Harriot, Thomas - Mss. 6782

656328

Invenire duas medias
continue proportionales,
inter
[Translation: To find two mean proportionals between given ]

sit data maior:

x y

.
data minor:

z

.
oportet inter

x y

z

invenire duas
medias continue proportionales.
centro

a

; intervallo

\frac{x y}{2}

, describitur
circulus

c b e

.
Agatur recti

a b

, quæ

= \frac{x y}{2}

sit recta

b c = z

Et producetur

b c

versus

d

Ita fiat

c d = c b

.
Agatur

d a e

.
Compleatur Rhombus

a b f e

Agatur recta

a h g

, ita ut

h g = a b

.
Et producetur

g a

n

.
Dico quod:

c b

o g

g b

o n

, sunt continue
proportionales.

[Translation: Let the greater given quantity be

x y

,
and the lesser given quantity be

z

.
Between

x y

and

z

one must find two continued proportionals.
With centre

a

and radius

\frac{x y}{2}

, draw the circle

c b e

.
Construct the line

a b

which equals

\frac{x y}{2}

and let the line

b c = z

and extend

b c

towards

d

.
Thus

c d = c b

.
Construct

d a e

.
Complete the rhombus

a b f e

Construct the line

a h g

so that

h g = a b

.
And extend

g a

towards

n

.
I say that

c b

o g

g b

o n

, are continyued proportionals.
]