rence, it will then come out, by ſubſtituting the augmented Quantities in the Equation of the Curve, that truly. There was therefore an error of exceſs in making , which followed from the erroneous Rule of Differences. And the meaſure of this ſecond error is . Therefore the two errors being equal and contrary deſtroy each other; the firſt error of defect being corrected by a ſecond error of exceſs.
XXlI. If you had committed only one error, you would not have come at a true Solution of the Problem. But by virtue of a twofold miſtake you arrive, though not at Science, yet at Truth. For Science It cannot be called, when you proceed blindfold, and arrive at the Truth not knowing how or by what means. To demonſtrate that z is equal to , let BR or dx be m and RN or dy be n. By the thirty third Propoſition of the firſt Book of the Conics of Apollonius, and from ſimilar
