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" ... any number divided by 9, will leave the same remainder, as the sum of its figures, or digits, divided by 9 : which may be thus demonstrated. "
Practical Arithmetic: Uniting the Inductive with the Synthetic Mode of ... - Page 260
by James Bates Thomson - 1864 - 384 pages
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Mathematics: Compiled from the Best Authors, and Intended to be ..., Volume 1

Samuel Webber - Mathematics - 1808 - 466 pages
...9, which belongs to no other digit whatever, except 3, namely, that any number divided by 9 leaves the same remainder, as the sum of its figures or digits divided by 9 ; which may be thus demonstrated. DEM0N. Let there be any number, as 3467 ; this separated into its...
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A Course of Mathematics ...: Composed for the Use of the Royal Military ...

Charles Hutton - Mathematics - 1811 - 406 pages
...which, except the number 3, belongs to no other digit whatever ; namely, that " any number divided by Q, will leave the same remainder as the sum of its figures or digits divided by 9 :" which may be demonstrated in this manner. Demonstration. Let there be any number proposed, as 4658....
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A System of Arithmetic: Reprinted from the Mathematical Text-book

Samuel Webber - Arithmetic - 1812 - 260 pages
...9, which belongs to no other digit whatever, except 3, namely, that any number divided by 9 leaves the same remainder, as the sum of its figures or digits divided by 9 ; which may be thus demon* strated. DEM0N. Let there be any number, as 3467 ; this separated into its...
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A System of Arithmetic: Reprinted from the Mathematical Text-book

Samuel Webber - Arithmetic - 1812 - 246 pages
...which belongs to no other digit 婦 hatever , except 3, namely, that any number divided by 9 leaves'the same remainder, as the sum of its figures or digits divided by 9 ; which may be thus demon strated. DEMON. Let there be any number, as 3467; this separated into its...
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A System of Practical Arithmetic: Applicable to the Present State of Trade ...

Jeremiah Joyce - Arithmetic - 1812 - 274 pages
...number 9, which belongs also to the number 3, but to none of the other digits; viz. that any number divided by 9, will leave the same remainder as the sum of digits divided by 9: thus 8769 divided by 9, leaves 1 as a remainder; and so will 8 + 7+6+7* or 18,...
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A New and Concise System of Arithmetick: Containing Vulgar, Decimal, and ...

Beriah Stevens - Arithmetic - 1822 - 436 pages
...the number 9, which, except the numbers, belongs to no other digit whatever ; viz. that any number divided by 9 will leave the same remainder as the sum of its figures or digits divided by 9 ; which is thus demonstrated : — Let the number 5432 be eiven : this separated into m several parts...
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A Course of Mathematics: For the Use of Academies, as Well as Private ...

Charles Hutton - Mathematics - 1822 - 616 pages
...number 9, which except the number 3, belongs to no other digit whatever ; namely, that ** any number divided by 9, will leave the same remainder as the sum of its figures or digit: divided by 9 ;" which may bt demonstrated in this manner. Demonstration. Let there be any number...
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Dictionary of the Mathematical and Physical Sciences, According to the ...

James Mitchell - Mathematics - 1823 - 666 pages
...proof answers, always be 9, or a multiple of 9. This proof depends upon this property, that any number divided by 9, will leave the same remainder, as the sum of its digits when divided by the same number. 3. Another proof is, the 1st, 3d, 5th, &c. being taken from...
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A Course of Mathematics for the Use of Academies: As Well as ..., Volume 1

Charles Hutton - Mathematics - 1825 - 608 pages
...number 9, which except the number 3, belongs to no other digit whatever; namely, that " any numl>er divided by 9 will leave the same remainder as the sum of it> figures or digits d ivided by 9 , which may be demonstrated in this manner. Demonstration Let there...
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The Practical Arithmetic: In which the Principles of Operating by Numbers ...

Arithmetic - 1829 - 196 pages
...586393 * This method of proof depends upon a properly of the number 9, which is, that " any number divided by 9, will leave the same remainder as the sum of its di?its divided by 9." nius. Take the number 465. This separated into its parts, becomes 400 -f 60-f-...
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