=1541.= If the Greeks had not cultivated Conic Sections, Kepler could not have superseded Ptolemy; if the Greeks had cultivated Dynamics, Kepler might have anticipated Newton.--WHEWELL, W. _History of the Inductive Science (New York, 1894), Vol. 1, p. 311._ =1542.= If we may use the great names of Kepler and Newton to signify stages in the progress of human discovery, it is not too much to say that without the treatises of the Greek geometers on the conic sections there could have been no Kepler, without Kepler no Newton, and without Newton no science in the modern sense of the term, or at least no such conception of nature as now lies at the basis of all our science, of nature as subject in the smallest as well as in its greatest phenomena, to exact quantitative relations, and to definite numerical laws. --SMITH, H. J. S. _Presidential Address British Association for the Advancement of Science, Section A; Nature, Vol. 8 (1873), p. 450._ =1543.= The silent work of the great Regiomontanus in his chamber at Nuremberg computed the Ephemerides which made possible the discovery of America by Columbus.--RUDIO, F. _Quoted in Max Simon’s Geschichte der Mathematik im Altertum (Berlin, 1909), Einleitung, p. xi._ =1544.= The calculation of the eclipses of Jupiter’s satellites, many a man might have been disposed, originally, to regard as a most unprofitable study. But the utility of it to navigation (in the determination of longitudes) is now well known.--WHATELY, R. _Annotations to Bacon’s Essays (Boston, 1783), p. 492._ =1545.= Who could have imagined, when Galvani observed the twitching of the frog muscles as he brought various metals in contact with them, that eighty years later Europe would be overspun with wires which transmit messages from Madrid to St. Petersburg with the rapidity of lightning, by means of the same principle whose first manifestations this anatomist then observed!...