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" If the product of two quantities is equal to the product of two others, either two may be made the extremes of a proportion and the other two the means. "
A Text-book of Geometry - Page 128
by George Albert Wentworth - 1888 - 386 pages
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Plane and Solid Geometry

Isaac Newton Failor - Geometry - 1906 - 440 pages
...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. CONCLUSION. a:b = c:d. PROOF ad = be....
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Plane and Solid Geometry

Isaac Newton Failor - Geometry - 1906 - 431 pages
...proportional to 2 and 6. 574 Find the third proportional to m and n. PROPOSITION m. 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 = be. CONCLUSION, a:b=c:d. PROOF ad = be....
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Elementary Algebra

George Albert Wentworth - Algebra - 1906 - 440 pages
...it appears that the fourth terra has one value and but one value. 380. If the product of two numbers is equal to the product of two others, either two may be made the extremes of a proportion and the other two the means. For, if ad = be, divide by bd, g = , а с b = d .-. a : 6 = с : d....
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Plane Geometry

Edward Rutledge Robbins - Geometry, Plane - 1906 - 268 pages
...(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...
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Plane and Solid Geometry

Edward Rutledge Robbins - Geometry - 1907 - 428 pages
...(Hyp.). Multiply by the common denomi. oy 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...
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Wentworth's Plane Geometry

George Albert Wentworth, David Eugene Smith - Geometry, Plane - 1910 - 287 pages
...the two antecedents of a proportion are equal, the two consequents are equal. 264. COROLLARY 3. If the product of two quantities is equal to the product...proportion in which the other two are made the means. For if ad = be, then, by dividing by bd, - = -, by Ax. 4. 6 a PROPOSITION II. THEOREM 265. If four...
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Elements of Plane Geometry

William Herschel Bruce, Claude Carr Cody (Jr.) - Geometry, Modern - 1910 - 286 pages
...: 8 = 3 : 24. Ex. 234. Find the value of x when 11 : 44 = 15 : x. PROPOSITION II. THEOREM. 328. If the product of two quantities is equal to the product of two others, either pair may be made the means and the other pair the extremes of a proportion. Given ad = be. To prove...
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Plane and Solid Geometry

George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 496 pages
...the two antecedents of a proportion are equal, the two consequents are equal. 264. COROLLARY 3. If the product of two quantities is equal to the product...proportion in which the other two are made the means. For if ad = be. then, by dividing by bd, - = -, by Ax. 4. 6 d PROPOSITION II. THEOREM 265. If four...
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Plane and Solid Geometry

George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 496 pages
...the two antecedents of a proportion are equal, the two consequents are equal. 264. COROLLARY 3. If the product of two quantities is equal to the product...proportion in which the other two are made the means. For if ad = be, then, by dividing by bd, - = -, by Ax. 4. 6 d PROPOSITION II. THEOREM 265. If four...
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Plane and Solid Geometry

George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 491 pages
...the two antecedents of a proportion are equal, the two consequents are equal. 264. COROLLARY 3. If the product of two quantities is equal to the product...proportion in which the other two are made the means. For if ad = 6c, then, by dividing by 6d, - = -, by Ax. 4. OL C PROPOSITION II. THEOREM 265. If four...
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