DelMonte, Guidubaldo
,
Mechanicorvm Liber
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<
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">PROPOSITIO III. </
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">Alio quoq; modo vecte vti poſsumus. </
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">Sit Vectis AB,
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cuius fulcimentum
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B; ſitq; ex puncto
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A pondus C appen
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ſum; ſitq; potentia
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in D vtcunq; inter
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AB ſuſtinens pon
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dus C. </
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<
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">Dico vt AB
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ad BD, ita eſſe potentiam in D ad pondus C. </
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<
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">Appendatur ex
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puncto D pondus E æquale ipſi C; & vt BD ad BA, ita fiat pon
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dus E ad aliud F. </
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<
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id
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N12C1D
">& cùm pondera CE ſint inter ſe ſe æqualia; erit
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pondus C ad pondus F, vt BD ad BA. </
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<
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">appendatur pondus
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F quoq; in D. </
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">& quoniam pondus E ad ipſum F eſt, vt grauitas
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ponderis E ad grauitatem ponderis F; & pondus E ad pondus F
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eſt, vt BD ad BA: vt igitur grauitas ponderis E ad grauitatem
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ponderis F, ita eſt BD ad BA. </
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<
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">vt autem BD ad BA, ita eſt gra
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uitas ponderis E ad grauitatem ponderis C; quare grauitas ponde
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ris E ad grauitatem ponderis F eandem habet proportionem,
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quam habet ad grauitatem ponderis C. </
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">pondera ergo CF eandem
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habent grauitatem. </
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<
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">ſit igitur potentia in D ſuſtinens pondus F,
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erit potentia in D ipſi ponderi F æqualis. </
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<
s
id
="
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">& quoniam pondus F
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in D æquè graue eſt, vt pondus C in A; habebit potentia in D
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eandem proportionem ad grauitatem ponderis F, quam habet ad
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grauitatem ponderis C. </
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<
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id
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">ſed potentia in D pondus F ſuſtinet; po
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tentia igitur in D pondus quoq; C ſuſtinebit: & pondus C ad po
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tentiam in D ita erit, vt pondus C ad pondus F; & C ad F eſt, vt
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BD ad BA; erit igitur pondus C ad potentiam in D, vt BD ad
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BA: & conuertendo, vt AB ad BD, ita potentia in D ad pondus
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C. </
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<
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id
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">potentia ergo ad pondus eſt, vt diſtantia à fulcimento ad pon
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deris ſuſpendium ad diſtantiam à fulcimento ad potentiam. </
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<
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demonſtrare oportebat. </
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In ſexta huius de libra.
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6
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Huius de libra.
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9
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Quinti.
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7
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Quinti.
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