THE first conchoid of Nicomedes Bbb (Fig. 110) on both sides of the perpendicular cDb approaches nearer always to the directrix or horizontal line AE, and yet will never coincide with it, altho' it be conceived to be produced on both sides ad infinitum.
For since only Db is perpendicular to AE, and all the rest ab are so much the more inclined to it by how much the more remote they are from the middle one Db, and all in the mean while are equal both to it and to one another, by Def. 13. it is evident that the points b and B will come so much the near∣er to AE, by how much the farther they recede from the mid∣dle line Db. And yet because the lines BAC and bac are all right ones, whose points A, a, are in a right line AE it is e∣qually as impossible that the point b or B, which is always in the conchoid should ever touch this right line, as it is impos∣sible that the point C should be in it, by vertue of the afore∣cited Def. Q. E. D.