 | James Harrington Boyd - 1901 - 812 σελίδες
..., lc n — -, b = — > с — -, (í = — deba 488. THEOREM III.— (The converse of Theorem I.) If the product of two quantities is equal to the product of two others, the four <trc proportionals, the terms of either product being taken as the means, and the terms of the other... | |
 | James Harrington Boyd - 1901 - 818 σελίδες
...from the equation ad = be: thus, he , ad ad ] be 486. THEOREM III.— (The converse of Theorem I.) If the product of two quantities is equal to the product of two others, the four are proportionals, the terms of either product being taken as the means, and the terms of the other... | |
 | Middlesex Alfred Bailey - 1902 - 336 σελίδες
...of the means.) ae x dh = bf x eg (We multiply the equations member by member.) ae : bf : : cg : dh (If the product of two quantities is equal to the product of two others, etc.) Hence, the principle, QED PROPOSITION LXXXVII. THEOREM Equimultiples of two quantities have the... | |
 | American School (Chicago, Ill.) - 1903 - 426 σελίδες
...the means. Let a : b = с : d ,, , . а с that is T =3 -, о а Clearing of fractions, ad = be П. If the product of two quantities is equal to the product of two others, one pair may be made the extremes, and the other pair the means, of a proportion. Let ad = be ТЧ-... | |
 | George Albert Wentworth - 1904 - 496 σελίδες
...b = b : q. Then b2 = ac. § 327 Whence, extracting the square root, PROPOSITION III. THEOREM. 329. If the product of two quantities is equal to the product of two others, either two may be made the extremes of the proportion in which the other tiuo are made the means. Let... | |
 | Fletcher Durell - 1904 - 382 σελίδες
.... Writing a and d as the extremes, and c and b as the means of a proportion, a : C=b : d, Art. 304. (if the product of two quantities is equal to the product of two other quantities, one pair may be made the extremes and the other pair the means of a proportion).... | |
 | Fletcher Durell - 1911 - 553 σελίδες
...Writing1 a and d as the extremes, and c and 5 as the means of a proportion, a : c— 1) : d, Art. 304. (if the product of two quantities is equal to the product of two other quantities, one pair may be made the extremes and the other pair the means of a proportion).... | |
 | Fletcher Durell - 1904 - 382 σελίδες
...product of the extremes equals the product of the means). .: b=vac. QED PROPOSITION III. THEOREM 804. // the product of two quantities is equal to the product of two other quantities, one pair may be made the extremes and the other pair the means of a proportion. •... | |
 | Edward Rutledge Robbins - 1906 - 268 σελίδες
...— (Hyp.). Multiply by the common denomiby nator, by and obtain, ay = bx (Ax. 3). QED 291. THEOREM. If the product of two quantities is equal to the product of two others, one pair may be made the extremes of a proportion and the other pair the means. Given : ay = bx. To... | |
 | Isaac Newton Failor - 1906 - 440 σελίδες
...third proportional to 2 and 6. 574 Find the third proportional to m and n. PROPOSITION in. THEOREM 330 If the product of two quantities is equal to the product of two others, either two may be made the extremes and the other two the means of a proportion. HYPOTHESIS. ad=bc.... | |
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Conversely, if the product of two quantities is equal to the product of two other quantities, the first two may be made the extremes, and the other two the means of a proportion. 
