Harriot, Thomas - Mss. 6784

403202

Sint duo circuli

b e d

b g c

contingant se in puncto

b

.
sit recta per centra

b o p c d

.
oportet describere circulum
contingentem duos circulos
datos, et lineam

b c

[Translation: Let there be two circles

b e d

and

b g c

touching in the point

b

.
Let the line through the centre be

b o p c d

.
One must draw the circle touching the two given circles and the line

b c

[…]
Jungantur puncta

r

d

.
fiat

s k

parallela

r d

.

[Translation:
Let the points

r

d

be joined.
Let

s k

be parallel to

r d

Bisecetur

k l

, puncta

m

.
agatur ad angulos rectos,

m a

.
fiat,

m a = m k

.
agatur

o a

, quæ secabit periferi-
am minoris circuli in

e

.
agatur

p a g

, quæ secabit perife-
riam maioris circulam in

g

.
Dico quod:

a m = a g = a e

.
et ideo, circulus per

m

g

e

,
erit
[Translation: Let

k l

be bisected at the point

m

.
There is constructed at right angles

m a

.
Let

m a = m k

.
There is constructed

o a

, which will cut the circumference of the smaller circle at

e

.
There is constructed

p a g

, which will cut the circumference of the larger circle at

g

.
I say that

a m = a g = a e

, and therefore the circle through

m

g

e

will be the one required.