Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 1: Opera mechanica
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CHRISTIANI HUGENII
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& </
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">- 2 ly = - 2 {ιι/θ} - 2 l
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.
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vel + θ yy = {ιι/θ} - 2 l
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xm - {μμ/θ}</
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.
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<
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<
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xml:space
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">- 2 ly = - 2{ιι/θ} + 2 l
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. </
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Ac proinde, utroque caſu, pro θ y y - 2 l y habebitur - {ιι/θ}
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+ θ z z - θ x x + 2 x m - {μμ/θ}. </
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<
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xml:space
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">Quò appoſitis reliquis quantita-
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tibus, ſumma prædicta contentis, θ x x - 2 x m + n n + k k,
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fiet tota ſumma, nempe quadratorum F A, F B, F C, F D,
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= θ z z + nn + k k - {μμ - ιι/θ}. </
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<
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xml:space
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">Quod apparet eſſe planum da-
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tum, cum hæ quantitates omnes datæ ſint; </
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<
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">ſemperque idem
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reperiri, ubicunque in circumferentia ſumptum fuerit pun-
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ctum F. </
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<
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<
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">Quod ſi puncta data diverſas gravitates habere ponantur,
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invicem commenſurabiles, ut ſi punctum A ponderet ut 2,
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B ut 3, C ut 4, D ut 7, eorumque reperto gravitatis cen-
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tro, circulus rurſus deſcribatur, ad cujus circumferentiæ
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punctum, à datis punctis rectæ ducantur, ac ſingularum
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quadrata multiplicia ſumantur ſecundum numerum ponderis
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puncti ſui; </
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">ut quadratum A F duplum, B F triplum, C F
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quadruplum, D F ſeptuplum; </
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<
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">dico rurſus ſummam omnium
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æqualem fore ſpatio dato, ſemperque eidem, ubicunque in
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circumferentia punctum ſumptum fuerit. </
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<
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">Patet enim hoc ex
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præcedenti demonſtratione, ſi imaginemur puncta ipſa mul-
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tiplicia ſecundum numeros attributæ cuique gravitatis; </
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<
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nempe in A duo puncta conjuncta ſint, in B tria, in C qua-
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tuor, in D ſeptem, atque illa omnia æqualiter gravia.</
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<
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">SI figura plana, vel linea in plano exiſtens, ali-
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ter atque aliter ſuſpendatur à punctis, quæ, in
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eodem plano accepta, æqualiter à centro gravitatis
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ſuæ diſtent; </
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<
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">agitatamotu in latus, ſibi ipſi iſochrona eſt.</
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