Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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DE CENTRO GRAVIT. SOLID.
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dem, cuius baſis eſt quadratum a b c d, & </
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<
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">& </
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<
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<
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in pyramidem, cuius eadé baſis, altitudoq; </
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<
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<
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g f ſemidiametri ſphæræ, & </
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<
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<
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xml:space
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ræ centrum, erit etiam centrum circuli, qui circa quadratũ
<
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a b c d deſcribitur: </
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<
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<
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tis centrum: </
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ſtratum eſt. </
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<
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xml:space
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">quare pyramidis a b c d e axis erit e g: </
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xml:space
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<
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midis a b c d f axis f g. </
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ramidis a b c d e, & </
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<
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ſpicuum eſt ex uigeſima ſecunda propoſitione huius, lineã
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e h triplam eſſe h g: </
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ponendoq; </
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">e g ipſius g
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h quadruplam. </
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<
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<
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">eadẽ
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ratione f g quadruplã
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ipſius g k. </
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<
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g, g f ſintæquales, & </
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<
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g, g _k_ neceſſario æqua-
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les erunt. </
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<
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ta propoſitione primi
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libri Archimedis de cẽ-
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tro grauitatis planorũ,
<
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totius octahedri, quod
<
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ex dictis pyramidibus
<
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conſtat, centrum graui
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tatis erit punctum g idem, quodipſius ſphæræ centrum.</
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<
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">Sit icoſahedrum a d deſcriptum in ſphæra, cuius centrū
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ſit g. </
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<
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enim ab angnlo a per g ducatur rectalinea uſque ad ſphæ
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ræ ſuperficiem; </
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">conſtat ex ſexta decima propoſitione libri
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tertii decimi elementorum, cadere eam in angulum ipſi a
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oppoſitum. </
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angulum a b c: </
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<
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">iunctæ b g, c g producantur, & </
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angulos e f, ipſis b c oppoſitos. </
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a b c, d e f ducantur plana ſphæram ſecantia. </
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