As far as I can tell the point with the Huygens de Sluse analysis of the cissoid of Diocles is that the area between the cissoid and the line is finite If this area for non negative is rotated about the line then the resulting volume is also finite it is times the corresponding area and looks like a glass tumbler or jar infinitely extended in one direction Meanwhile the volume inside the rotated cissoid is clearly infinite and it is the comparison of these two volumes which is interesting The area here is not a surface area as in Gabriel s Horn but in effect a cross sectional area