 | Euclides - 1821 - 294 pages
...is .concluded, that if there be four magnitudes proportional, the first is to the sum or difference of the first and second, as the third is to the sum or difference of the third and fourth. Note. . If A : B : : C : D, then A : A± B : : C : C±D. This... | |
 | Rev. John Allen - Astronomy - 1822 - 516 pages
...that, "if four magnitudes be proportional, " by converting, the first, is to the sum or difference of the first " and second, as the third, is to the sum or difference of the third " and fourth." PROP. XIX. THEOR. If the wAoie (^U), be to the wiwle (CD),... | |
 | Peter Nicholson - Architecture - 1823 - 210 pages
...so on to the succeeding orders. THEOREM 42. 122. If four quantities, a, b, c, d, be proportionals, the first will be to the sum of the first and second...as the third is to the sum of the third and fourth. For, since a, b, c, d, are proportionals, ad=be. To each side of this equation add the product ac,... | |
 | Pierce Morton - Geometry - 1830 - 584 pages
...1. in the preceding proposition,) if four magnitudes Л, B, C, D be proportionals, the first shall be to the sum of the first and second, as the third to the sum of the third and fourth : or, A : A • + B:fC:C+D.* PROP. [22]. If one magnitude be to... | |
 | Mathematics - 1835 - 684 pages
...Cor. 1. in the preceding proposition,) if four magnitudes A, B,C, D be proportionals, the first shall be to the sum of the first and second, as the third to the sum of the third and fourth : or, A : A + B;;C:C + D.* PROP. [22]. If one magnitude be to another... | |
 | George Darley - Euclid's Elements - 1836 - 172 pages
...called DIVIDENDO, or Division. ART. 174. In a series of four proportional right lines, the first is to the sum of the first and second as the third is to the sum of the third and fourth. Let AB be to CD as EF to GH. Then, AB is to the sum of AB and CD as EF is to the sum of EF and GH.... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...second, as the third, together with the fourth, is to the fourth. 24. By addition, when the first is to the sum of the first and second, as the third is to the sum of 'the third and fourth. second, is to the second, as the excess of the third above the fourth, is to the fourth. 26. By conversion,... | |
 | Andrew Bell (writer on mathematics.) - 1839 - 500 pages
...the second, as the sum of the third and fourth to the fourth ; (330.) By addition, when the first is to the sum of the first and second, as the third is to the sum of the third and fourth ; (331.) By division, when the excess of the first above the second is to the secoml, as the excess... | |
 | George Hutton (arithmetic master, King's coll. sch.) - 1844 - 276 pages
...3 :: 4 : 4-, which requires no demonstration. 6. If four quantities are proportionals, the first is to the sum of the first and second as the third is to the sum of the third and fourth; thus if 6 : 3 :: 8 : 4, then 6 : 6+3 ::8: 8 + 4; or 6: 9:: 8: 12; for 64-9=4, and 84-12=|. 7. If four... | |
 | Horatio Nelson Robinson - Algebra - 1846 - 276 pages
...:-. x : y Ami c : d : : x : y (Theorem 3.) If four magnitudes constitute a proportion, the first may be to the sum of the first and second, as the third...the given proportion, — = — Add unity to both ac members, and reducing to the form of a fraction, we have —£-=_ltf- Throwing this equation into... | |
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If four magnitudes constitute a proportion, the first will be to the sum of the first and second as the third is to the sum of the third and fourth. 
