If then the earth be found by the measuring of the Geometrician, to be more long
than broad, and yet hauing each long side equall, and each side of bredth likewise
equall, which is called Balongue droit, for the bringing of this forme into a square,
you must remember (or else hauing it set downe in writing table•• for the better re∣membrance)
what number of poles are in the length, and how many likewise in the
bredth, and to multiplie the length by the bredth, that is, the poles of the leng••h, by
the poles of the bredth: as for example, if the measurer haue found in ••he ••quall
length of a ground fiue and twenty poles, and in the equal bredth of the same ground
foure poles, he shall multiplie fiue and twentie by foure, and shall ••ay foure times fiue
and twentie are a hundred: this ground then by this multiplication is found to con∣taine
a hundred poles, and so by consequent an arpent, at a hundred poles to an ar∣pent,
and eighteene foot to a pole, and so in like manner as the length is more or lesse.
Likewise the bredth being lesse or greater, that the number of the length and bredth
be multiplied together, whether it be lesse or amount to more than an arpent, he shall
make his accounts and reckoning to fall proportionably, according to the greater or
lesse number of poles, as well of the length as of the bredth: as for example, if the
measurer haue found in the length of a ground seuen and thirtie poles and a halfe, and
in bredth one pole, he shall multiplie thirtie seuen poles and a halfe by one, and shall
say that this ground containeth thirtie seuen poles and a halfe, which is a quarter and
a halfe of an arpent, at a hundred poles to an arpent, and eighteene foot to euerie
pole: by the same meanes, if the ground be seuenteene pole long, and two pole and
sixe foot broad, in multiplying seuenteene pole by two pole and sixe foot, he shal find
a quarter and a halfe, two pole, three foot of an arpent: after a hundred pole to an ar∣pent,
and eighteene foot to a pole.
If the ground be found by measuring to be vnequall and vnlike, as well in the
length of the one side to the other, as in the bredth of the one end to the other; you
must remember, or for your better remembrance set downe in writing tables, the vne∣quall
numbers of the two sides, as also those of the two ends, and afterward to reduce
the two vnequall lengths, as also the bredths, into an equalitie, in the end multiply∣ing
the equall length by the bredth likewise made equall: as for example, if one of
the broad ends of the said ground doe containe foure poles, and the other two poles
onely, and the one of the sides of length containe sixteene poles, and the other tenne
poles, to bring and reduce the thing into a square, you must take of the two poles
by vvhich one of the broad ends is broader than the other, the halfe, that is to say,
one pole, and put it to the two poles of the other end, and thus each end will contain
his three poles a peece equally. And of the sixe poles wherein the one of the sides
doth exceed the other in length, to take also the halfe which is three pole, and to
put them to the tenne, so each of the sides vvill be thirteene pole a peec••: then af∣terward
to take the number of one bredth (made equall vvith the other, as vve haue
said) vvhich is three pole, for to multiplie one length (made equall likewise
with the other as we haue said) which is thirteene pole, and to account that three
times thirteene are thirtie nine: so there will be thirtie nine pole, which make a quar∣ter
and a halfe, one pole and a halfe, of an arpent, according to a hundred pole to an
arpent, and eighteene foot to euerie pole: so then you must follow this rule in euerie
thing that is Bal••ngue cornue, that is, fashioned after the manner of a horne, that is,
that the side and end which are of greatest contents, doe helpe and succour the other
which are the lesser, in yeelding of their owne so much vnto them, as may make side
equall with side, and end with end.
If the ground be fashioned like vnto a Wedge, that is to say, equally long on
both sides, but hauing one end broader than another; as for example, twentie pole
long, and seuen pole broad at the one end, and but three at the other: then you must
gather the two breadths together, which will make tenne pole: to take the halfe of
them, will be fiue, to multiplie the length withall, in the doing whereof you must
count fiue times twentie, and the summe will rise in all to a hundred pole, which