 | George E. Mercer, Mabel Bonsall - Arithmetic - 1914 - 324 pages
...the ratios may be expressed in fractional form and their values compared. When four numbers are in proportion, the product of the extremes equals the product of the means. Let the pupils test this equality with the proportions they have written and proved. Either extreme... | |
 | Claude Irwin Palmer, Daniel Pomeroy Taylor - Geometry, Plane - 1915 - 296 pages
...-g-; the reciprocal of ^ is 1 -5-f = -f . FUNDAMENTAL THEOREMS 398. Theorem. If four numbers form a proportion, the product of the extremes equals the product of the means. „. ac Given - = -. oa To prove ad = bc. Proof. Multiplying both ratios by bd, ad = bc. NOTE . A proportion... | |
 | John Charles Stone, James Franklin Millis - Geometry, Solid - 1916 - 196 pages
...of any triangle are concurrent at a point of trisection of each. § 118. (1) If four numbers are in proportion, the product of the extremes equals the product of the means. (2) If the product of two numbers equals the product of two other numbers, the four numbers are in... | |
 | John Charles Stone, James Franklin Millis - Geometry - 1916 - 298 pages
...may be proved by use of axioms. Let the student write the proofs in full. (1) If four numbers are in proportion, the product of the extremes equals the product of the means. That is, if - = -, then ad = be. ba Suggestion. Multiply both members by bd. (2) If the product of... | |
 | Herbert Edwin Hawkes, William Arthur Luby, Frank Charles Touton - Algebra - 1917 - 344 pages
...proportion. (See Axioms, pp. 39—40.) CL f Thus, in the proportion - = - both members may be multiplied by bd, giving ad = be. Here the first member is the...means. Therefore, in any proportion the product of the extreme« equals the product of the means. EXERCISES 1. Form proportions from the following by supplying... | |
 | Ludwig Frank - Mechanical drawing - 1917 - 224 pages
...and are called the terms. The first and last terms are the extremes and the middle terms, the means. In any proportion the product of the extremes equals the product of the means; hence, if three terms are given, the fourth may be found. The area of a surface is its measure expressed... | |
 | Herbert Edwin Hawkes, William Arthur Luby, Frank Charles Touton - Algebra - 1918 - 296 pages
...a proportion. (See Axioms, p. 16.) Thus, in the proportion - = - both members may be multiplied bd by bd, giving ad = be. Here the first member is the...product of the extremes equals the product of the means. 132. Proportions from equal products. The numbers which occur in a pair of equal products may be used... | |
 | Claude Irwin Palmer - Geometry, Solid - 1918 - 192 pages
...CHAPTER IV. PROPORTION AND SIMILARITY THEOREMS OF PROPORTION § 398. Theorem. If four numbers form a proportion, the product of the extremes equals the product of the means. § 399. Theorem. The mean proportional between two numbers equals the square root of their product.... | |
 | Claude Irwin Palmer, Daniel Pomeroy Taylor - Geometry - 1918 - 460 pages
...is -g-; the reciprocal of f- is 1 -r|-=-f. FUNDAMENTAL THEOREMS 398. Theorem. If four numbers form a proportion, the product of the extremes equals the product of the means. „. ac Given r= -. oa To prove ad=bc. Proof. Multiplying both ratios by bd, ad = be. NOTE . A proportion... | |
 | Clarence Wesley Sutton, Nels Johann Lennes - Business mathematics - 1918 - 488 pages
...same. This is true of any proportion in which the ratios are reduced to simplest form. Hence, ' In a proportion the product of the extremes equals the product of the means. This statement holds for any proportion whatever, whether the ratios are reduced to simplest form or... | |
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In any proportion, the product of the extremes equals the product of the means. 
