lineally

In terms of lines; linewise.

For copying drawings to a scale differing from the original; e.g., to reduce a drawing, lineally, one fifth: […]

By direct descent.

[…] I confess it was not without some pleasure that I found my self able to trace the particular Features, by which certain Families are distinguished, up to their Originals. I could plainly discover from whence one Family derives a long Chin […]. Who first brought the Pox into a noble House, which hath lineally descended in scrophulous Tumours to their Posterity.

Of the Rev. Mr. Slope’s parentage I am not able to say much. I have heard it asserted that he is lineally descended from that eminent physician who assisted at the birth of Mr. T. Shandy, and that in early years he added an "e" to his name, for the sake of euphony, as other great men have done before him.