...multiply the third term by the ratio of the first to the second, we shall obtain the fourth term. Again : the first term is to the third as the second is to the fourth; for^=3 and f$=3, therefore, whether we multiply 10 by 3, the ratio of 5 to 15, or 15 by 2, the ratio...

...(18), a and d may be taken as either the extremes or the means of a new proportion. 20. When we say the first term is to the third as the second is to the fourth, the proportion is taken by alternation, as in the second case, Article 18. When we say the second term...

...many men are there in the regiment? 7. Prove that if four quantities be proportional, the first ie to the third as the second is to the fourth. If a : b : : с : d, prove that a* + ab + b* _ c* + cd + d* a* _ ab + 6* c* — с d + d*' 8. Given the first...

...because tliis proportion gives PROPOSITION (385.) 4. When four quantities are in proportion, the Jlrst is to the third as the second is to the fourth. If a : b : : c : d, then a : c : : b : d . This is called proportion by Alternation. PROPOSITION (386.) 5. When four quantities...

...(18), a and d may be taken as either the extremes or the means of a new proportion. 20. When we say the first term is to the third as the second is to the fourth, the proportion is taken by alternation, as in the second case, Article 18. When we say the second term...

...(18), a and d may be taken as either the extremes or the means of a new proportion. 20. When we say the first term is to the third as the second is to the fourth, the proportion is taken by alternation, as in the second case, Article 18. When we say the second term...

...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 + dï...

...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 and the number of...

...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 only hold...

...—; Si C bd .-. ad = cb. But a and d are extremes; b and c, means. THEOREM II. In any proportion, the first term is to the third as the second is to the fourth. a:b = c:d; then, — = —- Multiply by —> and bdc ab be ab — — —> or — = —> or a: c =...