 | Charles Butler - Mathematics - 1814 - 528 pages
...wherefore a + b : b :: c+d: d; this is named COMPONENDO. Euclid is, 5. 66. In like manner, the first is to the sum of the first and second, as the third to the sum of the third and fourth. For since — — = , invertendo r= ;, also (Art. 62.) 6 d a+b... | |
 | 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
...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,... | |
 | Euclid - Euclid's Elements - 1833 - 216 pages
...(10). PROP. XXI. THEOR. If there be four magnitudes proportional (A to B as Fig. 23. C to D), the first is to the sum of the first and second, as the third to the sum of the third and fourth (A to sum of A and B, as C to sum of C andD). .., . . - ; Take a... | |
 | George Darley - Euclid's Elements - 1836 - 172 pages
...is 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
...the 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
...to 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... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...CF. If, therefore, four magnitudes, &c. . Cor. It would be proved in a similar manner, that the first is to the sum of the first and second, as the third to the sum of the third and fourth. PROP. XX. THEOR. — If there be three magnitudes, and other three,... | |
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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. 
