 | William Nicholson - 1809 - 716 sider
...of that quantity. Let x measure y by the units in n, then it will measure cy by the units in n e. 2. If a quantity measure two others, it will measure their sum or d.fference. Let a be contained in i, m times, and in y, n times ; thenma = x and na=y; therefore x... | |
 | James Wood - 1815 - 338 sider
...of that quantity. Let x measure y by the units in n, then it will measure cy by the units in nc. 2*. If a quantity measure two others, it will measure their sum or difference. Let a be contained in x, m times, and in y, n times; then ma=x and na = y ; therefore x ± y = ma ± na = rq + na ; ie... | |
 | William Nicholson - 1819 - 432 sider
...of that quantity. Let x measure y by the units in n, then will it measure cy by the units inn c. 2. If a quantity measure two others, it will measure their sum or difference. Let a be contained in x, m times, and in y, n times ; then ma = x and na = y ; therefore x±y=m o±na=m±n . a ; ie a... | |
 | William Foster - 1840 - 92 sider
...square required. APPENDIX, Proof of the Hule for finding the greatest common measure. LEMMA 1. If one quantity measure two others, it will measure their sum or difference. Let x measure a by the units in m, and b by the units in n, then a = mx and b = nx .-. a+b = (m±n)x, ie,... | |
 | James Wood - 1841 - 492 sider
...multiple of that quantity. Let x measure у by the units in n, then it will measure cy by the units in nc. 2d. If a quantity measure two others, it will measure...their sum or difference. Let a be contained m times in л?, and n times in y; then ma = x and na = y; therefore x¿=y = ma±na*= (т±и) o; that is, a is... | |
 | Wales Christopher Hotson - 1842 - 306 sider
...multiple of the other. For, if m measure x by the quotient p, it will measure px by the quotient^. LEM. 2. If a quantity measure two others, it will measure their sum or difference, For, if m measure x and y by the quotients p and q, so =x, and qm=y, 57. To investigate a method of... | |
 | James Wood - 1857 - 634 sider
...for since у = n,r, my emn#(Art. 81)=тп.л?, that is, л is contained mn times in my, or measures my by the units in mn. 2d. If a quantity measure two...their sum or difference. Let a be contained m times in .r, and n times in y; then ma = x, and na = y; therefore x±y = ma =tna«= (m±n)a; that is, e is contained... | |
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The truth of this rule depends upon these two principles ; 1". If one quantity measure another, it will also measure any multiple of that quantity. Let x measure y by the units in n, then it will measure cy by the units in nc. 