 | 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... | |
 | Herbert Ellsworth Slaught, Nels Johann Lennes - Algebra - 1917 - 674 pages
...results : Case I : ad = be. Proof. Writing a : b : : с : d, in the fractional form, - = c, we clear ba of fractions and obtain ad = be. That is : If four...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 have be... | |
 | 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... | |
 | Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Plane - 1918 - 360 pages
...ft.-* Proof : (1) Multiplying 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... | |
 | Herbert Ellsworth Slaught - 1918 - 344 pages
...a" c" Proof : (1) Multiplying 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... | |
 | Henry Charles Horstmann, Victor Hugo Tousley - Electric wiring - 1918 - 324 pages
...X. The values of A, B and R are known, and, since it is a well-known rule of arithmetic that in any proportion the product of the means equals the product of the extremes, we can find the value of X, since AXX=BXR, ' — 7 — =X, or in other words to A, find the value of... | |
 | Raleigh Schorling, William David Reeve - Mathematics - 1919 - 520 pages
...the whole hypotenuse and the segment of the hypotenuse adjacent to it. Because when four quantities are in proportion the product of the means equals the product of the extremes. Addition axiom. By factoring out c. The whole is equal to the sum of all its parts. By substitution.... | |
 | Raleigh Schorling, William David Reeve - Mathematics - 1919 - 510 pages
...extremes of a proportion. Exs. 1-2, Art. 366, illustrate a well-known law or theorem ; namely, that in a proportion the product of the means equals the product of the extremes. SI /» If the given proportion is - = -> then the law is algebraically stated thus : ad = bo. The theorem... | |
 | Edson Homer Taylor - Mathematics - 1919 - 272 pages
...the means. The four numbers which form a proportion are said to be proportional. Principle. In any proportion the product of the means equals the product of the extremes. If ~ = - , both members of the equation may be multiplied oa bybd. Then ad = be. This principle gives... | |
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In any proportion, the product of the means equals the product of the extremes. 
