239120
[Translation: ]
[Commentary:
The reference on this page is to Archimedes,
Liber de conoidibus et sphaeroidibus
(Archimedes 1558)
]
[Translation: ]
1.) Gradus circuli est periphæriæ est, totus
[Translation: A degree of a circumference is of the total circumference.
2.) Gradus anguli sphærici est quatuor rectorum
[Translation: A degree of a spherical angle is of four spherical right angles.
3.) Gradus superficiei sphæricæ est totius superficiei sphæricæ,
et est figura biangularis, comprehensa semi- periphæris ex circuli maximis
cuius uterque angulus est gradus
[Translation: A degree of a spherical surface is of the total spherical surface, and is a biangular figure, contained by two maximum semi-circumferences, in which either angle is the degree of the angle.
4.) Biangulum [???] est figura biangularis comprehensa duabus
semi periphæris ex maximis. Et dicitur dari quando unus angulorum
datur. Quoniam ut talis angulus ad 360 ita superficies bianguli
ad totam superficiei
[Translation: A biangle [???] is a biangular figure contained by two maximum semi-circumferences. And it is said to be given when one of its angles is given. Because as such an angle is to 360 degrees, so is the surface of the biangulum to the total surface of the sphere. ]
5.) Ex demonstratis Archimedæis, superficies sphæræ est æqualis illa
circulo plano cuius semidiameter est sphæræ diameter &
[Translation: From the demonstration of Archimedes, that the surface of a sphere is equal to that of a plane circle whose semidiameter is the diameter of the sphere.
[Translation: A degree of a circumference is of the total circumference.
2.) Gradus anguli sphærici est quatuor rectorum
[Translation: A degree of a spherical angle is of four spherical right angles.
3.) Gradus superficiei sphæricæ est totius superficiei sphæricæ,
et est figura biangularis, comprehensa semi- periphæris ex circuli maximis
cuius uterque angulus est gradus
[Translation: A degree of a spherical surface is of the total spherical surface, and is a biangular figure, contained by two maximum semi-circumferences, in which either angle is the degree of the angle.
4.) Biangulum [???] est figura biangularis comprehensa duabus
semi periphæris ex maximis. Et dicitur dari quando unus angulorum
datur. Quoniam ut talis angulus ad 360 ita superficies bianguli
ad totam superficiei
[Translation: A biangle [???] is a biangular figure contained by two maximum semi-circumferences. And it is said to be given when one of its angles is given. Because as such an angle is to 360 degrees, so is the surface of the biangulum to the total surface of the sphere. ]
5.) Ex demonstratis Archimedæis, superficies sphæræ est æqualis illa
circulo plano cuius semidiameter est sphæræ diameter &
[Translation: From the demonstration of Archimedes, that the surface of a sphere is equal to that of a plane circle whose semidiameter is the diameter of the sphere.