The 1810 date given for the first use of "screen" for magic lanterns and the like seems a little late to me.
In 1771, the Encyclopaedia Britannica:
Of the MAGIC LANTERN [...]
"[T]he rays [...] will paint an inverted picture [...] upon a white wall, a sheet or a screen of white paper."
In 1769, in "The Microscope made easy":
"Mention having been often made of a Screen to throw the Images of
Objects on, it is proper to inform the Reader, that such a Screen is
usually composed of a Sheet of the largest Elephant Paper, strained on
a frame, which slides up or down, or turns about at Pleasure on a
round wooden Pillar, in the Manner of some Fire-screens. Larger
Screens are likewise made sometimes with several Sheets of the same
Paper pasted together on Cloth, and let down from the Ceiling with a
Roller, like a large Map"
I particularly like the specific definition of a roll-down projector screen very much like those still used today.
As soon as I think I'm done, I find one from 1742, in Micrographia Nova: Or, a New Treatise on the Microscope
Thus if a lens of about 6, 8, or 10 Feet focal Distance, be fix'd in
the Scioptric Ball, then if the Sun shine strongly on the Objects
without, opposite to the Window, the Images of all will be distinctly
form'd on a Wall or large Sheet or Screen of white Paper placed in
the Focus of the Glass; the result of which will be a beautiful and
most perfect Piece of Perspective, if the Objects are Buildings,
&c. but Gardens, Fields, Meadows, Hills, Groves &c. present you with a most exquisite and inimitable Landscape
I love how the style conveys the excitement of what must have been a very new branch of science and the spectacle that it presented. Additionally, on the title page, the author Benjamin Martin quotes Psalm 111, v2 by reference in English (Psal.CXI.2.) and in full in Hebrew:
גְּדֹלִים, מַעֲשֵׂי יְהוָה; דְּרוּשִׁים, לְכָל-חֶפְצֵיהֶם.
My favourite translation, which seems most apt, is
Great are the works of the Lord; They are studied by all who delight in them
A very satisfying coincidence (given that I discovered him through an etymological search) is that Mr Martin (not, as I first thought, Jewish) published an early dictionary in 1749, 6 years before Samuel Johnson: the Lingua Britannica Reformata. Sadly his entry for screen doesn't reflect his own usage from 7 years earlier!
SCREEN, or SKREEN, 1 a device to keep off the wind
2 a device to keep off the heat of the fire
3 a wooden frame grated for the sifting corn, gravel &c.