Recognizing that the understanding was dependent on the other powers of the mind, Descartes resorted in his mathematical demonstrations to the use of lines, because he could find no method, as he says, more simple or more capable of appealing to the imagination and senses. He considered, however, that in order to bear the relationships in memory or to embrace several at once, it was essential to explain them by certain formulæ, the shorter the better. And for this purpose it was requisite to borrow all that was best in geometrical analysis and algebra, and to correct the errors of one by the other. Descartes was above all a mathematician, and as such he may be regarded as a forerunner of Newton and other scientists; at the same time he developed an exact scientific method, which he believed applicable to all departments of human thought. "Those long chains of reasoning," he says, "quite simple and easy, which geometers are wont to employ in the accomplishment of their most difficult demonstrations, led me to think that everything which might fall under the cognizance of the human mind might be connected together in the same manner, and that, provided only one should take care not to receive anything as true which was not so, and if one were always careful to preserve the order necessary for deducing one truth from another, there would be none so remote at which he might not at last arrive, or so concealed which he might not discover." REFERENCES Francis Bacon, _Philosophical Works_ (Ellis and Spedding edition), vol. IV, Novum Organum. J. J. Fahie, _Galileo; His Life and Work_. Galileo, _Two New Sciences_; translated by Henry Crew and Alphonse De Salvio. William Gilbert, _On the Loadstone_; translated by P. F. Mottelay. William Harvey, _An Anatomical Disquisition on the Motion of the Heart and Blood in Animals_. T. H. Huxley, _Method and Results_. D'Arcy Power, _William Harvey_ (in _Masters of Medicine_). FOOTNOTES: [1] This is Harvey's monogram, which he used in his notes to mark any original observation. CHAPTER VII SCIENCE AS MEASUREMENT--TYCHO BRAHE, KEPLER, BOYLE Considering the value for clearness of thought of counting, measuring and weighing, it is not surprising to find that in the seventeenth century, and even at the end of the sixteenth, the advance of the sciences was accompanied by increased exactness of measurement and by the invention of instruments of precision. The improvement of the simple microscope, the invention of the compound microscope, of the telescope, the micrometer, the barometer, the thermoscope, the thermometer, the pendulum clock, the improvement of the mural quadrant, sextant, spheres, astrolabes, belong to this period.