Harriot, Thomas - Mss. 6787

452227

[Commentary:

This is the first of four pages devoted to Proposition 14 from Chapter XIX of Variorum responsorum liber VIII (Viete 1593d, Chapter 19, Prop , a lengthy chapter on plane and spherical triangles.
XIV.
Prothechidion.
Data duorum maximorum in sphæra circulorum inclinatione, quorum unus secatur a tertio per alterius polos, arguitur quanta fit maxima differentia suarum a nodo longitudinum.
Et contra. Ex maxima differentia longitudinum a nodo, arguitur quanta fit circulum
Given the inclination of two great circles on a sphere, one of which is cut by a third through the pole of the other, there is to be found the greatest difference in their longitudes from the node. Conversely, from the greatest difference of longitudes from the node, there may be found the inclination of the In the crossed out sentence halfway down the page there are references to Finck and Clavius.
The reference to Thomas Finck is to his Geometriae rotundi libri XIIII (Finck .
The reference to Clavius is to his Triangula rectilinea, atque sphaerica (Clavius 1586, . ]

Vieta. lib. 8. resp. pag. 35. prop. 14. proch?on
[Translation: Viète, Responsorum liber VIII, page 35, Proposition ]

Ista propositio est utilis in calcu-
lationibus astronimicis. per eam cog-
noscitur maxima differentia inter
numerationes per Eclipticam et proprios
circulos planetorum, et ubi est &c.
Etiam:
æquationibus

[Translation: This proposition is useful in astronomical calculations. By it may be known the maximum difference between observations by the ecliptic and the nearest orbits of planets, and where it is.
Also, the equations of the ]

Sit triangulum rectangulum

A B C

, angulus rectus

C

. Quæritur
Maxima differentia inter

A B

A C

. Nam arcus

E B C

in diversis
positionibus inter

A

E

, facit diversis
differentias longitudinum

A B

A C

[Translation: Let

A B C

be a right-angled triangle with right angle at

C

. There is sought the maximum differene between

A B

and

A C

. For the arc

E B C

in various positions between

A

and

E

makes various differences of longitude

A B

and

A C

polo

A

. et per punctum

B

describatur
parallelus

O B D

. Ergo:

D C

est differentia inter

A B

A C

sit diameter paralleli

D O

et
sit perpendcularis illi,

B M

[Translation: Taking the pole

A

, there is drawn through

B

parallel

O B D

.
Therefore

D C

is the difference between

A B

and

A C

. Let the diameter parallel to it be

D O

and the perpendicuar to it

B M

Dico quando *

D M

linea est æqualis sinui

D C

, hoc est

D P

. Tum

M O

erit æqualis
semidiametro sphæræ, scilicet

H F

. et

D C

erit differentia quæsita maxima.
Pro demonstratione nota diagramma in Finkio pag. 393. et Clavium
[Translation: I say that when the line

D M

is equal to the sine

D C

, that is,

D P

, then

M O

will be equal to the semidiameter of a spehre, namely

H F

, and

D C

will be the sought maximum difference.

Hic notabo solummodo proportiones in Vieta.
Sit

G I

, sinus arcus

G F

, hoc est anguli

A

F I

erit sinus versus [???].

B D

est arcus similis

G F

. Sit

K L

æqualis

F I

. et

N O = D M

. ex in
[Translation: Here I have noted only the proportions in Viète. Let

G I

, be the sine of arc

G F

, that is of angle

A

. The versed sine will be

F I

. The arc

B D

is similar to

G F

. Let

K L

be equal to

F I

and

N O = D M

. The rest from the diagram.

*
Dico quando

H O

habet
ratio ad

D P

sinum

D C

:
eandem rationem quam

O M

M D

vel

L I

I F

. Tum

D C

erit
differentia maxima.
Vel melius ita:
Quando

H O

sit
parallela

D P

. hoc
est quando

C H O

est
rectus angulus.
Demonstratio
Habetur in alia
charta
[Translation: I say that when

H O

has the same ratio to

D P

, the sine of

D C

O M

M D

L I

I F

, then

D C

will be the maximum difference.
Or better thus: when

H O

is a right angle.
The demonstration is to be found in another sheet, ]

481 (241v)	482 (242)
483 (242v)	484 (243)
485 (243v)	486 (244)
487 (244v)	488 (245)
489 (245v)	490 (246)

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