 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...as the third is to its excess above the fourth. 27- By mixing, when the sum of the first and second, is to their difference, as the sum of the third and fourth to their difference. 28. By equality, when there is any number of magnitudes more than two, and as... | |
 | Andrew Bell (writer on mathematics.) - 1839 - 500 pages
...of the third above the fourth to the fourth ; (332.) By mixing, when the sum of the first and second is to their difference, as the sum of the third and fourth to their difference ; (333.) By direct equality, when there are several analogies, and two homologous... | |
 | John D. Williams - Algebra - 1840 - 216 pages
...inversely a : a±b ;• c TH. 8. If four quantities be proportional, then the sum of the first and second is to their difference as the sum of the third and fourth is to their difference. For, by theorem 6, ~|~ ~\ • od , a — bb — d , . . . . . bd and — ;... | |
 | John D. Williams - Algebra - 1840 - 634 pages
...a : «z±& : : с Тн. 8. If four quantities be proportional, then the sum of the first and second is to their difference as the sum of the third and fourth is to their difference. For, by theorem 6, g ' c~*~ ; ; ' bd . a — bb — d ... bd and — — —... | |
 | Bewick Bridge - Algebra - 1841 - 260 pages
...a±6 : : c : c±d. TH. 8. " If four quantities be proportional, then the sum of the first and second is to their difference as the sum of the third and fourth is to their difference." For by TH. 6^ — =— = — =- , and od — T— = — — ; invert the last... | |
 | George Hutton (arithmetic master, King's coll. sch.) - 1844 - 276 pages
...for 6—3=2. and 84-4 = 2. 8. If four quantities are proportionals, the sum of the first and second is to their difference, as the sum of the third and fourth is to their difference; thus, if 6 : 3 :: 8: 4, then 6+3 : 6-3 :: 8+4 : 8-4, or 9 : 3 :: 12 : 4, for... | |
 | James Bates Thomson - Geometry - 1844 - 268 pages
...division, 12—3:3:: 8—2 : 2. Hence, If four magnitudes, <Sfc. Cor. The sum of the fir?t and second is to their difference, as the sum of the third and fourth is to their difference. Since - - AB : B : : C— D : D; Then, (8. 3,) AB : CD : : B : D. And, (16.... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...i or (Sup. 2, schol. 2)AfB : A — B :: C + D : C — D: that is, if four numbers be proportional, the sum of the first and second terms is to their...the third and fourth terms is to their difference. It is evident, that if B be greater than A, the analogy would become B + A : B — A : : D+C:D—C.... | |
 | Admiralty - 1845 - 152 pages
...''• ~b~'~~d~ Or, ab:b::cd:d 89. If 4 quantities are proportionals, the sum of the first and second, is to their difference, as the sum of the third and fourth, is to their difference. That is, if a : b : : c : d then will a-\-b : a — b :: c-\-d : c— d For... | |
 | Scottish school-book assoc - 1845 - 444 pages
...quantities are proportional, they are also proportional by mixing; that is, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference. •dn di. "+' c+^ j T» KIT. •"-* c — ^ For Prop. 5th — =-— , and Prop.... | |
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If four magnitudes are in proportion, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference. 
