518259v
In hoc diagrammate ut in ante-
cedente, sit cuiscunque sphaæraæ
maximus circulus :
et axis . &c.
A terminis laterum polgoni
ducantur rectæ ad centrum .
Intelligatur superficies figuræ
compositæ ex conicis, ut
[Translation: In this diagram as in the previous ones, let any sphere have great circle and axis .
From the ends of the sides of the polygon draw the lines to the centre .
Let it be understood that the surface of the figure is composed from cones, as ]
cedente, sit cuiscunque sphaæraæ
maximus circulus :
et axis . &c.
A terminis laterum polgoni
ducantur rectæ ad centrum .
Intelligatur superficies figuræ
compositæ ex conicis, ut
[Translation: In this diagram as in the previous ones, let any sphere have great circle and axis .
From the ends of the sides of the polygon draw the lines to the centre .
Let it be understood that the surface of the figure is composed from cones, as ]
Intelligatur etiam conus
cuius altitudo, ,
sit æqualis perpen-
diculari a centro
sphæræ ad latus
unum polygoni.
et basis circa diametrum ,
Sit æqualis superficiei figuræ compositæ ex conicis.
Dico quod:
Conus = solidæ figuræ comprehensæ a dictis conicis
[Translation: Let there be understood also a cone whose altitude is , which is equal to the perpendicular from the centre of the sphere to the side of one polygon, and the base about the diameter .
Let the figures composed from cones be equal in area.
I say that: the cone = the solid figures composed from the said conical ]
cuius altitudo, ,
sit æqualis perpen-
diculari a centro
sphæræ ad latus
unum polygoni.
et basis circa diametrum ,
Sit æqualis superficiei figuræ compositæ ex conicis.
Dico quod:
Conus = solidæ figuræ comprehensæ a dictis conicis
[Translation: Let there be understood also a cone whose altitude is , which is equal to the perpendicular from the centre of the sphere to the side of one polygon, and the base about the diameter .
Let the figures composed from cones be equal in area.
I say that: the cone = the solid figures composed from the said conical ]
Ita similiter in altero
hemisphærio:
cum tot residuis conorum supra dictis = tot et talibus conis æqualibus supra
[Translation: Thus similarly in the other hemisphere.
since all the remaining above said cones = as many and the same equal cones as above ]
hemisphærio:
cum tot residuis conorum supra dictis = tot et talibus conis æqualibus supra
[Translation: Thus similarly in the other hemisphere.
since all the remaining above said cones = as many and the same equal cones as above ]
Sed omnium conorum altitudines sunt æquales, nempe .
et aggregatum ex omnnibus basibus = superficie figuræ compositæ
ex conicis.
Ergo: […] = solidæ figuræ coprehensæ a dictis conicis
superficiebus.
Quod fuit
[Translation: But all the altitudes of the cones are equal, namely, to ;
and the sum of all the bases = the surface of the figure composed from cones.
Therefore = the solid figure composed of the said cones.
Whcih was to be ]
et aggregatum ex omnnibus basibus = superficie figuræ compositæ
ex conicis.
Ergo: […] = solidæ figuræ coprehensæ a dictis conicis
superficiebus.
Quod fuit
[Translation: But all the altitudes of the cones are equal, namely, to ;
and the sum of all the bases = the surface of the figure composed from cones.
Therefore = the solid figure composed of the said cones.
Whcih was to be ]