A Porism Concerning Cyclic Quadrilaterals

<table class="table-group" id="tab1"><tr><td><table class="table"><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr class="thead"><td align="left">Algebra</td><td align="center">“Sphere”</td><td align="center">Formula represented geometrically</td></tr><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr><td align="left"><svg height="11.6875" id="M171" style="vertical-align:-0.20474pt" version="1.1" viewbox="0 0 12.65 11.6875" width="12.65" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.363)"><path d="M708 165q-34 -105 -63 -154q-134 -26 -204 -26q-99 0 -177.5 29t-125 77t-70.5 105.5t-24 119.5q0 157 120 253t307 96q40 0 79.5 -5t76.5 -13.5t40 -8.5l23 -151l-33 -7q-23 80 -72 114.5t-142 34.5q-79 0 -123.5 -86t-44.5 -207q0 -140 49 -227.5t125 -87.5
q84 0 133 36.5t94 117.5q6 -2 17.5 -5.5t14.5 -4.5zM313 50q-81 98 -81 286q0 175 79 267q-79 -35 -122 -107.5t-43 -159.5q0 -99 44.5 -174t122.5 -112z" id="x2102"></path></g>
</svg> (complex numbers) </td><td align="center">Circle </td><td align="center">Relativistic velocities </td></tr><tr><td align="left"><svg height="11.175" id="M172" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 14.6625 11.175" width="14.6625" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.113)"><path d="M810 350q0 -173 -123 -267q-107 -83 -297 -83h-352v28q62 5 76 19.5t14 77.5v400q0 63 -14 77.5t-76 19.5v28h405q194 0 282 -85q85 -82 85 -215zM712 336q0 80 -30 143t-88 97q-66 41 -170 41q-62 0 -78 -13q-13 -9 -13 -57v-416q0 -55 24.5 -75t81.5 -20q133 0 203 86
t70 214zM290 131v390q0 62 -7.5 79.5t-30.5 17.5q-24 0 -31.5 -17.5t-7.5 -79.5v-390q0 -62 7.5 -79.5t31.5 -17.5q23 0 30.5 17.5t7.5 79.5z" id="x1D53B"></path></g>
</svg> (hyperbolic numbers) </td><td align="center">Hyperbola </td><td align="center">Trigonometric tangents</td></tr><tr><td align="left"><svg height="11.6875" id="M173" style="vertical-align:-0.20474pt" version="1.1" viewbox="0 0 13.5 11.6875" width="13.5" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.363)"><path d="M763 274q-50 -6 -60.5 -17t-10.5 -55v-86q0 -63 8 -95q-8 -2 -35.5 -7.5t-41 -8l-39.5 -7.5t-45 -7t-43 -4t-45 -2q-182 0 -294.5 93t-112.5 243q0 84 35.5 151t95 108t135 63t158.5 22q80 0 214 -29l16 -156l-31 -6q-18 87 -71 121.5t-143 34.5q-79 0 -128.5 -80.5
t-49.5 -216.5q0 -77 19.5 -146t65 -118t108.5 -49q57 0 94 17q19 9 27.5 23t8.5 43v85q0 54 -17.5 67t-99.5 19v28h282v-28zM324 48q-45 49 -68.5 125t-23.5 160q0 81 22 153t63 118q-80 -33 -125.5 -103.5t-45.5 -167.5q0 -88 45.5 -167.5t132.5 -117.5z" id="x1D53E"></path></g>
</svg> (dual numbers) </td><td align="center">Parallel lines </td><td align="center">Regular addition </td></tr><tr class="table-tr"><td colspan="3"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Geometry

tab1

Table 1

Table 1: A Porism Concerning Cyclic Quadrilaterals 