APPENDIX XI. ON HORNER’S METHOD OF SOLVING EQUATIONS.

becomes |001704, and is quite useless. The next step, separately written (which is not, however, necessary in working), is


54	759	780036	48	734354(0

Here the dividend 734354 does not contain the divisor 780036, and we, therefore, write 0 as a root figure and make another contraction, or begin with

At the next contraction the first column becomes |0054759, and is quite useless, so that the remainder of the process is the contracted division.

and the root required is 21·36094137.

I now write down the complete process for another equation, one root of which lies between 3 and 4: it is

x³ - 10x + 1 = 0

1	0		-10		-1(3·111039052073099	0796
	3		-1			2000
6		1700		209000
9	0			1791		19769000
9	1			188300		743369000000
9	2			189231		172311710273000
9	30			19016300		991247447681
9	31			19025631		39462875420
9	32			1903496300	0	0			1391491559
9	33	0		1903524299	0	9			58993123
9	33	1		1903552298	2	7	0	0	1886047
9	33	2		1903560698	0	5	9	1	172835
9	33	30	0	1903569097	8	5	6	3	1515
9	33	30	3	1903569144	5	2	2		183
9	33	30	6	1903569191	1	8	8		12
9	33	30	90	1903569193	0	6			1

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