271136
[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 , & dato puncto , describere per semicirculum, qualis est , ita vt ducatur contingens , fiat ipsi æqualis.
Given a semicircle and a point , draw through a semicircle , so that when the tangent is drawn, is equal to . ]
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 , & dato puncto , describere per semicirculum, qualis est , ita vt ducatur contingens , fiat ipsi æqualis.
Given a semicircle and a point , draw through a semicircle , so that when the tangent is drawn, is equal to . ]
Vide Commandinum in pappo pag.
De Sectione Determinata.
[Translation: On a determinate section. ]
[Translation: On a determinate section. ]
Sit data recta linea ; et in ea puncta, et : oportet ipsam ita
secare in puncto : ut
secare in puncto : ut
1. Constructio:
Sit media proportionalis
inter et . Fiat æqualis
; Dividatur bisariam
in : et fiat æqualis .
Connectantur et . et lineæ
fiat æqualis .
Dico quod punctum est punctum quæ-
[Translation: 1. Construction
Let be a mean proportional between and . Make equal to . is bisected at . And make equal to . Connect and , and make equal to the line
fiat æqualis .
I say that the point is the point sought
Sit media proportionalis
inter et . Fiat æqualis
; Dividatur bisariam
in : et fiat æqualis .
Connectantur et . et lineæ
fiat æqualis .
Dico quod punctum est punctum quæ-
[Translation: 1. Construction
Let be a mean proportional between and . Make equal to . is bisected at . And make equal to . Connect and , and make equal to the line
fiat æqualis .
I say that the point is the point sought
2. Constructio:
Sint , , et æquales. Sit media
proportionalis inter et . Dividatur
bisariam in . Centro , describatur periferia
. Erigitur perpendicularis . Fiat
æqualis . Et per et ducatur linea ad
. Et fiat æqualis .
Dico quod est punctum
[Translation: 2. Construction
Let , , and be equal. Let be the mean proportional between et . is bisected at . With centre , there is drawn the circumference . There is erected the perpendicular . Make equal to . And thorugh and there is drawn the line to . And make equal to .
I say that is the point sought.
Sint , , et æquales. Sit media
proportionalis inter et . Dividatur
bisariam in . Centro , describatur periferia
. Erigitur perpendicularis . Fiat
æqualis . Et per et ducatur linea ad
. Et fiat æqualis .
Dico quod est punctum
[Translation: 2. Construction
Let , , and be equal. Let be the mean proportional between et . is bisected at . With centre , there is drawn the circumference . There is erected the perpendicular . Make equal to . And thorugh and there is drawn the line to . And make equal to .
I say that is the point sought.
3i. Constructio:
fiat
[…]
bisecetur in
[…]
Dico quod est punctum
[Translation: 3rd Construction
make
bisect at
I say that is the point sought.
fiat
[…]
bisecetur in
[…]
Dico quod est punctum
[Translation: 3rd Construction
make
bisect at
I say that is the point sought.