The compleat surveyor containing the whole art of surveying of land by the plain table, theodolite, circumferentor, and peractor ... : together with the taking of all manner of heights and distances, either by William Leybourn.

PROB. XIII. To divide a right line given into two parts, which shall have such proportion one to the other as two given right lines.

[illustration]

THe line given is AB, and it is required to divide the same into two parts, which shall have such proportion one to the other, as the line C hath to the line D.

First, from the point A, draw the line AE, at pleasure, making the angle EAB; then take in your Compas∣ses the line C, and set it from A to F, also take the line D, and set it from F to E, and draw the line EB, then from the point F, draw the line FG parallel to EB, cutting the given line AB in the point G; 〈◊〉〈◊〉 is the line AB divi∣ded into two parts in the point G, being in proportion one to the other, as the line C is to the line D; for,

• As AE to AB ∷ so AF to AG.

Arithmetically.

LEt the line AB contain 40 Perches, and let the line C be 20, and the line D 30; and let it be required to divide the line AB into two parts, being in proportion one to the other, as the line C is to the line D.

First, Adde the lines C and D together, their summe is 50, then say by the Rule of Proportion: If 50 (which is the summe of the two given terms) give 40 the whole line AB, what shall 30, the greater given term give? Multiply and divide, and you shall have in the quotient 24 for the greater part of the line AB, which being taken from 40 the whole line, there remains 16 for the other part AG; for,

• As AE to AB ∷ so FE to GB.
• As 50 to 40 ∷ so 30 to 24.