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Therefore in what proportion QS is cut in
R, in the same proportion (by the 10 of the 6 of Euclide)
Let aZ be cut in c. and so let b
running from a to c in the first moment,
cut off ac from aZ, the line or sine
cZ remaining.
And from this cZ let b
proceeding in the second moment, cut off the like segment, or part,
as QR to QS: and let that bee cd,
leauing the sine. dZ. From which therefore in the
third moment, let b in like manner, cut off the
segment de, the sine eZ being left
behinde. From which likewise in the fourth moment, by the motion of
b, let the segment cf be cut off,
leauing the sine fZ. From this fZ in the
fifth moment, let b in the same proportion cut off the
segment fg, leauing the sine gZ, and so
forth infinitly. I say therfore out of the former definition, that
here the line of the whole sine aZ, doth proportially
decrease into the signe gZ, or into any other last
sine, in which b stayeth, and so in others.
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| A Corollary |
Hence it followeth that by this decrease in
equall moments (or times) there must needes also bee left
proportionall lines of the same proportion.
For what continuall proportion there is before
of the sines to be diminished, aZ, cZ,
dZ, eZ, fZ, gZ,
hZ, iZ, and kZ, &c.
and of the segments cut off from them ac, cd, de,
ef, fg, gh, hi, and ik,
there must needes be also the same proportion of the sines
remaining, that is, cz, dz, ez, fz,
gz, hz, iz, and kz, as may
manifestly appeare by the 19 Prop. 5 and 11. Prop. 7,
Euclid.
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