The _Horizon_ (ὁρίζων) is commonly understood as the boundary of the visible earth and heaven. In the doctrine of the sphere, this boundary is _a great circle_, that is, a circle of which the plane passes through the centre of the sphere; and, therefore, an entire hemisphere is always above the horizon. The term occurs for the first time in the work of Euclid, called _Phænomena_ (Φαινόμενα). We possess two treatises written by Autolycus[42\3] (who lived about 300 B. C.) which trace _deductively_ the results of the doctrine of the sphere. Supposing its diurnal motion to be uniform, in a work entitled Περὶ Κινουμένης Σφαῖρας, "On the Moving Sphere," he demonstrates various properties of the diurnal risings, settings, and motions of the stars. In another work, Περὶ Ἐπιτολῶν καὶ Δύσεων, "On Risings and Settings,"[43\3] _tacitly_ assuming the sun's motion in his circle to be uniform, he proves certain propositions, with regard to those risings and settings of the stars, which take place at the same time when the sun rises and sets,[44\3] or _vice versâ_;[45\3] and also their _apparent_ risings and settings when they cease to be visible after sunset, or begin to be visible after sunrise.[46\3] {132} Several of the propositions contained in the former of these treatises are still necessary to be understood, as fundamental parts of astronomy. [Note 42\3: Delambre, _Astron. Ancienne_, p. 19.] [Note 43\3: Delambre, _Astron. Anc._ p. 25.] [Note 44\3: _Cosmical_ rising and setting.] [Note 45\3: _Acronycal_ rising and setting; (ἀκρονυκίος, happening at the extremity of the night.)] [Note 46\3: _Heliacal_ rising and setting.] The work of Euclid, just mentioned, is of the same kind. Delambre[47\3] finds in it evidence that Euclid was merely a book-astronomer, who had never observed the heavens. [Note 47\3: _Ast. Anc._ p. 53.] We may here remark the first instance of that which we shall find abundantly illustrated in every part of the history of science; that man is _prone_ to become a deductive reasoner;--that as soon as he obtains principles which can be traced to details by logical consequence, he sets about forming a body of science, by making a system of such reasonings. Geometry has always been a favorite mode of exercising this propensity: and that science, along with Trigonometry, Plane and Spherical, to which the early problems of astronomy gave rise, have, up to the present day, been a constant field for the exercise of mathematical ingenuity; a few simple astronomical truths being assumed as the basis of the reasoning. _Sect._ 9.--_The Globular Form of the Earth._