 | Herbert Ellsworth Slaught, Nels Johann Lennes - Algebra - 1915 - 402 pages
...fractional form, - = c, we clear 6 d of fractions and obtain ad = bc. That is : If four numbers are in proportion, the product of the means equals the product of the extremes. Case II : b : a : : d : c. We are to show that if - = -, then- = - . bdac Proof. From Case I, we have... | |
 | George Wentworth, David Eugene Smith - Arithmetic - 1915 - 324 pages
...terms are called the means. In the proportion | = ££, we see that 7 x 15 = 3 x 35. That is, in any proportion, The product of the means equals the product of the extremes. We also see that if x : 21 = 35 : 105, x 35 21 = 105' then ^ = ., 21 x 35 Therefore, in any proportion,... | |
 | Henry Lewis Rietz, Arthur Robert Crathorne, Edson Homer Taylor - Algebra - 1915 - 266 pages
...J:x = x: 10 - x. 37. (1 - x) : (1 + x) = (2 - x) : (2 + x). 60. Properties of proportions. I. In any proportion, the -product of the means equals the product of the extremes. For, in a _ с when we multiply each member by bd, we obtain ad = be. TT T. а с , ... , ab II. If... | |
 | Ernst Rudolph Breslich - Mathematics - 1916 - 392 pages
...applied to a pro- antecedent portion consequent 206. The following theorems have been proved: 1. In a proportion the product of the means equals the product of the extremes. 2. If the product of two factors equals the product of two others, proportions may be formed by taking... | |
 | George Clinton Shutts, Wilbert Walter Weir - Arithmetic - 1916 - 280 pages
...proportion ' = ' ' ' numerically is the same :xs & = 11,. An important working principle of proportion is: The product of the means equals the product of the extremes. 2. Find x in the proportion •!} = l?.. SOLUTION: x = 7 * *-' = 21. O Find x in the proportions: /ff... | |
 | George William Myers, George Edward Atwood - Algebra - 1916 - 362 pages
...of Proportionality. The equation, ad = bc, furnishes the test of proportionality, which is: In any proportion the product of the means equals the product of the extremes. Exercise 126 Test whether the following expressions are proportions: I- A=tt 2. 1 = -V3- 3. f = ff... | |
 | William Charles Brenke - Algebra - 1917 - 212 pages
...т = - or oc = b2 we have b = ± Vac. Also, с is called the b с 114. Laws of Proportion. 1. In a proportion, the product of the means equals the product of the extremes. 2. If two products, each containing two factors, are equal, either pair of factors may be taken as the... | |
 | Herbert Ellsworth Slaught, Nels Johann Lennes - Algebra - 1917 - 674 pages
...fractional form, - = c, we clear ba of fractions and obtain ad = be. That is : If four numbers are in proportion, the product of the means equals the product of the extremes. Case II : • 6 : a : : d : c. We are to show that if - = -, then- = -. bdac Proof. From Case I, we... | |
 | Herbert Ellsworth Slaught - 1918 - 344 pages
...both members of the equation ? = ^ by 6d, we get ad = 6c. Ax. 3, § 71 That is, if four numbers are in proportion, the product of the means equals the product of the extremes. (2) Dividing both members of the equation 6c = ad by ac, we get * = *. Ax. 4, §71 ac This process is called... | |
 | Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Plane - 1918 - 360 pages
...both members of the equation ? = ^ by 6d, we get ad = be. Ax. 3, § 71 That is, if four numbers are in proportion, the product of the means equals the product of the extremes. (2) Dividing both members of the equation be = ad by ac, we get 5 = -. Ax. 4, §71 ac This process is called... | |
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In any proportion, the product of the means equals the product of the extremes. 
