 | John Radford Young - 1855 - 218 pages
...Z c. Theorem 3. If four quantities of the same kind are in proportion, they are also in proportion when taken alternately ; that is, the first is to the third as the second to the fourth. Let a : b '.: c '. d, that is, •=•=-;. Multiply by -, then -=-;: that oa ' cca is,... | |
 | James Cornwell - 1855 - 380 pages
...y. Rut by a former proposition, " If the first be to the second as the third is to the fourth, then the first is to the third as the second is to the fourth ; " hence the last proposition may take the form, 1 : A :: В : y,butby(I.)l : A : : В : x. Hence,... | |
 | Theodore Strong - Algebra - 1859 - 570 pages
...proportion A : 0 : : В : D. In words, when the terms of a proportion are all of the same kind, they will be proportional when taken alternately ; that is, the first is to the third as the second to the fourth. The same things being supposed ; since — = --., we shall OD have — = ^ or mA : nC... | |
 | Euclides - 1860 - 288 pages
...the terms of an analogy, so that they continue still to be proportionals : 21. By alternation, when the first is to the third, as the second is to the fourth. 22. By inversion, when the second is to the first, as the fourth is to the third. 23. By composition,... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...dlternando, by permutation or alternately; when there are four proportionals, and it is inferred that the first is to the third, as the second is to the fourth. V. 16. 14. Invertendo, by inversion; when there are four proportionals, and it is inferred, that the... | |
 | 1877 - 188 pages
...each side. How many men are there in the regiment? 7. Prove that if four quantities be proportional, the first is to the third as the second is to the fourth. If a : b : : с : d, prove that a* + а Ъ + Ь* _ с* + с d + <£г as _ ¿~6 4- ¿2 ~ с« — ~cd... | |
 | William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...proportions II. and III. are true when I. is true, it follows, that, if four quantities are proportional, the first is to the third as the second is to the fourth; that is, they are proportional by alternation. Also the second is to the first as the fourth to the... | |
 | London univ, exam. papers - 1878 - 164 pages
...each side. How many men are there in the regiment? 7. Prove that if four quantities be proportional, the first is to the third as the second is to the fourth. If a : b : : c : d, prove that C - c 8. Given the first and last terms of an arithmetical progression... | |
 | Isaac Todhunter - Euclid's Elements - 1880 - 426 pages
...alternando, by permutation or alternately; when there are four proportionals, and it is inferred that the first is to the third, as the second is to the fourth. V. 16. 14 Invertendo, by inversion; when there are four proportionals, and it is inferred, that the... | |
 | James Mackean - 1881 - 510 pages
...— When four quantities are proportional, they are also proportional when taken alternately ; or, the first is to the third as the second is to the fourth. If a : b :: с : d, then ad=bc (Prop. I.) Dividing by dc, ab - = -j, and ... а: с ::b :d. This will... | |
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Permutando, or alternando, by permutation or alternately; when there are four proportionals, and it is inferred that the first is to the third, as the second is to the fourth. 
