. The principles of projective geometry applied to the straight line and conic . quadrangle, whichare collinear with a given vertex ofits diagonal points triangle, isdivided harmonically by tliat vertexand the opposite side of tJie diagonalpoints triangle. This is practically the theoremproved in the last article, but onaccount of its importance the proofis restated. Conversely: If two pencils of four rays,which have a self-correspo7idi7igray in the line joining their vertices,have also two axes of perspective,then the pencils are harmonic. In the figure if s and s be theaxes of perspective, (
. The principles of projective geometry applied to the straight line and conic . quadrangle, whichare collinear with a given vertex ofits diagonal points triangle, isdivided harmonically by tliat vertexand the opposite side of tJie diagonalpoints triangle. This is practically the theoremproved in the last article, but onaccount of its importance the proofis restated. Conversely: If two pencils of four rays,which have a self-correspo7idi7igray in the line joining their vertices,have also two axes of perspective,then the pencils are harmonic. In the figure if s and s be theaxes of perspective, (abed) = {abcd) = (abdc). Harmonic Property of thequadrilateral and constructionof harmonic conjugates. The angle between any pair ofsides of a quadrilateral, whichintersect on a given side of itsdiagonal triangle, is divided har-monically by tliat side and the linejoining the opposite vertex of tliediagonal triangle to the point ofintersection of the pair of sides. This is practically the theoremproved in the last article, but onaccount of its importance the proofis
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Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometryprojective
