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[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, . ]
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 ]
[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 ]
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
, angulus rectus . Quæritur
Maxima differentia inter et
. Nam arcus in diversis
positionibus inter et , facit diversis
differentias longitudinum et
[Translation: Let be a right-angled triangle with right angle at . There is sought the maximum differene between and . For the arc in various positions between and makes various differences of longitude and .
, angulus rectus . Quæritur
Maxima differentia inter et
. Nam arcus in diversis
positionibus inter et , facit diversis
differentias longitudinum et
[Translation: Let be a right-angled triangle with right angle at . There is sought the maximum differene between and . For the arc in various positions between and makes various differences of longitude and .
polo . et per punctum describatur
parallelus . Ergo:
est differentia inter et
sit diameter paralleli et
sit perpendcularis illi,
[Translation: Taking the pole , there is drawn through parallel .
Therefore is the difference between and . Let the diameter parallel to it be and the perpendicuar to it .
parallelus . Ergo:
est differentia inter et
sit diameter paralleli et
sit perpendcularis illi,
[Translation: Taking the pole , there is drawn through parallel .
Therefore is the difference between and . Let the diameter parallel to it be and the perpendicuar to it .
Dico quando * linea est æqualis sinui , hoc est . Tum erit æqualis
semidiametro sphæræ, scilicet . et erit differentia quæsita maxima.
Pro demonstratione nota diagramma in Finkio pag. 393. et Clavium
[Translation: I say that when the line is equal to the sine , that is, , then will be equal to the semidiameter of a spehre, namely , and will be the sought maximum difference.
semidiametro sphæræ, scilicet . et erit differentia quæsita maxima.
Pro demonstratione nota diagramma in Finkio pag. 393. et Clavium
[Translation: I say that when the line is equal to the sine , that is, , then will be equal to the semidiameter of a spehre, namely , and will be the sought maximum difference.
Hic notabo solummodo proportiones in Vieta.
Sit , sinus arcus , hoc est anguli . erit sinus versus [???].
est arcus similis . Sit æqualis . et . ex in
[Translation: Here I have noted only the proportions in Viète. Let , be the sine of arc , that is of angle . The versed sine will be . The arc is similar to . Let be equal to and . The rest from the diagram.
Sit , sinus arcus , hoc est anguli . erit sinus versus [???].
est arcus similis . Sit æqualis . et . ex in
[Translation: Here I have noted only the proportions in Viète. Let , be the sine of arc , that is of angle . The versed sine will be . The arc is similar to . Let be equal to and . The rest from the diagram.
*
Dico quando habet
ratio ad sinum :
eandem rationem quam
ad vel ad
. Tum erit
differentia maxima.
Vel melius ita:
Quando sit
parallela . hoc
est quando est
rectus angulus.
Demonstratio
Habetur in alia
charta
[Translation: I say that when has the same ratio to , the sine of as to or to , then will be the maximum difference.
Or better thus: when is a right angle.
The demonstration is to be found in another sheet, ]
Dico quando habet
ratio ad sinum :
eandem rationem quam
ad vel ad
. Tum erit
differentia maxima.
Vel melius ita:
Quando sit
parallela . hoc
est quando est
rectus angulus.
Demonstratio
Habetur in alia
charta
[Translation: I say that when has the same ratio to , the sine of as to or to , then will be the maximum difference.
Or better thus: when is a right angle.
The demonstration is to be found in another sheet, ]