History of the Conflict Between Religion and Science

by John William Draper

SCIENCE AND ECCLESIASTICISM. But during the eighteenth century the balance was introduced as an instrument of chemical research. Now, if the phlogistic hypothesis be true, it would follow that a metal should be the heavier, its oxide the lighter body, for the former contains something—phlogiston—that has been added to the latter. But, on weighing a portion of any metal, and also the oxide producible from it, the latter proves to be the heavier, and here the phlogistic hypothesis fails. Still further, on continuing the investigation, it may be shown that the oxide or calx, as it used to be called, has become heavier by combining with one of the ingredients of the air.

To Lavoisier is usually attributed this test experiment; but the fact that the weight of a metal increases by calcination was established by earlier European experimenters, and, indeed, was well known to the Arabian chemists. Lavoisier, however, was the first to recognize its great importance. In his hands it produced a revolution in chemistry.

The abandonment of the phlogistic theory is an illustration of the readiness with which scientific hypotheses are surrendered, when found to be wanting in accordance with facts. Authority and tradition pass for nothing. Every thing is settled by an appeal to Nature. It is assumed that the answers she gives to a practical interrogation will ever be true.

Comparing now the philosophical principles on which science was proceeding, with the principles on which ecclesiasticism rested, we see that, while the former repudiated tradition, to the latter it was the main support while the former insisted on the agreement of calculation and observation, or the correspondence of reasoning and fact, the latter leaned upon mysteries; while the former summarily rejected its own theories, if it saw that they could not be coordinated with Nature, the latter found merit in a faith that blindly accepted the inexplicable, a satisfied contemplation of "things above reason." The alienation between the two continually increased. On one side there was a sentiment of disdain, on the other a sentiment of hatred. Impartial witnesses on all hands perceived that science was rapidly undermining ecclesiasticism.

MATHEMATICS. Mathematics had thus become the great instrument of scientific research, it had become the instrument of scientific reasoning. In one respect it may be said that it reduced the operations of the mind to a mechanical process, for its symbols often saved the labor of thinking. The habit of mental exactness it encouraged extended to other branches of thought, and produced an intellectual revolution. No longer was it possible to be satisfied with miracle-proof, or the logic that had been relied upon throughout the middle ages. Not only did it thus influence the manner of thinking, it also changed the direction of thought. Of this we may be satisfied by comparing the subjects considered in the transactions of the various learned societies with the discussions that had occupied the attention of the middle ages.

But the use of mathematics was not limited to the verification of theories; as above indicated, it also furnished a means of predicting what had hitherto been unobserved. In this it offered a counterpart to the prophecies of ecclesiasticism. The discovery of Neptune is an instance of the kind furnished by astronomy, and that of conical refraction by the optical theory of undulations.

But, while this great instrument led to such a wonderful development in natural science, it was itself undergoing development—improvement. Let us in a few lines recall its progress.

The germ of algebra may be discerned in the works of Diophantus of Alexandria, who is supposed to have lived in the second century of our era. In that Egyptian school Euclid had formerly collected the great truths of geometry, and arranged them in logical sequence. Archimedes, in Syracuse, had attempted the solution of the higher problems by the method of exhaustions. Such was the tendency of things that, had the patronage of science been continued, algebra would inevitably have been invented.

To the Arabians we owe our knowledge of the rudiments of algebra; we owe to them the very name under which this branch of mathematics passes. They had carefully added, to the remains of the Alexandrian School, improvements obtained in India, and had communicated to the subject a certain consistency and form. The knowledge of algebra, as they possessed it, was first brought into Italy about the beginning of the thirteenth century. It attracted so little attention, that nearly three hundred years elapsed before any European work on the subject appeared. In 1496 Paccioli published his book entitled "Arte Maggiore," or "Alghebra." In 1501, Cardan, of Milan, gave a method for the solution of cubic equations; other improvements were contributed by Scipio Ferreo, 1508, by Tartalea, by Vieta. The Germans now took up the subject. At this time the notation was in an imperfect state.

The publication of the Geometry of Descartes, which contains the application of algebra to the definition and investigation of curve lines (1637), constitutes an epoch in the history of the mathematical sciences. Two years previously, Cavalieri's work on Indivisibles had appeared. This method was improved by Torricelli and others. The way was now open, for the development of the Infinitesimal Calculus, the method of Fluxions of Newton, and the Differential and Integral Calculus of Leibnitz. Though in his possession many years previously, Newton published nothing on Fluxions until 1704; the imperfect notation he employed retarded very much the application of his method. Meantime, on the Continent, very largely through the brilliant solutions of some of the higher problems, accomplished by the Bernouillis, the Calculus of Leibnitz was universally accepted, and improved by many mathematicians. An extraordinary development of the science now took place, and continued throughout the century. To the Binomial theorem, previously discovered by Newton, Taylor now added, in his "Method of Increments," the celebrated theorem that bears his name. This was in 1715. The Calculus of Partial Differences was introduced by Euler in 1734. It was extended by D'Alembert, and was followed by that of Variations, by Euler and Lagrange, and by the method of Derivative Functions, by Lagrange, in 1772.