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
| George Albert Wentworth - Algebra - 1886 - 284 pages
...a : b : : с : d, then а.1 od By multiplying by bd, ad= be. 287. If the product of two numbers be **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, by dividing by bd, ^- = —, bd bd M 288. The equation... | |
| Webster Wells - Geometry - 1886 - 392 pages
...a : b = b : c. Then by §242, 62=ac. Whence, b = Vac. PROPOSITION II. THEOREM. 244. CONVERSELY, 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. Dividing... | |
| William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...numbers is equal to the square root of their product. 6, Conversely, if the product of two numbers **is equal to the product of two others, either two may be made the extremes,** and the other two the means, of a proportion. For, if we have given ah 9 = a\ then, dividing by bb... | |
| George Albert Wentworth - Algebra - 1888 - 514 pages
...the above that the fourth term can have one, and but one, value. 191. 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, then, dividing by bd, a- = —, bd bd H.'. a : b = С... | |
| Algebra - 1888 - 492 pages
..., bc . ad ad From this equation, a = -=• , d =. — , о = — , с ==-=-• aa с b 368. IV. // **the product of two quantities is equal to the product of two others,** the factors of either product ni.ay be made the extremes, and the factors of the other product the... | |
| James Bates Thomson - 1888 - 336 pages
...Art. 363, J = £ Clearing of fractions, ae = JV Again, 9 : 6 : : 6:4, and 4x9 = 6*. THEOREM Ш. [f (he **product of two quantities is equal to the product of two others,** the four quantities arc proportional ; the factors of either product being taken for ¿he extremes,... | |
| Charles Davies - Algebra - 1889 - 330 pages
...if we divide both members of ( 2 ) by ca, we shall have, - . = - ; or, a : b : : c : d. Hence, ac If **the product of two quantities is equal to the product, of two** other quantities, the first two may be made the means, and the second two the extremes, of a proportion.... | |
| Webster Wells - Algebra - 1890 - 604 pages
...is equal to the product of the extremes divided by the other mean. 384. (Converse of Art. 381.) 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 = 6e. Dividing... | |
| George Albert Wentworth - Algebra - 1891 - 550 pages
...the above that the fourth term can have one, and but one, value. 280. 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 = bc, then, dividing by bd, ad_ be bd-bd' iz л a : b = с... | |
| George Albert Wentworth - Algebra - 1891 - 380 pages
...the above that the fourth term can have one, and but one, value. 315. 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 = bc, then, dividing by bd, or / (л- с'- v / 316. Transformations... | |
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