ALTERNATE

(Lat. alternat us, changed by turns.) In Botany, parts are said to be alternate with each other when one is placed upon the stem a little higher or a little lower than the other; the word is chiefly applied to leaves, and is used in distinction to opposite, in which parts arise from the same plant on opposite sides of the stem. Alternate. (Geometry.) When two straight lines are intersected by a third, the interior angles on the opposite sides of the intersecting line are said to be alternate. Thus A M N and M N D are alternate angles; and so also are B M N and M N C. A \M B If the two straight lines A B and C D be parallel, the alternate angles are equal. In proportion, the alterC W o_ nate terms are the first and third, \ and also the second and fourth, and the terms of a proportion are said to be taken alternately, or by alternation, when the second and third are made td change places: and it is a well-known theorem, that a proportion subsisting among four quantities of the same kind is not disturbed by this change. Thus, \l a -.h:: c: d, then, alternately, a: c:: b: d. [s. 50]