Page:Mathematical collections and translations, in two tomes - Salusbury (1661).djvu/313

standing of which, I ought first to advertise you, that when ever the new Star, or other Phænomenon is near to the earth, turning with a Diurnal motion about the Pole, it will seem to be farther off from the said Pole, whilst it is in the lower part of the Meridian, then whilst it is above, as in this Figure [being fig. third of this Dial.] may be seen. In which the point T. denotes the centre of the Earth; O. the place of the Observator; the Arch VPC the Firmament; P. the Pole. The Phænomenon, [or appearance] moving along the Circle FS. is seen one while under the Pole by the Ray OFC. and another while above, according to the Ray OSD. so that the places seen in the Firmament are D. and C. but the true places in respect of the Centre T, are B, and A, equidistant from the Pole. Where it is manifest that the apparent place of the Phænomenon S, that is the point D, is nearer to the Pole than the other apparent place C, seen along the Line or Ray OFC, which is the first thing to be noted. In the second place you must note that the exces of the apparent inferiour distance from the Pole, over and above the apparent superiour distance from the said Pole, is greater than the Inferiour Parallax of the Phænomenon, that is, I say, that the excesse of the Arch CP, (the apparent inferior distance) over and above the Arch PD, (the apparent superior distance) is greater then the Arch CA, (that is the inferiour Paralax.) Which is easily proved; for the Arch CP. more exceedeth PD, then PB; PB, being bigger than PD, but PB. is equal to PA, and the excesse of CP, above PA, is the arch, CA, therefore the excesse of the arch CP above the arch PD, is greater than the arch CA, which is the parallax of the Phænomenon placed in F, which was to be demonstrated. And to give all advantages to the Author, let us suppose that the parallax of the star in F, is the whole excesse of the arch CP (that is of the inferiour distance from the pole) above the arch PD (the inferiour distance.) I proceed in the next place to examine that which the observations of all Astronomers cited by the Authour giveth us, amongst which, there is not one that maketh not against himself and his purpose. And let us begin with these of Buschius, who findeth the stars distance from the pole, when it was superiour, to be 28 gr. 10 m. and the inferiour to be 28 gr. 30 m. so that the excesse is 0 gr. 20 m. which let us take (in favour of the Author) as if it all were the parallax of the star in F, that is the angle TFO. Then the distance from the Vertex [or Zenith] that is the arch CV, is 67 gr. 20 m. These two things being found, prolong the line CO, and from it let fall the perpendicular TI, and let us consider the triangle TOI, of which the angle I is right angle, and the angle IOT known, as being vertical to the angle VOC, the distance of the star from the Vertex, Moreover in the triangleTIF,