Harriot, Thomas - Mss. 6785

361181

Invenire diamterum sphæræ
in tetraedro
[Translation: To find the diameter of a spehre inscribed in a ]

Sit tetraædrum

a b c d

g

vero centrum trianguli

a b c

Sit

d g

diameter sphæræ
circumscribentis. et

f

centrum.

a e

b e

c e

, sunt latera cubi
inscripti in eadem sphæra.

b g h

recta est perpendicularis ad

a c

.
et ad diametrum sphæræ

d g e

.
Est igitur

b g e

triangulum rectangulum
si habentur

g e

, dabitur

f g

semidiameter
sphæræ
[Translation: Let there be a tetrahedron

a b c d

with

g

the centre of the triangle

a b c

. Let

d g e

be the diameter of the circumscribing sphere, and

f

the centre.

a e

b e

c e

, are the sides of cubes inscribed in the same sphere. The straight line

b g h

is perpendicular to

a c

and to

d g e

, the diameter of the sphere. Therefore

b g e

is a right-angled triangle; if we have

g e

then we are given

f g

, the semidiameter of the sought sphere.