531266
[Translation: ]
Animadvertendum quod quælibet harum specier irrationalium producit quadratum
trinomium compositum ex binomio et Et quodlibet bino-
mium huiusmodi speciei logisticæ continet in se implicite duas subspecies. Quod
si in singulis distincte explicatur, ex istis 5 irrationalibus fient 10. Ut
alijs chartis sequentibus
[Translation: It is to be noted that any of these irrationals squared produces a trinomial composed of a binome and a medial. And any binome of this form in letters contains in itself two subforms. Which if in each case are set out, from these five irrationals there arise 10. As will appear in the following sheets.
[Commentary:
The irrationals defined by Euclid
Book of the Elements
are binomes, bimedials, and so on. For their definitions and properties see Add MS
f.
f. . Here Harriot defines some further irrational quantities, all of them involving fourth roots, which do not fall into any of Euclid's categories. See also Add MS 6782
f. . ]
De speciebus irrationalium ab Euclide
[Translation: On types of irrationals missed by ]
[Translation: On types of irrationals missed by ]
[Translation: ]
Animadvertendum quod quælibet harum specier irrationalium producit quadratum
trinomium compositum ex binomio et Et quodlibet bino-
mium huiusmodi speciei logisticæ continet in se implicite duas subspecies. Quod
si in singulis distincte explicatur, ex istis 5 irrationalibus fient 10. Ut
alijs chartis sequentibus
[Translation: It is to be noted that any of these irrationals squared produces a trinomial composed of a binome and a medial. And any binome of this form in letters contains in itself two subforms. Which if in each case are set out, from these five irrationals there arise 10. As will appear in the following sheets.