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43.)
[[margin notes not related to text]]
To one already graduated. 
A Telescope with two plano-convex- [[strikethrough]] lens [[/strikethrough]] lenses in contact for an Eye-glass.
2 equal double convex lenses joined; their focus, & serves for an Eye-lens to a Telescope
A rule for finding the Apertures, Focal Distance of Eye-lenses, & Magnifying Power of Telescopes.
V. Rowning's Philosophy part III. p.177. And No. 4. of Philos. Trans. or Vol. I. p.191. of Lowthorp's Abridgment
The same Rule is in Smith's Optics Vol.I .p.143. Art.355.
Ratio of the focal lengths in double convex lenses to the Radius of their Spheres.
Light thought to decrease as the Cubes of the Distances and not as the Squares.
[[/margin]]

that they might the better be compared together.
The Best way I can conceive to divide a Quadrant into degrees, is to calculate the chord of 8°. degrees and lay it off from and add it to 120°. and then by 64 bisections, the degrees are had, and whatever small Error should be in the Chord of the 8°. it will be bisected 64 Times, & thereby become very small, if anything in one degree. But if the Arch cannot be enlarged beyond a Quadrant; then take the Chord of 4°. and add it to 60°. (found by [[strikethrough]] twice repeating the Radius [[/strikethrough]] laying of the Radius for a Chord) then 32 Bisections will give the degrees and the Error (if any) in laying of the 4°. will be divided into [[strikethrough]] 64 [[/strikethrough]] 32 parts, & so become imperceptable in a single degree.
In finding this Chord of 4°, or of 8°, Whether or no it would not be better to find a Triangle whose 3 Sides shall be integers, [[insertion]] & [[/insertion]] one ^ [[insertion]] of them [[/insertion]] the radius of the given Quadrant; and lay off this Triangle from the Center of the Quadrant, &c. &c. ?
[[note in right margin]] Any arc (A) divided into a given number of parts (N)=90) nearly: and (B)=30) of these divisions to A; then divide A+B into(N+B)120 parts by continual bisection; will be very nearly true of A divided into 90 parts, thus may any arc be divided into any given parts by bisections only. [[/margin]]
[[drawn image: "Case I" a fairly straight AB line, bisected, with arches labelled DE and GH at either end]]
[[drawn image: "Case II" a curve AB, bisected, with arches labelled DE and GH at either end]]
To divide the Arc AB into any Number of equal parts, suppose 5: Approximate the distance very near; then begin from one of the points, as B, & at every division describe a small arch, the last of which, [[strikethrough]]E[[/strikethrough]]DE, will fall beyond the point A, if the Approximated distance be too great, as in case I: But if that distance were too small then DE falls short of the point A, as in case II. Then with the same approximated extent, begin from the other point, as A, & at every division describe an Arch to intersect the former in the points o, o, o, o; through these intersections, and the given center, draw a Right line to touch the Arch AB which will give the true points of division required. This method occurred to me whilst contemplating and writing the above, on the same Subject. Indeed the approximated distance must be very exact, [[strikethrough]] or else [[/strikethrough]] for what ever error you set out with, that whole error will, by this way, insinuate itself into each of the divisions, as is Evident by inspection, from the Lines divided below, where the black dots upon the lines shew the true divisions, & the figures the repetition of the Error. So that this method can only help to draw the lines to a finer point.
[[drawn image: "Case I. Approximation too great." lines, "even" and "odd," bisected with dots in the middle of drawn arches]]
[[drawn image: "Case II. Approximation too little." lines, "even" and "odd," bisected with dots in between drawn arches]]