Smart, Edward Howard · London : Macmillian and Co. · leaf 66
ngle FAB, we haveFD.AH.BC= +DA.HB.CF. 38 PROJECTIVE GEOMETRY AH HB AE EB AH AE HB EB Also considering the transversal DCE cutting the sides ofthe same triangle, by Menelaus theorem FD.AE. BC= -DA. EB . CF. It follows that or .*. the range AH BE is harmonic. .*. the pencil obtained by joining F to… … Fig. 146. Turning to Fig. 14&, we have to prove for the completequadrilateral that the sides e, /, g of the diagonal triangle aredivided harmonically by ab^ cd; hc^ ad; and ca, bd respectively. HARMONIC FORMS 39 Let Tc be the join of hd and e/, I that of ef and ac. Then it has been proved that…
Geometry, Projective
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