But the Vasco de Gama of his day was Leibnitz. His triumphant optimism rounded the Cape of theological Good Hope. He gave the chief impulse to modern intellectual commerce. Full freighted, as he was, with Western thought, he revived the forgotten interest in the Old and Eastern World, and brought the ends of the earth together. Circumnavigator of the realms of mind, wherever he touched, he appeared as discoverer, as conqueror, as lawgiver. In mathematics, he discovered or invented the Differential Calculus,--the logic of transcendental analysis, the infallible method of astronomy, without which it could never have compassed the large conclusions of the "Mecanique Celeste." In his "Protogaea," published in 1693, he laid the foundation of the science of Geology. From his observations, as Superintendent of the Hartz Mines, and those which he made in his subsequent travels through Austria and Italy,--from an examination of the layers, in different localities, of the earth's crust, he deduced the first theory, in the geological sense, which has ever been propounded, of the earth's formation. Orthodox Lutheran as he was, he braved the theological prejudices which then, even more than now, affronted scientific inquiry in that direction. "First among men," says Flourens, "he demonstrated the two agencies which successively have formed and reformed the globe,--fire and water." In the region of metaphysical inquiry, he propounded a new and original theory of Substance, and gave to philosophy the Monad, the Law of Continuity, the Preëstablished Harmony, and the Best Possible World. Born at Leipzig, in 1646,--left fatherless at the age of six years,-- by the care of a pious mother and competent guardians, young Leibnitz enjoyed such means of education as Germany afforded at that time, but declares himself, for the most part, self-taught [6]. [Footnote 6: "Duo, ihi profuere mirifice, (quae tamen alioqui ambigna, et pluribus noxia esse solent,) primum quod fere essem [Greek: autodidaktos], alterum quod quaererem nova in unaquaque scientia." --LEIBNIT. _Opera Philosoph_. Erdmann. p. 162.]