In the very first sonnet the speaker asks the young man to have children so that his beauty will be passed on to succeeding generations. In this way the speaker praises the beauty of the young man.
The structure of this poem does not exactly follow the general pattern noted above. The reader should note the use of the word but at the beginning of the second quatrain (line 5). This word (or the word yet) often indicates a shift in direction. In this case, the poem is shifting from a general statement in the first quatrain to a more specific situation described in the other ten lines of the sonnet.
In the first quatrain the speaker tells how people in general ("we") desire that beauty continues. The student should remember that the word fair during the Renaissance means beautiful, and so "fairest" (in line 1) means the most beautiful. The first line thus indicates that people desire to see the most beautiful creations (people, animals, or even plants) increase or reproduce. In the second line, the speaker likens the idea of beauty to a rose. A person may plant the seeds of a beautiful rose bush so that the beauty will continue in succeeding generations. So, when the original rose ("the riper") withers and dies, the new generation of roses produced from its seeds ("his tender heir") will reflect the same remarkable beauty ("his memory"). Similarly, the beauty of a human being can be passed down to his or her children.