Also the degree, par aventure, of Iuppiter or of a-nother planete, was in the first degree of Pisces in longitude, and his latitude was 3 degrees meridional; tho tok I the point of A, and sette it in the firste degree of Pisces on the ecliptik, and thanne sette I the point of F dounward in the same signe, by-cause that the latitude 40 was south 3 degrees, that is to seyn, fro the heved of Pisces; and thus have I 3 degrees by-twixe bothe prikkes; thanne sette I the degree of the longitude up-on the orisonte. Tho tok I my label, and leide it fix upon the degree of the longitude; tho sette I the point of A on my label, evene over the ecliptik lyne, in the ende 45 evene of the degree of the longitude, and sette the point of F endlang in my label the space of 3 degrees of the latitude fro the zodiak, this is to seyn, southward fro the ecliptik, toward the bordure; and turned my riet til the prikke of F sat up-on the orisonte; thanne saw I wel that the body of Iuppiter, in his 50 latitude of 3 degrees meridional, ascended with 14 degrees of Pisces _in horoscopo_. And in this maner maistow wirke with any latitude meridional, as I first seide, save in Capricorne. And yif thou wolt pleye this craft with the arysing of the mone, loke thou rekne wel hir cours houre by houre; for she ne dwelleth nat in a degree of 55 hir longitude but a litel whyle, as thou wel knowest; but natheles, yif thou rekne hir verreye moeving by thy tables houre after houre, [thou shall do wel y-now]. EXPLICIT TRACTATUS DE CONCLUSIONIBUS ASTROLABII, COMPILATUS PER GALFRIDUM CHAUCIERS AD FILIUM SUUM LODEWICUM, SCOLAREM TUNC TEMPORIS OXONIE, AC SUB TUTELA ILLIUS NOBILISSIMI PHILOSOPHI MAGISTRI N. STRODE, ETC. SUPPLEMENTARY PROPOSITIONS. 41. UMBRA RECTA. Yif it so be that thou wilt werke by _umbra recta_, and thou may come to the bas of the toure, in this maner thou schalt werke. Tak the altitude of the tour by bothe holes, so that thy rewle ligge even in a poynt. Ensample as thus: I see him thorw at the poynt of 4; than mete I the space be-tween me and the tour, and I 5 finde it 20 feet; than be-holde I how 4 is to 12, right so is the space betwixe thee and the tour to the altitude of the tour. For 4 is the thridde part of 12, so is the space be-tween thee and the tour the thridde part of the altitude of the tour; than thryes 20 feet is the heyghte of the tour, with adding of thyn owne persone to thyn 10 eye. And this rewle is so general in _umbra recta_, fro the poynt of oon to 12. And yif thy rewle falle upon 5, than is 5 12-partyes of the heyght the space be-tween thee and the toure; with adding of thyn owne heyght. 42. UMBRA VERSA.