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[[left margin]] From the Gents Mag for 1737. Vol. 7 p. 611. [[/left margin]]

[[underlined]] Some Theorems from which the Parallax of the Sun may be deduced, and is here deduced with great Exactness. [[/underlined]]

1. ON the first Day of [[underlined]] July [[/underlined]], 1735, it pleased that Divine Providence, which governs all Things, to permit that I should find a most accurate Method for determining the Sun's parallax [[underlined]] a priori [[/underlined]] : A Word which Sir [[underlined]] Isaac Newton [[/underlined]] used often in that Sense.
2. The Principles which I made use of, in all my Enquiries for that Parallax, were those which that Great Man has so well established, in that Part of his Book which is irreprehensible. Only I made use now and then of some [[underlined]] Theorems [[/underlined]] more.
3. [[underlined]] The first Theorem is, [[/underlined]] That in those Stereographic Maps, where a Terrestrial or Celestial Hemisphere is projected upon a Plan parralel to a Meridian, the Eye being supposed in the Surface of the Sphere; and the Line drawn from the Eye thro' the Center of the Sphere being perpendicular to the Plan of the Proje ^ [[insertion]] c [[/insertion]] tion; All the Angles formed upon the Sphere (where any Circles great or small or their Tangents intersect each other) are equal to the Angles representing them in the Projection. I communicated this Theorem to Others, and particularly Mr. DE MOIVRE, R.S.S. before the year 1692; and to him I showed the Demonstration of it.

[[left margin]] Fig. 51. [[/left margin]]

4. [[underlined]] The second Theorem [[/underlined]] is as follows. [[underlined]] Definition. [[/underlined]] If such a Stereographic Projection, as I have just now described, be extended on all Sides [[underlined]] in infinitum [[/underlined]], so that it may contain a Representations of y [[superscript]] e [[/superscript]] whole Sphere; And if about each Pole all the Parallels be drawn in it by intire Circles from Minute to Minute, or from Second to Second: and the Whole be turned about the infinite Axis passing thro' the Poles: I call any of the Spherical Surfaces thus f [[strikethrough]] ar [[/strikethrough]] [[insertion]] or [[/insertion]] med by an intire Revolution, [[underlined]] A Stereographic Sphere. [[/underlined]]

[[underlined]] Second Theorem [[/underlinde]]. In any proposed Stereographic Sphere

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edited for spacing and insertion tags -megshu