Ceva, Giovanni
,
Geometria motus
,
1692
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<
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">Imagines velocitatum ſimilium motuum ſint BCDE,
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GMKI, & iuxta eas percurrantur ſpatia A, F. </
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poni ex rationibus temporum BE ad GI, & ex ea veloci
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tatem extremarum ED ad IK. </
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ad GH, intelligatur que GHLI figura ſimilis ipſi BDE. Quo
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niam ſpatium A ad F, hoc eſt imago BCDE ad imaginem
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GMKI componitur ex ratione imaginis BCDE ad figu
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ram ſibi ſimilem GHLI, & ex ratione huius ad imaginem
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GMKI: prior ratio eſt duplicata homologorum laterum̨
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BE ad GI, ſeu eſt compoſita ex BE ad GI, & ex huic ſimi
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li ratione ED ad IL, & ratio altera, imaginis ſcilicet GHLI
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ad imaginem GMKI eſt, vt LI ad IK; ergo ex æquali ima
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go BCDE ad imaginem GMKI, hoc eſt ſpatium A ad ſpa
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tium F, componetur ex ratione temporum BE ad GI, & ex
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rationibus ED ad LI, & IL ad IK, ſcilicet nectetur ex ra
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tione BE ad GI, & ED ad IK, quæ poſtrema cum ſit ratio
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velocitatum extremarum ED ad IK; conſtat, quod propo
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ſuimus, ſpatia ſimilium motuum componi ex ratione tem
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porum, & ex ratione homologarum velocitatum, hoc eſt
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extremarum. </
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Tab.
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2.
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Fig.
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5</
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Pr.
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2.
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huiu.
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Corollarium.
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Si tempora fuerint æqualia, ſimilium motuum ſpatia
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vt extremæ, vel ſummæ velocitates, & contra, ſi iſtæ æquales
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ſint, erunt ſpatia vt tempora.
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Corollarium II.
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Cum ſpatia ſimilium motuum nectantur ex ratione tem
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porum & ex ea velocitatum ſummarum, ſeu earum, quæ
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ad inſtantia ſimiliter ſumpta in rectis BE, GI, constat ex
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lem: infra cor.
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2.
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pr.
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3.
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huius tempora componi ex rationi
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bus ſpatiorum ſimilium motuum, & ex recìproca dictarum
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