6830 Trigonometry 



Plane Triangles 6830 



T , , 1 1 , TT , Non-Euclidean trigonometry, plane, of 3-di- 



Hentity, m arc tang- + n arc tang - = k j , solu- mensional homogeneous space. Rethy, M. 



tion in integers. Stormer, C. Par. S. Mth. 

 Bll. 27 (1899) 160-. 

 , cos 36 - cos 72 = , proof. Volpicelli, P. 



Em. At. 16 (1862-63) 85. 

 , if S cos x r = 0, 2 cos (x r + a) = 0, then shall 



2cos(av + 0) = 0. Laisant, C. A. Par. S. 



Mth. Bll. 15 (1887) 198-. 



Inaccessible points, distance between 2. Boy- 

 man, J. R. Grunert Arch. 18 (1852) 452-. 



, . Ladame, H. (jun.) Neuch. 



Bll. 7 (pt. 2) (1866) 403-. 



., 3. Lemoine, E. As. Fr. C. E. 



(1884) (Pt. 2) 47-. 



straight line, problem. Gelin, E. Mathesis 

 9 (1889) 93-. 



Inequalities, trigonometrical. Femvick, E. 



Mth. Gz. 1 (1900) 107-. 

 Inequality, case. Genese, R. TF. As. Fr. C. E. 



(1894) (Pt. 2) 134-. 

 Isoperimetric figures, simple demonstrations. 



Steiner, J. Berl. Ab. (1836) 117-. 

 Landen's substitution, geometrical representa- 

 tion. Schellbach, C. H. Crelle J. Mth. 91 



(1881) 347-. 

 Logarithmic sines and tangents of small arcs, 



finding. Burgess, J. Edinb. E. S. P. 22 



(1900) 265-. 

 Logarithms, graphic notation. Haro, . As. 



Fr. C. E. (1887) (Pt. 2) 128-. 

 Maximum and minimum, problems. Burg, A. 



Wien Jb. Pol. I. 8 (1826) 213-. 



product of tangents of n angles whose sum 

 is given. (a + 6<90, etc.) Gerono, G. C. 

 N. A. Mth. 17 (1858) 360-. 



de Moivre's theorem. Barfuss, F. W. Grunert 



Arch. 7 (1846) 3-. 

 , analogue in plane point system. Hyde, 



E. W. Science 4 (1896) 344; A. Mth. 11 



(1896-97) 129-. 



, demonstration, elementary. Davidov, 

 A. Y. (xn) Eec. Mth. (Moscou) 2 (1867) 

 (Pt. 2) 20-' 



, without imaginaries. Gopel, A. 

 Grunert Arch. 6 (1845) 102-. 



(xn) Mag. Tud. Ak. Etk. (Mth.) 4 (1877) 

 (No. 7) 25 pp. 



Parallelograms formed from any three elements. 

 Cebysev, P. [1879] St Pet. Ac. Sc. Mm. 

 (Rs.) 36 (*1880) (Suppl.) No. 3, 40pp. 



symmetric about axis. Cebysev, P. [1878] 

 St Pet. Ac. Sc. Mm. (Rs.) 34 (* 1879) (Suppl.) 

 No. 3, 16 pp. 



Partial fraction and product, developments for 

 trigonometric functions. Schroter, H. Z. 

 Mth. Ps. 13 (1868) 254-. 



Plane Triangles. 



Ambiguous case. Grunert, J. A. Grunert 



Arch. 2 (1842) 333-. 

 Angles, construction for difference of two. 



Walker, J. J. QJ. Mth. 8 (1867) 323-. 

 , property. Arndt, F. Grunert Arch. 6 



(1845) 333-; 8 (1846) 111-. 

 , relations between trigonometrical ratios. 



Dostor, G. Arch. Mth. Ps. 65 (1880) 188-. 



in terms of sides. Borenius, H. G. [1839] 

 Helsingf. Acta 1 (1840) 159-. 



, Newton's Arithmetica Univer- 



salis, prob. xi., solution and generalisation. 



Leblais, A. Presse Sc. 2 (1863) 687-. 

 Area. Tweedie, C. [1900] Edinb. Mth. S. P. 



19 (1901) 2-. 

 , determinant value. Dostor, G. Arch. 



Mth. Ps. 57 (1875) 204-. 



of indeterminate triangle. Gyory, S. [1860] 

 (xn) Mag. Ak. Ets. (Mth. Term.) 2 (1861- 

 62) 59-. 



in terms of bisectors. Sacchi, G. N. A. 

 Mth. 1 (1862) 332-. 



sides. Gerono, G. C. Gergonne 



A. Mth. 15 (1824-25) 305-. 

 , Hero's theorem. Hultsch, F. 



Z. Mth. Ps. 9 (1864) 225-. 

 , . Panek, A. Casopis 20 



(1891) 310- ; Fschr. Mth. (1891) 607. 

 , proof of the " Three Brothers." 



Kinkelin, H. Grunert Arch. 39 ' 



187-. 



, that e xi = cos x + i sin x. Bauer, K.L. . < Ownert J. A . 



Arch. Mth. Ps. 46 (1866) 355-. 

 , symbolic use. Dupuis, N. F. [1891-95] 



Cn. E: S. P. & T. 9 (1892) (Sect. 3) 43-; 2 



(1896) (Sect. 3) 167-. 

 Navigation problems, graphical solutions. 



Anon. Nt. 47 (1892-93) 547-. 

 Negative quantities, use. Waille, J. [1876] 



(xn) Doubs S. Mm. 1 (1877) 33-. 

 Networks, trigonometrical, of low order. 



Zrzavy, F. Prag Sb. (1872) 107-. 

 Nomenclature. Bjorling, E. G. Stockh. Ak. 



Hndl. (1846) 275-, 299-. 

 Non-Euclidean trigonometry. Story, W. E. 



Am. J. Mth. 4 (1881) 332-; 5 (1882) 



180-. 



, fundamental equations derived by ele- 

 mentary method. Rethy, M. Arch. Mth. 



Ps. 58 (1876) 416-. 



Grunert Arch. 40 (1863) 134-. 

 . , synthetic demonstration. Degen, 



C. F. [1821] Kiob. Dn. Vd. Selsk. Afh. 1 



(1824) 129-. 

 Hypotenuse, approximation to. Buquoy, G. 



von. Oken Isis (1826) 570-, 662-. 

 Mensuration, notes on. Durdn Loriga, J. J. 



G. Teix. J. Sc. 12 (1895) 45-; Fschr. Mth. 



(1893-94) 928. 

 Pothenot's problem. Clausen, T. As. Nr. 20 



(1843) 69-. 

 , Lehmann's theorem. Hartner, . 



Wien SB. (1849) (Ab. 2) 216-. 

 Problems, important, solution. Korselt, A. 



Arch. Mth. Ps. 17 (1900) 275-. 

 Eational right-angled triangles, incommen- 

 surability of angles. Berdelle, C. As. Fr. 



C. E. (1890) (Pt. 2) 186-. 



466 





