As if the segment of the Index be 60 parts: and the segment also of the transome be 60: And the Length given be 250 foote: By the Rule of three, the height also shall be 250 foote: as thou seest in the example underneath: For as ae is to ei; so is aeo to ou, by the [12 e vij]. But here unto the height found, you must adde the height of the measurer: Which if it be 4 foot, the whole height shall be 254 foote.
Therefore
13. If the sight be from the beginning of the Index (perpendicular to the magnitude to be measured) by the names of the transome, unto the ends of some known part of the height, as the distance of the Names is, unto the rest of the transome above them, so shall the known part be unto the part sought.
Or thus: If the sight passe from the beginning of the Index being right, by the vanes of the transversary, to the tearmes of some parts; as the distance of the vanes is unto the rest of the transversary above the index, so is the part knowne unto the remainder: H.
This is a consectary of a knowne part of an height, from whence the rest may be knowne, as in the figure.
As ou is unto uy, so is ei to is. For as ou, is unto ua: so is ei unto ia, by the [12 e vij]. And as ua, is to uy, so is ia unto is; and by right, as ou, is to uy, so is ei, to is. Here thou hast three bounds of the proportion. Let therefore ou, be 20 parts: uy 30: And ei, the knowne part, let it be
15 foote: Therefore thou shalt conclude is, the rest to be 22½.