Commandino, Federico
,
Liber de centro gravitatis solidorum
,
1565
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æqualibus baſibus, quorum axes cum baſibus æquales an
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gulos faciant. </
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<
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cd ita eſſe, ut axis
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ef ad axem gh: nam ſi axes ad planum baſis recti ſint, il
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lud perſpicue conſtat: quoniam eadem linea, & axem & ſoli
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di altitudinem determinabit. </
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<
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">Si uero ſint inclinati, à pun
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ctis eg ad ſubiectum planum perpendiculares ducantur
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ek, gl: & iungantur fk, hl. </
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">rurſus quoniam axes cum ba
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ſibus æquales faciunt angulos, eodem modo demonſtrabi
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tur, triangulum efK triangulo ghl ſimile eſſe: & ek ad gl,
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ut ef ad gh. </
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<
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">Solidum autem ab ad ſolidum cd eſt, ut
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eK ad gl. </
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monſtrare oportebat.</
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poteſt, priſmata omnia & pyramides, quæ trian
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gulares baſes habent, ſiue in eiſdem, ſiue in æqua
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libus baſibus conſtituantur, eandem proportio
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nem habere, quam altitudines: & ſi axes cum ba
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ſibus æquales angulos contineant, ſimiliter ean
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dem, quam axes, habere proportionem: ſunt
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enim ſolida parallelepipeda priſmatum triangula
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res baſes
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habentiũ
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dupla; & pyramidum ſextupla.</
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15. quinti</
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28. unde
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cimi.</
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7. duode
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cimi.</
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<
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">Priſmata omnia & pyramides, quæ in eiſdem,
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uel æqualibus baſibus conſtituuntur, eam inter
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ſe proportionem habent, quam altitudines: & ſi
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axes cum baſibus faciant angulos æquales, eam
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etiam, quam axes habent proportionem.</
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