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  "body": "\n## Summary\n\nA perspectivity maps the points of one line to the points of another line by central projection from a fixed point, the centre.\nIt is the basic map of [[projective geometry|N32Z68F0D3]] and models what an eye at the centre sees.\nA composition of perspectivities is called a projectivity, and on the real projective line the projectivities are exactly the [[projective transformations|P1MKTF7MWQ]].\nPerspectivities preserve the [[cross-ratio|09ASMRMD67]].\n\n## Explanations\n\n### L1 human\n\nStand at a point $O$ and look at points on a line $\\ell$.\nEach line of sight from $O$ through a point $X$ of $\\ell$ hits a second line $m$ at a point $X'$.\nThe map $X \\mapsto X'$ is the perspectivity from $\\ell$ to $m$ with centre $O$.\nEqual steps on $\\ell$ usually become unequal steps on $m$, as in a perspective drawing of a fence.\n",
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