 | 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 several parts becomes 3000+400+60+7;... | |
 | 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. This, separated... | |
 | 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 several parts becomes... | |
 | 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 several parts becomes... | |
 | Jeremiah Joyce - Arithmetic - 1812 - 274 pages
...property 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,... | |
 | Charles Hutton - Arithmetic - 1818 - 646 pages
...property of the number 9, which except the number 3, belongs to no other digit whatever j n .MI u , that " any number divided by 9, will leave the same remainder as ihe sum of its figures or digits divided by 9 :" which may be demonstrated in this manner. De ti.unstration.... | |
 | Beriah Stevens - Arithmetic - 1822 - 436 pages
...on a 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...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 will... | |
 | Charles Hutton - Mathematics - 1822 - 616 pages
...a property 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 be any number... | |
 | Nicolas Pike - Arithmetic - 1832 - 538 pages
...other digit whatever; viz, thru any number divided by 9, will leave the fame remainder, as the fum of its figures, or digits, divided by 9: which may be thus demonftraled. lh-mcijlration. Let there be any number, as 5432; this, Separated in(o its feverjl parts,... | |
 | James Mitchell - Mathematics - 1823 - 666 pages
...must, when 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... | |
| |
... 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. 
