Page:Philosophical Transactions - Volume 003.djvu/20

From Wikisource
Jump to navigation Jump to search
This page has been validated.

(646)

My Method for Squaring the Hyperbola is this:

Let AB be one Asymptote of the Hyperbola EdC; and let AE and BC be parallel to th'other: Let also AE be to BC as 2 to 1; and let the Parallelogram ABDE equal 1. See Fig. 1. And note, that the Letter x every where stands for Multiplication.

Supposing the Reader knows, that EA. αζ. KH. βη. dθ. γχ. δλ. εμ. CB. &c. are in an Harmonic series, or a series reciproca primanorum sue arithmetice proportionalium (otherwise he is referr'd for satisfaction to the 87, 88, 89, 90, 91, 92, 93, 94, 95, prop. Arithm. Infinitor. Wallisij:)

I say &c. infinitum.
&c.
&c.


For (in Fig. 2, & 3) the Parallelog. And (in Fig. 4.) the Triangl. Note.
&c. &c.
&c. &c.

And