The English globe being a stabil and immobil one, performing what the ordinary globes do, and much more / invented and described by the Right Honorable, the Earl of Castlemaine ; and now publish't by Joseph Moxon ...

The Use of the LINE of LINES marked with L.

I. To divide a Line into any number of equal parts.

SUPPOSE your Line were to be divided in 23 equal parts, take it between your Compasses, and opening your Sector, place one foot of your said Compasses on the 23 division of the Sector, and the other foot on the 23 over against it, and the distance between the Figures 1 and 1▪ on the said Sector will give you one equal Division of your Line, and the distance between 2 and 2, will give you two equal Divisions of it, and in this man∣ner proceed till you quite run over it, as you design.

II. To find the proportion between any two Lines.

SET over the greater Line at 100, and 100 on the Sector, then taking the lesser between your Compasses, find where it will be just set over also, or lye parallel to the former, which hapning suppose at 50 and 50, you may conclude, that the Proportion re∣quired, is as 100 to 50.

III. To divide a Line as any other Line proposed is di∣vided; that is to say, according to any Proportion.

SUppose you saw a Line, containing 65 equal parts of the Sector devided into three pieces, the first containing five equal parts of the Sector, the other fifteen, so that the last must be 45; then suppose you would divide (after this proportion) another Line, containing but thirteen equal parts of the Sector; Open your Compasses at 13, or length of the Line to be devi∣ded, and putting it over at 65, and 65 on the Sector, the Pa∣rallel at 5 and 5 will be the first division of the Line to be divi∣ded, and one equal part of the Sector in value; the Parallel at 15 and 15 will be the second, and three equal parts in value; and the remainder (being 9 in value,) will be the third; and thus you may do in all other cases.

IV. To encrease or diminish a Line in any Proportion.

SUppose the Proportion were as 4 to 7, take the Line given between your Compasses, and setting it over on your Sector, at the Figures 4 and 4, the distance from 7 to 7 will be a Line encreast (in respect of the given one) as is the Proportion of 4 to 7; In like manner you must do, if any other Proportion were requir'd.

Now if you would diminish a Line as is 7 to 4, put over the Line given at 7 and 7, and the distance of 4 and 4 is the re∣quir'd proportion.

V. Two Lines being given, to find a Third Proportional.

FIND by your Compasses how many parts of the equal Di∣visions of your Sector will measure both your given Lines, so that supposing the one to contain 10 parts, and the other 20, set the second Line (i. e. the Line 20) over at 10, and 10 on the Sector, and the distance or Parallel at 20, and 20 on the Sector, will be 40, the requir'd Proportional.

VI. Three Lines being given, to find a Fourth Proporti∣onal.

THE value of the Lines being found as before, and supposing the first to be 10, the second 20, the third 30, put over the second Line (to wit, 20) at 10 and 10. (the value of the first Line) and the distance or Parallel at 30 and 30. (or value of the third Line) will be 60, the required Proportional.