My first definition is of a line, of length, and of a point. “The way,” say I, “of a body moved, in which magnitude (though it always have some magnitude) is not considered, is called a line; and the space gone over by that motion, length, or one and a simple dimension.” To this definition you say, first, “what mathematician did ever thus define a line or length?” Whether you call in others for help or testimony, it is not done like a geometrician; for they use not to prove their conclusions by witnesses, but rely upon the strength of their own reason; and when your witnesses appear, they will not take your part. Secondly, you grant that what I say is true, but not a definition. But to tell you truly what it is which we call a line, is to define a line. Why then is not this a definition? “Because,” say you in the first place, “it is not a reciprocal proposition.” But by your favour it is reciprocal. For not only the way of a body whose quantity is not considered is a line, but also every line is, or may be conceived to be, the way of a body so moved. And if you object that there is a difference between _is_ and _may be conceived to be_, Euclid, whom you call to your aid, will be against you in the fourteenth definition before his eleventh Element; where he defines a sphere just as convertibly as I define a line; except you think the globes of the sun and stars cannot be globes, unless they were made by the circumduction of a semicircle; and again in the eighteenth definition, which is of a cone, unless you admit no figure for a cone, which is not generated by the revolution of a triangle; and again, in the twentieth definition, which is of a cylinder, except it be generated by the circumvolution of a parallelogram. Euclid saw that what proper passion soever should be derived from these his definitions, would be true of any other cylinder, sphere, or cone, though it were otherwise generated; and the description of the generation of any one being by the imagination applicable to all, which is equivalent to convertible, he did not believe that any rational man could be misled by learning logic to be offended with it. Therefore this exception proceedeth from want of understanding, that is, from ignorance of the nature, and use of a definition.