6810 



Planimetry. Quadrilaterals 



6810 



Quadrangles, complete. Neuberg, J. Mathesis 



11 (1891) 33-, 67-, 81-, 189-. 

 , transformation. Gob, A. As. Fr. C. R. 



(1894) (Pt. 2) 294-. 



Quadrilaterals. (See also 7210.) 



Fraczkieicicz, A. (vi Adds.) Krk. Boczn. 



Uniwers. 15 (1833) 123-. 

 Fenwick, S. Mathematician 2 (1847) 285-. 

 Baur, C. W. Schlomilch Z. 4 (1859) 236-. 

 Farjon, F. N. A. Mth. 11 (1892) 41-. 

 Area. Dostor, G. J. N. A. Mth. 7 (1848) 69-. 



with given sides, maximum. Enneper, A. 

 Gott. Nr. (1885) 175-. 



, minimum. Sturm, R., & Lampe, 



E. Crelle J. Mth. 96 (1834) 78-. 



in terms of vertices, determinant expression. 

 Dostor, G. .N. A. Mth. 13 (1874) 559-. 



Centroid. Commie;-, . N. A. Mth. 2 (1843) 



392-. 

 , when external. Matzka, W. Grunert 



Arch. 18 (1852) 352-. 

 Common or re-entrant quadrilateral, equations 



of condition. Shortrede, R. Beng. J. As. 



S. 11 (1842) 28-, 207-. 

 Complete quadrilateral. Schlomilch, O. Leip. 



B. (1854) 4-. 

 . Mansion, P. [1875] Mess. Mth. 5 



(1876) 158-. 

 . Kantor, S. [1877-79] Wien Ak. Sb. 



76 (1878) (Ab. 2) 774-; 78 (1879) (Ab. 2) 



172- ; 79 (1879) (Ab. 2) 757-. 

 ,6 circles of. Schlomilch, 0. Schlo- 

 milch Z. 2 (1857) 274-. 

 , properties. Ehlert, A. [1882] Arch. 



Mth. Ps. 69 (1883) 332-. 

 , relating to bisectors. Sancery, L. 



N. A. Mth. 14 (1875) 145-. 



and quadrangle, involutory properties, 

 generalisation. Loria, G. Mil. I. Lomb. 

 Ed. 18 (1885) 491-. 



, theorem. Steiner, J. Gergonne A. 

 Mth. 18 (1827-28) 302-. 



Cyclic quadrilateral. Greiner, M. Arch. Mth. 

 Ps. 60 (1877) 178-. 



of two circles, properties. Dostor, G. 

 N. A. Mth. 6 (1867) 57-. 



(or rather tetrastigm) , properties. Nager, 



J. Mh. Mth. Ps. 7 (1896) 325-. 

 Deltoid, plane or skew (2 isosceles triangles on 



common base). Reuschle, C. G. Z. Mth. 



Ps. 10 (1865) 506-. 

 Doubly-centric quadrilaterals. Schlomilch, 



0. X. Z. Mth. Ps. 23 (1878) 193-. 



. Beyel, C. Z. Mth. Ps. 44 (1899) 237-. 



Harmonic quadrilateral. Neuberg, J. Mathesis 



5 (1885) 202-, 217-, 241-, 265-. 

 In- and circum-quadrilaterals. Schumacher, 



J. Arch. Mth. Ps. 2 (1885) 383-. 

 . Langr, J. Casopsis 28 (1899) 244- ; 



Fschr. Mth. (1899) 458. 



, properties. Durrande, J. B. Ger- 

 gonne A. Mth. 15 (1824-25) 133-. 



In-quadrilateral with diagonals at right angles. 



Sancenj, L. N. A. Mth. 10 (1871) 487-. 

 In-quadrilaterals. Grunert, J. A. Grunert 



Arch. 5 (1844) 428- ; 8 (1846) 335. 



In-quadrilaterals, Girard's three, having equal 

 sides and inscriptible in same circle. Dostor, 

 G. Arch. Mth. Ps. 66 (1881) 27-. 



, metric relations. Zimmermann, O. Arch. 

 Mth. Ps. 7 (1889) 64-. 



Middle points of diagonals in straight line, 

 Gauss's proof. Hall, A. Mess. Mth. 4 

 (1868) 137. 



Miquel's theorem, generalisation to n lines. 

 Kantor, S. [1877-79] Wien Ak. Sb. 76 



(1878) (Ab. 2) 753-; 78 (1879) (Ab. 2) 789-. 

 Orthogonal quadrilateral, 57 propositions. 



Beyel, C. Z. Mth. Ps. 34 (1889) 218-, 290-. 

 Parallelograms, most simple, symmetrical 



about an axis. Tchebitchef, P. L. As. Fr. 



C. E. (1878) 159-. 

 Properties. Dostor, G. Arch. Mth. Ps. 48 



(1868) 245-. 

 Quadrilateral with opposite sides equal. Lu- 



dicke, M. A. F. Gilbert A. 56 (1817) 198-, 



334-, 439- ; 64 (1820) 341-. 

 Quadrilaterals derived from quadrilateral, 



metrical properties. Bretschneider, C. A. 



Grunert Arch. 3 (1843) 84-. 



and triangles, theorems. Vecten, . Ger- 

 gonne A. Mth. 9 (1818-19) 293-. 



Eational quadrilaterals. Kummer, E. E. Crelle 



J. 37 (1848) 1-. 

 Sides and diagonals, relation between. Grunert, 



J. A. Grunert Arch. 38 (1862) 373-. 

 Square with angles situated on four straight 



lines. Clausen, T. St Pet. Ac. Sc. Bll. 7 



(1864) 177-. 



through four points, construction and 

 generalisation. Crelle, A. L., & Lehmus, . 

 Crelle J. 34 (1847) 280- . 



Squares connected with two circles, problems, 

 analytical. Mack, L. Arch. Mth. Ps. 64 



(1879) 225-. 



, decomposition into four superposable parts. 



Brunei, G. Bordeaux S. Sc. PV. (1896-97) 



161-. 

 , division into n equal squares, problem. 



Stmcell, T. P. Des Moines Anal. 2 (If 



73-. 



(1875) 



, properties. Westcott, 0. S. Am. As. P. 



(1883) 94-. 

 Trapezium, centroid, construction. Walker, 



J. J. QJ. Mth. 9 (1868) 338-. 

 , properties. Davies, T. S. Tilloch Ph. 



Mg. 68 (1826) 116-. 



Eectilinear figures, cutting into equal portions. 



Gerwien, . Crelle J. 10 (1833) 228-. 

 , geometry. Neuberg, J. As. Fr. C. E. 



(1893) (Pt. 2) 26-. 

 , logical order of treatment. End res, . 



Toul. Mm. Ac. 4 (1860) 339-. 

 , simpler than triangle, and their ap- 

 plication in theory. Matzka, W. Grunert 



Arch. 8 (1846) 365-. 

 Set square, measurement with false. Grunert, 



J. A. Grunert Arch. 18 (1852) 477-; 25 



(1855) 230-. 

 Similar figures. Grouard, A. (x) Par. S. 



Phlm. Bll. 2 (1865) 68-, 104- ; 7 (1871) 4-, 



51-, 74-, 115- ; 10 (1873) 34-. 



441 



