Stevin, Simon
,
Mathematicorum hypomnematum... : T. 4: De Statica : cum appendice et additamentis
,
1605
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*DE* S*TATICÆ PRINCIPIIS*.
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<
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xml:space
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">6 THEOREMA. 8 PROPOSITIO.</
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<
s
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echoid-s1963
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xml:space
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">Securiculæ gravitatis centrum rectam parallelorum la-
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terum biſectricen
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ita ſecat, ut ſegmentum biſectricis mi-
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nori latericon terminum ad reliquum ſit, ut majoris pa-
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ralleli lateris duplum minore auctum, ad duplum mino-
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ris cum majore.</
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<
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xml:space
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xml:space
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E F, & </
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<
s
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">gravitatis centrum G, Q*VAESITVM*. </
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A B, & </
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xml:space
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">Duplam A B cum D C, ſegmentis G E, G F proportionales eſſe de-
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monſtrandum eſto. </
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<
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">P*RAEPARATIO*. </
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<
s
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in punctis H, I, parallelæ ab his terminis K L, M N, contra latus D C inter-
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ſecent E F in O & </
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<
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<
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K L in puncto R, atque harum interſectionum puncta connectat Q R.</
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">DEMONSTRATIO.</
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recta B F, & </
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<
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">etiam in recta
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K L, centrum erit in concurſu R, eâdem ra-
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tione Q erit centrum gravitatis trianguli
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A B D. </
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lorum jugum crit, in quo utriuſq; </
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idem eſt ſecuriculæ A B C D gravitatis cen-
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trum conſiſtit, ſed idem per propoſ. </
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</
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quadranguli A B C D. </
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<
s
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">Triangula autem
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C D B, A B D, intra eaſdem parallelas ex
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hypotheſi cõſiſtentia, erunt ut baſes, hoc eſt, D C ad A B, ut C D B ad A B D,
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ſed ſic per 1 propoſ. </
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">radius G Q ad G R, atque ita P G ad G O (quia
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clauduntur parallelis M N, K L) omiſſis itaque mediis, ut D C ad A B ſic
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G P ad G O. </
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<
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">Ideoq́ue (per 15, 16 & </
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s
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<
s
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xml:space
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">ut dupla D C
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cum A B, ad duplam A B auctam ipſa D C, ſic dupla G O, aucta G P, ad du-
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plam G P plus ipſa G O. </
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<
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s
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G F item duplici G O plus G P. </
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<
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xml:space
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">Quamobrem ut D C bis plus A B, ad A B
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bis plus D C, ſic G E ad G F. </
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<
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tatis centrum, &</
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</
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<
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<
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">Dato cum totius plani, tum ſegmenti cujus ad reliquum
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ratio ſit nota, gravitatis centro; </
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<
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invenire.</
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<
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<
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<
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xml:space
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B D A, F centrum eſto. </
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<
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<
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tis centrum invenire.</
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