Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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<
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ABL
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Globus,
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C
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centrum ejus,
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BPV
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Rota ei inſiſtens,
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E
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centrum Rotæ,
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B
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punctum contactus, &
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P
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punctum datum in pe
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rimetro Rotæ. </
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ABL
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ab
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A
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per
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B
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verſus
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L,
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& inter eundum ita revolvi ut ar
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cus
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AB, PB
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ſibi invicem ſemper æquentur, atque punctum illud
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P
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in perimetro Rotæ datum interea deſcribere Viam curvilineam
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AP.
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Sit autem
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AP
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Via tota curvilinea deſcripta ex quo Rota
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Globum tetigit in
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A,
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& erit Viæ hujus longitudo
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AP
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ad duplum
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ſinum verſum arcus 1/2
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PB,
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ut 2
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CE
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ad
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CB.
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Nam recta
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CE
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(ſi
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opus eſt producta) occurrat Rotæ in
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V,
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junganturque
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CP, BP,
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EP, VP,
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& in
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CP
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productam demittatur normalis
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VF.
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Tan
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gant
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PH, VH
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Circulum in
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P
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&
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V
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concurrentes in
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H,
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ſecetque
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PH
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ipſam
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VF
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in
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G,
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& ad
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VP
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demittantur normales
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GI, HK.
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