TITLE: How did Leibniz prove that $\sin (x)$ is not an algebraic function of $x$?
QUESTION [8 upvotes]: In the Wikipedia article about transcendental numbers we can read the following: 
The name "transcendental" comes from Leibniz in his 1682 paper where he proved that sin(x) is not an algebraic function of x.
I would like to know can someone reproduce here the proof of Leibniz of the non-algebraicity of $\sin$ or point me to the place on the internet where we have this proof.
I do not know German or Latin so if someone has the link where this is proved it would be OK if it is written in English.
Although I am an amateur it seems to me that in the time of Leibniz the techniques for proving the non-algebraicity of functions were not developed enough so it would be nice to see how he proved that for $\sin$.

REPLY [4 votes]: Leibniz's paper with the term "transcendental" is : DE VERA PROPORTIONE CIRCULI AD QUADRATUM CIRCUMSCRIPTUM IN NUMERIS RATIONALIBUS EXPRESSA, Act.Erudit.Lips.1682.
Reprinted into:

Gottfried Wilhelm von Leibniz, Leibnizens mathematische Schriften, herausgegeben von C.I.Gerhardt (1858), page 118-on; see page 120:


transcendens inter alia habetur per aequationes gradus indefiniti.

For the proof, see: PRAEFATIO OPUSCULI DE QUADRATURA CIRCULI ARITHMETICA, page 93-on; see page 98.