 | Webster Wells - Algebra - 1879 - 468 pages
...the following proportions : a : с = b : d, bid — a'.c, с : d = a : b, d : b = с : a, etc. 345. If four quantities are in proportion, they will be in proportion by ALTERNATION ; that is, the antecedents will have to each other the same ratio as the consequents. Thus,... | |
 | William Frothingham Bradbury - Geometry - 1880 - 260 pages
...that is j £ Adding 1 to each member j + 1 = 5 ~^~ 1 that is o + o , b = c T « : ll THEOREM VI. 18. If four quantities are in proportion, they will be in proportion by division. Let a :b = c : d ac that is l — 'd Subtracting 1 from each member ^ — 1 = ^ — 1 o —... | |
 | James Bates Thomson, Elihu Thayer Quimby - Algebra - 1880 - 360 pages
...— = r = r = &c. (Art. 200.) 6 + Й+/+&С. 6 369. These changes may all be expressed as follows : If four quantities are in proportion, they will be in proportion by Alternation, Inversion, Composition, or Division. ТНЕОвЕМ V. 370. If four quantities are in... | |
 | Alfred Hix Welsh - Geometry - 1883 - 326 pages
...1. A mean proportional between two quantities equals the square root of their product. THEOREM III. If four quantities are in proportion, they will be in proportion by alternation. Let « : b :: o : d; then will «:<•:: b : d. For, (1) aXd-hXc - - Th. I. (1) -f- dc... | |
 | Edward Brooks - Algebra - 1888 - 344 pages
...then (Theo. L), bo -ad ; dividing by ac, — — _ ¡ ao whence, 6 : о : : d : a THEOREM VII. • If four quantities are in proportion, they will be in proportion by COMPOSITION. Let a : b :: с : (I; then will a + 6 : 6 :: c + d : d. H' adding 1 to each aide, -H-1-... | |
 | George Albert Wentworth - Geometry - 1888 - 264 pages
...t iS, bd or, a + b : b = c + d : d. In like manner, a + 6:a=c + <f:e. PROPOSITION VII. Q. E D. 301. If four quantities are in proportion, they will be in proportion by division ; that is, the difference of the first two terms will be to the second term as the difference... | |
 | Edward Albert Bowser - Algebra - 1888 - 868 pages
...a: c : : b : d, b: a : : d : c, b:d :: a : c, c: d :: a:b, etc., are all true provided that ad = be. If four quantities are in proportion they will be in proportion by (3) Inversion. — If a:b :: c : d, then b : a : : d:c. TI ac * , a , c For - = - ; therefore 1 -t-... | |
 | James Wallace MacDonald - Geometry - 1889 - 80 pages
...the other two the extremes of a proportion. Proposition IV. A Theorem. Proposition V. A Theorem. 121. If four quantities are in proportion, they will be in proportion by alternation. Proposition VI. A Theorem. 122. If four quantities are in proportion, they will be in... | |
 | James Wallace MacDonald - Geometry - 1894 - 76 pages
...quantities are in proportion, they will be in proportion by alternation. Proposition VI. A Theorem. 122. If four quantities are in proportion, they will be in proportion by composition. Proposition VII. A Theorem. 123. If four quantities are in proportion, they will be in... | |
 | George Albert Wentworth - Geometry - 1888 - 466 pages
...each member of the equation by -. c Then a- = bj cd or. a : <? = b : d. QED PROPOSITION V. 299. // four quantities are in proportion, they will be in proportion by inversion ; that is, the second term will be to the first as the fourth to the third. Let a:b = c:d. To prove... | |
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If four quantities are in proportion, they will be in proportion by COMPOSITION... 
