# Catalogue Entry: NATP00221

## Newton's Waste Book (Part 2)

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^{[9]} October 1664

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^{[22]} For the first equation of the first sort

^{[23]} For the 2^{d}

^{[24]} For the 3^{d}

^{[25]} For the 4^{th}

^{[26]} For the 5^{t}

^{[27]} For the 6^{t} &c

^{[28]} For the first Equation of the seacond Sort

^{[29]} For the seacond

^{[30]} For the 3^{d}.

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^{[33]} November 1664

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^{[39]} November 1664

^{[40]} A

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^{[49]} B

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^{[51]} This line is a streight one the equation being divisible by $\mathrm{b}=\mathrm{y}=0$

^{[52]} Endeavor not to find the quantity
d
in these cases, but suppose it given^{[Editorial Note 1]}

^{[Editorial Note 1]} There is a line connecting the end of this note to the following one

^{[53]} Or else C ☞

^{[54]} December

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^{[58]} ☞

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^{[62]} F

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^{[64]} G

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^{[66]} December 1664

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^{[69]} Theorema

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^{[71]} December 1664.

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^{[83]} Feb 1664

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^{[86]} Another way.

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^{[88]} December 1664

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^{[94]} Of compound force.

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^{[101]} May 20^{th} 1665

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^{[103]} Observation 1^{st}

^{[104]} Observacion 2^{d}

^{[105]} An universall theorem for tangents to crooked lines, when $\mathrm{y}\perp \mathrm{x}$.

^{[106]} See Des Cartes his Geometry. booke 2^{d}, pag 42, 46, 47. Or thus,
$\begin{array}{ccccccccc}{\mathrm{x}}^{3}& -& \mathrm{b}\mathrm{x}\mathrm{x}& -& \mathrm{c}\mathrm{d}\mathrm{x}& +& \mathrm{d}\mathrm{y}\mathrm{x}& +& \mathrm{b}\mathrm{c}\mathrm{d}\\ 2& & 1& & 0& & 0& & -1& \end{array}$
{
$\frac{2\mathrm{x}\mathrm{x}\mathrm{y}-\mathrm{b}\mathrm{x}\mathrm{y}}{-\mathrm{d}\mathrm{x}}\phantom{\rule{0.5em}{0ex}}\frac{+\mathrm{b}\mathrm{c}\mathrm{d}\mathrm{y}}{\mathrm{d}\mathrm{x}\mathrm{x}}=\mathrm{v}$
}. And
$\frac{\mathrm{b}\mathrm{c}\mathrm{y}}{\mathrm{x}\mathrm{x}}+\frac{\mathrm{b}\mathrm{y}}{\mathrm{d}}-\frac{2\mathrm{x}\mathrm{y}}{\mathrm{d}}=\mathrm{v}$
.

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^{[108]} An universall theorem for drawing tangents to crooked lines when
x
&
y
intersect at any determined angle

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^{[110]} A=

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^{[Editorial Note 2]} The rest of the page is damaged.