Harriot, Thomas - Mss. 6785

363182

Sphæram solidam bisecare
secundum datam
[Translation: To bisect a solid sphere in a given ]

Sit

Y

centrum sphæræ
et axis

A B

, quæ dividatur
in puncto

C

secundum datam
rationem

d

c

[Translation: Let

Y

be the centre of the sphere, and the axis

A B

, which is divided at the point

C

in the given ratio

d

c

Secet axim

A B

, linea

D E

ad angulos rectos in puncto

C

.
Manifestum est quod planum circuli cuius diameter

D E

dividit
superficiem sphæræ secundum rationem
[Translation: The line

D E

cuts the axis

A B

at right angles in the point

C

.
It is clear that the plane of the circle whose diameter is

D E

divides the surface of the sphere in the given ratio.

Pro divisione soliditatus ita agendum:
Fiat

E F = 2 Y C = C G

. Et dividetur arcus

F U E

in tres
æquales partes, et subtensæ unius partis fiat æqualis

Y K

.
Et per punctum

K

agatur

H K L

ad angulus rectus cum

A B

.
Dico quod:
Planum circuli cuius diameter

H K L

bisecet solidum sphæram
secundum datam rationem.
vel, ita:
fiat:

Y K

sinus duplus tertiæ partis arcus illius, cuius

Y C

est sinus.
et per punctum

K

fit divisio secundum datam rationem;

a m p; c .

[Translation: For the division of solidity, it is to be done thus:
Construct

E F = 2 Y C = C G

, and divide the arc

F U E

into three equal parts; and the chore of one part is equal to

Y K

. And through the point

K

is drawn

H K L

at right angles to

A B

.
I say that: the plane of the circle with diameter

H K L

bisects the solid sphere in the given ratio.
Or, thus:
Construct

Y K

, twice the sine of the third part of that arc of which

Y C

is the sine; and through the point

K

make the division in the given ratio, etc.