Stevin, Simon
,
Mathematicorum hypomnematum... : T. 4: De Statica : cum appendice et additamentis
,
1605
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2 L*IBER* S*TATICÆ*
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<
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<
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xml:space
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">Centrum gravitatis pyramidis axem ita ſecat ut ſegmen-
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tum vertici vicinius reliqui ſit triplum.</
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<
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">Pyramidis ABCD baſis triangulæ, vertex A, baſis BCD, axis
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à B ad E centrum gravitatis trianguli ADC eſto BE, hinc ab A ad cen-
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trum gravitatis oppoſitæ hedræ BCD eſto AF quæ per antecedentem pro-
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poſ. </
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<
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<
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dium connectens, ita ſecatur ab E trianguli ADC
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gravitatis centro per 4 propoſ. </
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<
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vertici conterminum reliqui E H ſit duplum, pari ra-
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tione BF dupla erit rectæ FH. </
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<
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tio B F ad FH, per Ptolemaicam {δι}αςρεσιν lib. </
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">componetur è ratione BG ad GE
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& </
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">EA ad AH, ſubducta igitur ratione EA 2 ad
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AH 3 de ratione B F 2 ad FH 1 reliqua erit ratio
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BG 3 ad GE 1.</
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<
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xml:space
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">Verumenimverò in pyramide baſis quadrangulæ demonſtratio hinc deriva-
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ta hujuſmodi erit: </
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aſſurgat à baſi BCDE, & </
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igitur hac in pyramides componentes quarum
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baſes ECB, ECD & </
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">axes AG, AH, centra
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item gravitatis I, K, etiam totius pyramidis cen-
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trum fuerit per 16 propoſ. </
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<
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xml:space
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">in jugo IK, videlicet in
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L cõmuni axis & </
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">jugi interſectione, ſed in trian-
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gulo AGH, recta IK baſi GH parallela eſt, la-
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tera enim A G, AH proportionaliter ſecantur in
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I & </
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<
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">K per priorem partem, itaque AL quoque
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tripla erit ipſius L F nam ob ſimilitudinem ut AI
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ad IG, ſic AL ad LF, ſimillima in ceteris à
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quamlibet multangula baſi aſſurgentibus pyrami-
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dibus ratio quoque fuerit.</
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<
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">Denique coni tum circularis quam ellipticæ baſis demonſtratio eodem re-
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dit, cum enim ex antecedente parte pyramis baſis quoquomodo polygonæ
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axem gravitatis incîdat ratione tripla, in cono verò baſis ellipticæ vel cir-
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cularis pyramis poteſt inſcribi quæ à dato cono quamcunque minimi ſolidi
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differentia abſit, itaque intervallum centrorum gravitatis dati & </
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minus erit quâcunque minima diſtantia, unde ſyllogiſmus talis inſtituitur.</
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<
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Itaqueista puncta nullo intervallo à ſe mutuò abſunt.</
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à gravitatis centro ſecatur, videlicet utſummum & </
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<
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plum. </
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