. The principles of projective geometry applied to the straight line and conic . In the figure let ACBAVEbe any inscribed hexagon, and letK, L, M be the points of inter-section of pairs of opposite AB meet AG R, and BCmeet AC in T. By the anharmonic property ofthe circle (Art. 73) {) = {). Therefore taking intercepts onAB and GB, {BRKA) = {BGMT). Since these ranges have a self-corresponding point at B, the linesRG, KM, and TA, which join cor-responding points, are the points K, L, M arecollinear. In the figure let achach beany circumscribed hexagon, a
. The principles of projective geometry applied to the straight line and conic . In the figure let ACBAVEbe any inscribed hexagon, and letK, L, M be the points of inter-section of pairs of opposite AB meet AG R, and BCmeet AC in T. By the anharmonic property ofthe circle (Art. 73) {) = {). Therefore taking intercepts onAB and GB, {BRKA) = {BGMT). Since these ranges have a self-corresponding point at B, the linesRG, KM, and TA, which join cor-responding points, are the points K, L, M arecollinear. In the figure let achach beany circumscribed hexagon, andlet k, I, m be the connectors ofpairs of opposite vertices. Letah. ac be r, and hc. ac be t. By the anharmonic property oftangents to a circle (Art. 73) {a . hcha) = (c. hcba). Therefore joining these rangesto ah and ch, (6VA-a) = (hcmt). Since these pencils have a self-corresponding ray in h, the pointsre, km, and ta, which are the inter-sections of corresponding rays, arecollinear. Therefore the lines k, I,m are concurrent. Projective Theorems for the Circle 163 91. De
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Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometryprojective
