 | Jeremiah Joyce - Arithmetic - 1812 - 274 pages
...of the 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,... | |
 | Beriah Stevens - Arithmetic - 1822 - 436 pages
...property of 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... | |
 | Charles Hutton - Mathematics - 1822 - 616 pages
...of the 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... | |
 | James Mitchell - Mathematics - 1823 - 666 pages
...this 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 the sum... | |
 | Thomas Keith - Arithmetic - 1825 - 360 pages
...as if you divided the product of the two first numbers by 9 or 3. 9. Any number divided by 9 or 3, will leave the same remainder as the sum of its digits divided by 9 or 3. Hence, if any number is divisible by 9 or 3, the sum of its digits is likewise divisible by 9... | |
 | 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... | |
 | Zadock Thompson - Arithmetic - 1826 - 176 pages
...the number 9, which belongs to noother number, except 3, namely, that any number divided by 9 leaves the same remainder as the sum of its digits divided by 9. Thus 436 divided by 9, Hie remainder is 4 ; the sum of the digits in 436 is (4+34-6=) 13 and 13 divided... | |
 | Alexander Jamieson - Industrial arts - 1829 - 654 pages
...not, it is certainly wrong. This proof depends upon a singular property of the number 9; viz. 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 fur multiplication is drawn from a particular property... | |
 | Arithmetic - 1829 - 196 pages
...1142 4752 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-... | |
 | Charles Hutton - Mathematics - 1831 - 632 pages
...of the 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 are digits divided by 9:" which may be demonstrated in this manner. Demomlration. Let there... | |
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... any number divided by 9 will leave the same remainder as the sum of its digits divided by 9. 
