's fractions, analysis. Kramp, C. 

 Erfurt N. Acta 1 (1799) 257-. 



Eectification, approximate. Gergonne, J. D. 



Gergonne A. Mth. 8 (1817-18) 245-. 

 , new method. Srfttek, J. Casopis 21 (1892) 



83-; Fschr. Mth. (1892) 530-. 

 Segment, calculation. Grunert, J. A. Arch. 



Mth. Ps. 44 (1865) 363-. 



containing given angle, instrument for de- 

 scribing. Rollet de I'Isle, . Ev. Mar. et 

 Col. 128 (1896) 90-. 



Segments, Greek approximate formulae (Hero). 



Tannery, P. Bordeaux S. Sc. Mm. 5 (1883) 



347-. 

 Self-polar circle. Grunert, J. A. Arch. Mth. 



Ps. 41 (1864) 132-. 

 Semicircles, Apollonius's problem. Sangro, G. 



Nap. At. Ac. 2 (1825) 41-. 

 Shoemaker's knife (a/>/37?Xos) . Mackay, J. S. 



Edinb. Mth. S. P. 3 (1885) 2-. 

 Stewart's properties, demonstration. Strong, T. 



[1814] Conn. Mm. Ac. 1 (1816) 393-. 

 Systems of circles. Cayley, A. QJ. Mth. 2 



(1858) 83-. 

 . Gehrke, J. N. Ts. Mth. 9 (B) (1898) 



11-; Fschr. Mth. (1898) 436. 

 , with application to Dupin's cyclides. 



Hoist, E. Christiania F. (1885) No. 15, 4 pp.; 



Fschr. Mth. (1885) 574-. 



, new method of representation. 

 Fiedler, W. As. Fr. C. E. 10 (1881) 127-. 



Tangent circles. Guibal, . Nancy Mm. S. 



Sc. (1843) 67-. 

 Tangents, trapeziums, etc. Hey, R. Phil. 



Trans. (1814) 348-. 

 Theorem. Miquel, A. Liouv. J. Mth. 3 (1838) 



485-. 

 Theorems. Brioschi, F. N. A. Mth. 15 (1856) 



462-. 

 . Jefdbek, W. [1880] Arch. Mth. Ps. 66 



(1881) 325-. 

 Transformations. Larmor, A. B. A. Ep. 



(1887) 607. 



Circular billiards problem. Transon, (Prof.) A. 



N. A. Mth. 9 (1850) 340-. 



. Auric, . N. A. Mth. 13 (1894) 215-. 



Congruent figures, propositions. Petersen, J. 



N. Ts. Mth. 9 (B) (1898) 1-; Fschr. Mth. 



(1898) 431. 

 , relative positions. Zeuthen, H. G. Mth. 



Ts. 5 (1863) 97-. 

 Constructions. Smith, H. J. S. Camb. and 



Dubl. Mth. J. 7 (1852) 118-. 

 , class. Feldblum, M. Wiad. Mt. 4 (1900) 1-. 



of 2nd degree, aids to. Adler, A. Wien 

 Ak. Sb. 99 (1891) (Ab. 2a) 846-. 



founded on the circle. Study, . Bonn 

 Niedr. Gs. Sb. (1897) 80-. 



, linear. Kirkman, T. P. Manch. Ph. S. 



Mm. 9 (1851) 279-. 

 , Mascheroni's, theory. Adler, A. Wien Ak. 



Sb. 99 (1891) (Ab. 2a) 910-. 



in mensuration. Bangma, 0. S., & Keyser, 

 J. F. Amst. Mengelwerk 2 (1816) 1-. 



plane and in space with the straight line 



only. Tilly, J. de. Mathesis 5 (1885) 124-. 



435 



EE2 



