(Note on collaboration: If you do the homework in pairs or groups, please list the name(s) of your collaborator(s) on what you each turn in.)
"[A] quality uniformly difform is one in which if any three points [of the subject line] are taken, the ratio of the distance between the first and the second to the distance between the second and the third is as the ratio of the excess in intensity of the first point over that of the second point to the excess of that of the second point over that of the third point, calling the first of those three points the one of greatest intensity.
"Let us clarify this first with respect to a quality uniformly difform which is terminated at no degree and which is designated or imagined by Tri. ABC. With the three perpendicular lines BC, FG, and DE erected, then let HE be drawn parallel to line DF and similarly GK parallel to line FB. Therefore, the two small triangles CKG and GHE are formed and they are equiangular. Hence, by [proposition] VI.4 of [the Elements of] Euclid, GK/EH =CK/GH, CK and GH being excesses. And since GK=FB and similarly EH =DF, so FB/DF= CK/GH, FB and DF being the distances on the base of the three points and CK and GH being the excesses of altitude proportional to the intensity of these same points. Since, therefore, the quality of line AB is such that the ratio of the intensities of the points of the line is as the ratio of the altitudes of the lines perpendicularly erected on those same points, that which has been proposed is evidently clear, namely that the ratio of the excess in intensity of the first point over the second to the excess of the second over the third is the same as the ratio of the distance between the first and second points to the distance between the second and the third, and similarly for any other three points. Hence what we have premised in regard to a quality difform in this way is quite fitting, and so it (this quality) was well designated by such a triangle."