As therefore uo, is unto oy: so is, ur, unto nl. And backward, as nl, is to ur; so is, yo, unto ou, as here thou seest:
| nl,————ur: | yo,————ou. |
Therefore furthermore by composition of the Antecedent with the Consequent unto the Consequent, by the 5 c 9 ij. Arith. As nl, and ur, are unto ur: so are yo, and ou, unto ou, that is yu, unto ou, on this manner.
| nl,————ur, | yo,————ou, | |
| nr, | ou, | |
| ——————————————— | ||
| ... ur, | yu, ou, | |
there is given nl, and ur, for the first proportionall: ur, for the second: and yu, for the third: Therefore there is also given ou, for the fourth: Which ou, subducted out of uy, there remaineth oy, that is, as, the lesser altitude sought.
For let the parts of the yard be 12. and 6. and the summe of them 18. Now as 18. is unto 12. so is the whole altitude uy, 190. foote, unto the excesse 126⅔ foote. The remainder therefore 63⅓ foote, shall be as, the lesser heighth sought.
But thou maist more fitly dispose and order this proportion thus: As ur, is unto nl: so is uo unto oy. Therefore by Arithmeticall composition, as ur, and nl, are unto nl: so uo, and oy, that is, the whole uy, is unto oy, that is, unto as. For here a subduction of the proportion, after the composition is no way necessary, by the crosse rule of societia, thus:
The second station might have beene in o, the end of the perpendicular from a. But by taking the ayme out of the toppe of the lesser altitude, the demonstration shall be yet againe more easie and short, by the two triangles at the yard aei, and aef, resembling the two whole triangles aou, and aoy, in like situation, the parts of the