Page:The Analyst; or, a Discourse Addressed to an Infidel Mathematician.djvu/45

Rh Triangles, as 2x to y o is m to $$n + z = \frac{my}{2x}$$. Likewie from the Nature of the Parabola yy + 2yn + nn = xp + mp, and 2yn + nn = mp: wherefore $$\frac{2yn + nn}{p} = m$$: and becaue yy = px, $$\frac{yy}{p}$$ will be equal to x, Therefore ubtituting thee values intead of m and x we hall have $$n+z = \frac{my}{2x} = \frac{2yynp+ynnp}{2yyp}$$: i. e. $$n+z = \frac{2yn+nn}{2y}$$ which being reduced gives $$z = \frac{nn}{2y} = \frac{dydy}{2y}$$ Q.E.D.

XXIII. Now I oberve in the firt place, that the Concluion comes out right, not becaue the rejected Square of dy was infinitely mall; but becaue this error was compenated by another contrary and equal error. I oberve in the econd place, that whatever is rejected, be it ever o mall, if it be real and conequently makes a real error in the Premies, it will produce a proportional real error in the Concluion. Your Theorems therefore cannot be accurately true, nor your Problems accurately olved, in virtue of Premies, Rh