| Webster Wells - Geometry - 1899 - 450 pages
...Vac.' Proof. From (1), V = ac. (§ 232) . -. b = -Vac. PROP. II. THEOREM. 234. (Converse of Prop. I.) **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. Given ad = bc. (1)... | |
| George Albert Wentworth - Geometry - 1899 - 496 pages
...V- = ac. § 327 Whence, extracting the square root, b — -vac. QED 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 two are made the means. Let... | |
| William James Milne - Geometry - 1899 - 396 pages
...proportion the product of whose extremes or means is 60 ; 72; 84; 80; 64; 144; x2y2, xyz; xyzc. Theorem. 1f **the product, of two quantities is equal to the product of two others,** either two may be made the extremes of a proportion of which tlie other two are the means. Data : ad... | |
| Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...equal to the square root of their product, Extracting the square root of both members, b = Vac. 94. **If the product of two quantities is equal to the product of two** other quantities, the factors of either product may be made the means, and the other two the extremes,... | |
| George Edward Atwood - 1900 - 276 pages
...— b = — c = — 428. If the product of two numbers is equal to the product of two other numbers, **the factors of either product may be made the extremes, and the factors of the other** product the means, of a proportion. 1. 2. 3. 4. ad = bc ad = bc ad = bc ad=bc ad_bc_ ad_bc ad_bc ad_bc... | |
| James Harrington Boyd - Algebra - 1901 - 818 pages
...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... | |
| James Harrington Boyd - Algebra - 1901 - 816 pages
..., 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... | |
| Middlesex Alfred Bailey - Algebra - 1902 - 318 pages
...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.) - Engineering - 1903 - 428 pages
...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 - Geometry - 1904 - 496 pages
...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... | |
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