 | Admiralty - 1845 - 152 pages
...a—bc — d ''• ~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 . \a— bc — d a~bc +... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...:: C + D : C — D: that is, if four numbers be proportional, the sum of the first and second terms is to their difference, as the sum of the third and fourth terms is to their difference. It is evident, that if B be greater than A, the analogy would become... | |
 | Horatio Nelson Robinson - Algebra - 1846 - 276 pages
...or a : b — a :: c : d — c. (Theorem 4.) If four magnitudes be proportional, the sum of the first and second is to their difference, as the sum of the...Admitting that a : b :: c : d, we are to prove that a-\-b : a — b :: c-\-d : c — d From the same hypothesis, (Theorem 3.) gives a * a-\-b :: c : c-\-d And... | |
 | Joseph Ray - Algebra - 1848 - 252 pages
...— PROPOSITION IX. — If four quantities are in proportion, the sum of the first and second will be to their difference, as the sum of the third and fourth is to their difference. Let a:6::c:d, (1.) Then will a+6 : a— 6 : : c+d : c—d. From the 1st, by composition, Art. 250,... | |
 | Horatio Nelson Robinson - Algebra - 1848 - 354 pages
...a : b — a : : c : d — c. (Theorem 4.) Jf four magnitudes be proportional, the sum of the first and second is to their difference, as the sum of the third and fourth i* to their difference. Admitting that a : b : : c : d , we are to prove that a+6 : a — b : : c+rf... | |
 | Stephen Chase - Algebra - 1849 - 348 pages
...by compounding. (o) Lat., from divide, to separate; by separating. Hence, Cor. The sum of the first and second is to their difference, as the sum of the third and fourth is to their difference. Thus 3:2 = 6:4; .-. 3+2 : 3—2 = 6+4 : 6—4. Hence (J§ 234-236), § 237. If four quantities be in... | |
 | Horatio Nelson Robinson - Algebra - 1850 - 358 pages
...c—tt. or a : b—a : : c : d—c. (Theorem 4.) If four magnitudes be proportional, the sum of the first and second is to their difference, as the sum of the...a—b ; : c-\-d : c—d From the same hypothesis, (Theorem 3.) gives a : a+6 : : c : c-\-d And a : a—b : : c : c—d Changing the means, (which will... | |
 | Horatio Nelson Robinson - Algebra - 1851 - 346 pages
...a : b — a : : c : d — c. (Theorem 4.) If four magnitudes be proportional, the sum of the first and second is to their difference, as the sum of the...Admitting that a : b : : c : d, we are to prove that a-\-b : a — b : : c-\-d : c — d From the same hypothesis, (Theorem 3.) gives a : a+6 : : c : c-\-d And... | |
 | Joseph Ray - Algebra - 1852 - 408 pages
...275. PROPOSITION IX. — If four quantities are in proportion, the sum of the first and second will be to their difference, as the sum of the third and fourth is to their difference. Let a : b : : c : d (1), then will a+6 : a — b : : c-\-d : c — d. From the 1st, by Composition,... | |
 | James William M'Gauley - 1854 - 284 pages
...means, ac — ad=ac — be ad=be 24. We may mix : and, then, " the sum of the first and second terms is to their difference, as the sum of the third and fourth is to their difference." a:b: :C:d Mixing, a-\-b:a — b: :c-\-d:C—d Multiplying extremes, and means, ac-\-bc— ad— bd=ac—... | |
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In place of adding unity, subtract it, and we shall find that a : a — b :: c : c — d. or a : b — a :: c : d — c. (Theorem 4.) If four magnitudes be proportional, the sum of the first and second is to their difference, as the sum of the third and... 
