Harriot, Thomas, Mss. 6784

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[Commentary:
The problem pursued in this and many other folios in Add MS 6784 is 'the determinate section', as set out in Pappus, Mathematicae collectiones (Pappus , Book 7. For a statement of the problem see Add MS 6784 f. .
There is a particular reference on this folio to page 214 of Commandino's edition of Pappus. Page 214 is part of Commandino's lengthy commentary to Proposition 85, also denoted Lemma XI.
Problema V. Propos. LXXXV.
Semicirculo positione dato ABC, & dato puncto D, describere per D semicirculum, qualis est DEF, ita vt ducatur contingens BC, fiat AD ipsi BE æqualis.
Given a semicircle ABC and a point D, draw through D a semicircle DEF, so that when the tangent BC is drawn, AD is equal to BE. ]
Vide Commandinum in pappo pag.
De Sectione Determinata.
[Translation: On a determinate section. ]
Sit data recta linea HK; et in ea puncta, D et L: oportet ipsam DK ita
secare in puncto G: ut
1. Constructio:
Sit DP media proportionalis
inter AD et DK. Fiat LM æqualis
DK; Dividatur MH bisariam
in N: et fiat DO æqualis MN.
Connectantur O et P. et lineæ OP
fiat æqualis OG.
Dico quod punctum G est punctum quæ-

[Translation: 1. Construction
Let DP be a mean proportional between AD and DK. Make LM equal to DK. MH is bisected at N. And make DO equal to MN. Connect O and P, and make OG equal to the line OP
fiat æqualis OG.
I say that the point G is the point sought
2. Constructio:
Sint DL, DR, et HV æquales. Sit DS media
proportionalis inter RD et DK. Dividatur VK
bisariam in T. Centro T, describatur periferia
VXK. Erigitur perpendicularis TX. Fiat TY
æqualis DS. Et per Y et S ducatur linea ad
Z. Et fiat TG æqualis YZ.
Dico quod G est punctum
[Translation: 2. Construction
Let DL, DR, and HV be equal. Let DS be the mean proportional between RD et DK. VK is bisected at T. With centre T, there is drawn the circumference VXK. There is erected the perpendicular TX. Make TY equal to DS. And thorugh Y and S there is drawn the line to Z. And make TG equal to YZ.
I say that G is the point sought.
3i. Constructio:
fiat hl=dl
[…]
bisecetur nh in o
[…]
Dico quod g est punctum
[Translation: 3rd Construction
make hl=dl

bisect nh at o

I say that g is the point sought.

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