Which of these sentences is correctly written and punctuated?

1.)keeping his active mind challenging roosevelt improved his stamp collection, and read books on american history, politics, and biography.

2.to keep his active mind challenging, roosevelt improved his stamp collection, reading books on american history politics and biography.

3)keeping his active mind challenged roosevelt improved his stamp collection reading books on american history, politics, and biography.

4)to keep his active mind challenged, roosevelt improved his stamp collection and read books on american history, politics, and biography.

The sentence that is correctly written and punctuated is 4, that is, "to keep his active mind challenged, Roosevelt improved his stamp collection and read books on American history, politics, and biography". This is the case because there is parallelism between the coordinated elements (the verbs), that is, they are both in the past simple tense ("improved" and "read"). What is more, it should be "challenged" instead of "challenging" and the -to infinitive clause of purpose is the right option to tell that to reach his goal (keeping his mind challenged) he improved his stamp collection and so on.

source text: from the sketch here given it will be seen, that our good grandmothers differed considerably in their ideas of a fine figure, from their scantily dressed descendants of the present day. a fine lady, in those times, waddled under more clothes even on a fair summer's day, than would have clad the whole bevy of a modern ball room. nor were they the less admired by the gentlemen in consequence thereof. on the contrary, the greatness of a lover's passion seemed to increase in proportion to the magnitude of its object—and a voluminous damsel, arrayed in a dozen of petticoats, was declared by a low-dutch sonnetteer of the province, to be radiant as a sunflower, and luxuriant as a full blown cabbage. certain it is, that in those days, the heart of a lover could not contain more than one lady at a time; whereas the heart of a modern gallant has often room enough to accommodate half a dozen - - the reason of which i conclude to be, either that the hearts of the gentlemen have grown larger, or the persons of the ladies smaller — this however is a question for physiologists to determine. add punctuation to the following excerpt. writing under the name of diedrich knickerbocker washington irving aimed his potent satire at as diverse topics as political rivals such as thomas jefferson to the very ideal of looking back on the past affectionately: a fine lady, in those times, waddled under more clothes even on a fair summer's day, than would have clad the whole bevy of a modern ball room. a voluminous damsel, arrayed in a dozen of petticoats, was declared by a low-dutch sonnetteer of the province, to be radiant as a sunflower, and luxuriant as a full blown cabbage. in those days, the heart of a lover could not contain more than one lady at a time; whereas the heart of a modern gallant has often room enough to accommodate half a dozen