Page:Mathematical collections and translations, in two tomes - Salusbury (1661).djvu/384

 described within the same, and neerer to the pole A, shall wholly be included in the illuminated part; as on the contrary, the opposite ones towards the Pole B, contained within the parallel LM, shall remain in the dark. Moreover, the arch AI being equal to the arch FD, and the arch AF, common to them both, the two arches IKF and AFD shall be equal, and each a quadrant or 90 degrees. And because the whole arch IFM is a semicircle, the arch FM shall be a quadrant, and equal to the other FKI; and therefore the Sun O shall be in this state of the Earth vertical to one that stands in the point F. But by the revolution diurnal about the standing Axis AB, all the points of the parallel EF passe by the same point F: and therefore in that same day the Sun, at noon, shall be vertical to all the inhabitants of the Parallel EF, and will seem to them to describe in its apparent motion the circle which we call the Tropick of Cancer. But to the inhabitants of all the Parallels that are above the parallel EF, towards the North pole A, the Sun declineth from their Vertex or Zenith towards the South; and on the contrary, to all the inhabitants of the Parallels that are beneath EF, towards the Equinoctial CD, and the South Pole B, the Meridian Sun is elevated beyond their Vertex towards the North Pole A. Next, it is visible that of all the Parallels, only the greatest CD is cut in equal parts by the Terminator of the light IM. But the rest, that are beneath and above the said grand circle, are all intersected in parts unequal: and of the superiour ones, the semidiurnal arches, namely those of the part of the Terrestrial surface, illustrated by the Sun, are bigger than the seminocturnal ones that remain in the dark: and the contrary befalls in the remainder, that are under the great one CD, towards the pole B, of which the semidiurnal arches are lesser than the seminocturnal, It is likewise apparently manifest, that the differences of the said arches go augmenting, according as the Parallels are neerer to the Poles, till such time as the parallel IK comes to be wholly in the part illuminated, and the inhabitants thereof have a day of twenty four hours long, without any night; and on the contrary, the Parallel LM, remaining all in obscurity, hath a night of twenty four hours, without any day. Come we next to the third Figure of the Earth, placed with its centre in the point Cancer, where the Sun seemeth to be in the first point of Capricorn. We have already seen very manifestly, that by reason the Axis AB doth not change inclination, but continueth parallel to it self, the aspect and situation of the Earth is the same to an hair with that in the first Figure; save onely that that Hemisphere which in the first was illuminated by the Sun, in this remaineth obtenebrated, and that cometh to be luminous, which in