Harriot, Thomas, Mss. 6785

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361181
Invenire diamterum sphæræ
in tetraedro
[Translation: To find the diameter of a spehre inscribed in a ]
Sit tetraædrum abcd
g vero centrum trianguli abc
Sit dg diameter sphæræ
circumscribentis. et f centrum.
ae, be, ce, sunt latera cubi
inscripti in eadem sphæra.
bgh recta est perpendicularis ad ac.
et ad diametrum sphæræ dge.
Est igitur bge triangulum rectangulum
si habentur ge, dabitur fg semidiameter
sphæræ
[Translation: Let there be a tetrahedron abcd with g the centre of the triangle abc. Let dge be the diameter of the circumscribing sphere, and f the centre. ae, be, ce, are the sides of cubes inscribed in the same sphere. The straight line bgh is perpendicular to ac and to dge, the diameter of the sphere. Therefore bge is a right-angled triangle; if we have ge then we are given fg, the semidiameter of the sought sphere.

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