. The principles of projective geometry applied to the straight line and conic . 76 Principles of Projective Geometry fji 1 CA\AD CD J_CA^^ AD CD BA CA_RA^ CA• • BD CD ~ BD ■ CD .-. {ADBC) = {ADBC).(3) If P and P correspond in the two homographic ranges and that AB. CP AP. BCAB ^ AC ^ APSince the ranges arc projective, (ACBP) = (ACBP), _ AB .CP•• ~ 1^ 1_ AC AP = 0. 1AC 1A^ [] 1 JP , ^ (4) If Q, i2 be the double points of two projective ranges and AA and BB pairsof corresponding points then {QAnA) = {). (5) If a st
. The principles of projective geometry applied to the straight line and conic . 76 Principles of Projective Geometry fji 1 CA\AD CD J_CA^^ AD CD BA CA_RA^ CA• • BD CD ~ BD ■ CD .-. {ADBC) = {ADBC).(3) If P and P correspond in the two homographic ranges and that AB. CP AP. BCAB ^ AC ^ APSince the ranges arc projective, (ACBP) = (ACBP), _ AB .CP•• ~ 1^ 1_ AC AP = 0. 1AC 1A^ [] 1 JP , ^ (4) If Q, i2 be the double points of two projective ranges and AA and BB pairsof corresponding points then {QAnA) = {). (5) If a straight hne meet the sides of BA and BC of a triangle ABC in Cj andJj respectively, and the lines joining P, any point on the line, to C and A meet theopposite sides in C and A, prove that ACi AC CA^ ^ = 1 By projection from P, (.•lS(7i(7) = (-li?^ {ABCiC) + {CBAiA) = l. (6) Draw a line through a given point to meet the sides of a given triangle inthree points which with the given point form a range of given anharmonic Projective Forms Anharmonic 77 Let 0 be the given point. Draw any transversal to meet the sides in a point A on this line such that {OACB) has the given anharmonic A to A to meet AB in A. Let OA meet AB and AC in C and B. ThenOABC is the required transversal. (7) Prove the following test for collinearity of the three points 6>, J/, N; OABCand OABC are any two straight lines through 0 ; also AMB, BMA\ BNC, BNCare straight lines. Then the required condition for collinearity is that ^4^, BB\CC are concurrent. In Art. 35 s will not pass through 0 unless the ranges are in perspective, inwhich case AA\ BB\ CC are concurrent. (8) Two ranges ABCD and ABCD on diifereut lines have a common point A ;CD and CD meet at V. Show that {AB, CD)x{AB, GD)= V{BB, CD).In the figure (ABCD) = {) = {ADDC).Therefore{ABCD){ABCD) = {ABCD){ADDC) D^ = {DCBA){DCAD) = {DCBD) = {BDDC)= {). (9) A 0, BO, CO connect the vertices of a triang
Size: 1875px × 1333px
Photo credit: © Reading Room 2020 / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometryprojective
