developed from the germ that Diophantus had left.  Mohammed Ben Musa furnished the solution of quadratic equations, Omar Ben Ibra him that of cubic equations.  The Saracens also gave to trigonometry its modern form, substituting sines for chords, which had been previously used; they elevated it into a separate science.  Musa, above mentioned, was the author of a “Treatise on Spherical Trigonometry.”  Al-Baghadadi left one on land-surveying, so excellent, that by some it has been declared to be a copy of Euclid’s lost work on that subject.

Arabian astronomy.  In astronomy, they not only made catalogues, but maps of the stars visible in their skies, giving to those of the larger magnitudes the Arabic names they still bear on our celestial globes.  They ascertained, as we have seen, the size of the earth by the measurement of a degree on her surface, determined the obliquity of the ecliptic, published corrected tables of the sun and moon fixed the length of the year, verified the precession of the equinoxes.  The treatise of Albategnius on “The Science of the Stars” is spoken of by Laplace with respect; he also draws attention to an important fragment of Ibn-Junis, the astronomer of Hakem, the Khalif of Egypt, A.D. 1000, as containing a long series of observations from the time of Almansor, of eclipses, equinoxes, solstices, conjunctions of planets, occultations of stars—­observations which have cast much light on the great variations of the system of the world.  The Arabian astronomers also devoted themselves to the construction and perfection of astronomical instruments, to the measurement of time by clocks of various kinds, by clepsydras and sun-dials.  They were the first to introduce, for this purpose, the use of the pendulum.

In the experimental sciences, they originated chemistry; they discovered some of its most important reagents—­ sulphuric acid, nitric acid, alcohol.  They applied that science in the practice of medicine, being the first to publish pharmacopoeias or dispensatories, and to include in them mineral preparations.  In mechanics, they had determined the laws of falling bodies, had ideas, by no means indistinct, of the nature of gravity; they were familiar with the theory of the mechanical powers.  In hydrostatics they constructed the first tables of the specific gravities of bodies, and wrote treatises on the flotation and sinking of bodies in water.  In optics, they corrected the Greek misconception, that a ray proceeds from the eye, and touches the object seen, introducing the hypothesis that the ray passes from the object to the eye.  They understood the phenomena of the reflection and refraction of light.  Alhazen made the great discovery of the curvilinear path of a ray of light through the atmosphere, and proved that we see the sun and moon before they have risen, and after they have set.