 If four quantities are in proportion, they are in proportion by composition; that is, the sum of the first two terms is to the second term as the sum of the last two terms is to the fourth term.  A Text-book of Geometry - Page 134by George Albert Wentworth - 1889 - 242 pagesFull view - About this book
 | Webster Wells - 1885 - 368 pages
...third. Let a : b = с : d. Then, ad — be. Whence, b : a = d : c. 299. In any proportion the terms are in proportion by. Composition ; that is, the sum of the first two terms is to the first term, as the sum of the last two terms is to the third ter.n. Let a : b — с : d.... | |
 | Edward Brooks - Algebra - 1888 - 344 pages
...their product, Let a : b :: b : c; then (Theo. L), b'-ac, and 6 — j/ac. Therefore, etc. THEOREM V. If four quantities are in proportion, they will be in proportion by ALTERNATION. Let a : о :: о: d; then, ad — be; dividing by do, — - — ; о а whence, a : о... | |
 | 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-... | |
 | Charles Davies - Algebra - 1889 - 330 pages
...of ( 1 ), we shall have^ 7 = ^; or, b : a : : d : c . . . (6.) Hence, the following principle : 4. If four quantities are in proportion, they will be in proportion by inversion. If we add' 1 to both members of ( 1 ), and also subtract 1 from both members, we shall have,... | |
 | 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 inversion. 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... | |
 | Webster Wells - Algebra - 1890 - 604 pages
...third. Let a : b = с : d. Then, ad = 6e. Whence, b : a = d : c. 387. In any proportion the terms are in proportion by Composition ; that is, the sum of the first two terms is to the first term as the sum of the last two terms is to the third term. Let a : b = с : d. Then,... | |
 | George W. Lilley - Algebra - 1892 - 420 pages
...member, у + 1 — -, + 1, a+b c+d -r = -j-~ Therefore, a + b :b :: c + d : d. Hence, VI. If four numbers are in proportion, they will be in proportion by composition; that is, the sum of the first two will be to the second as the sum of the last two is to the fourth. Let a : b : : с : d. ac By definition,... | |
 | Education - 1893 - 786 pages
...a temple is 13.09 ft. in circumference, and its volume is 818. 125 cu. feet. What is its height? 8. If four quantities are in proportion, they will be in proportion by division. Give the proof. 9. Demonstrate: — The radius perpendicular to a chord bisects the chord... | |
 | George P. Lilley - Algebra - 1894 - 522 pages
...member, 7+ 1 = -. + 1, a+b _ c+d ~ь~Т" Therefore, a + b : b :: c + d : d. Hence, VI. If four numbers are in proportion, they will be in proportion by composition ; that is, the sum of the first two wi\l be to the second as the sum of the last two is to the fourth. Let a : b :: с : d. ac By definition,... | |
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