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 128by George Albert Wentworth - 1888 - 386 pagesFull view - About this book
| 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.... | |
| 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.... | |
| 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.... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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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