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157
[i]ntersection of the lines ID, EC, that is in the point N;
therefore N is in the line LH & it has been shewn
that M is in the same line; therefore MN passes
through the points L,H viz. of contact of BC, DE: & in
like manner the points of contact of the other tangents
may be found.
Cor. And likewise if in a conic section five points be
A, B, C, D, E be given; the lines which touch the section
in those points are easily found, the section not being
given in position.
Let A be called the first point, B the second, ^^{& so on.}&C.
join the four first points A, B, C, D by the ^^right lines AB, BC,
CD, DA, meeting one an ^^each other in the points F, G: like-
wise ^^join AC, BD; then because the lines AC, BD are ins-
cribed in a section (by Prop . 8 . of this B.) The points F, G,
& the point of concourse of the lines which touch the sec-
tion in B, D will be in a right line, that is F G will
pass through the point of concourse of this^ese tangents.
Omitting the point A, let BCDE be a quadrilateral
contained by the other four sides & let the points
H, K be the intersections of the sides & join EC; then
because EC, BD are inscribed in a conic section, then
points H, K of intersection of the sides & the point of [...]
course of the tangents which touch the section in B, D
will be in a right line, that is HK will pass through
this point of concourse of the tangents; but this sam[e]

[Page description]
This is a single cut leaf paper that was found inserted in the manuscript. It is not part of the manuscript, neither in terms of textual content, nor materially (manuscript is parchment, this is paper). Part of the page in the left margin is cut, and consequently the beginning of the first seven lines is cut and not legible. The number on top of the page is written in graphite, while the main text is written in regular ink.
The text (transcribed by a much later cursive hand) is extracted from Robert Simson's Sectionum conicarum. Robert Simson was a seventeenth century Scottish mathematician.