Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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LIBER
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PRIMUS.</
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LEMMA XXVI.
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Trianguli ſpecie & magnitudine dati tres angulos ad rectas tot
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idem poſitione datas, quæ non ſunt omnes parallelæ, ſingulos ad
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ſingulas ponere.
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<
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>Dantur poſitione tres rectæ infinitæ
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AB, AC, BC,
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& opor
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tet triangulum
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DEF
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ita locare, ut angulus ejus
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D
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lineam
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AB,
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angulus
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E
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lineam
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AC,
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& angulus
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F
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lineam
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BC
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tangat. </
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DE,
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DF
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&
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EF
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deſcribe
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tria circulorum ſeg
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menta
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DRE, DGF,
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EMF,
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quæ capiant
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angulos angulis
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BAC,
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ABC, ACB
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æquales
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reſpective. </
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>Deſcriban
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tur autem hæc ſegmen
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ta ad eas partes linea
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rum
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DE, DF, EF
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ut
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literæ
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DRED
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eodem
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ordine cum literis
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BACB,
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literæ
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DGFD
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eodem cum literis
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ABCA,
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& literæ
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EMFE
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eodem cum
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literis
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ACBA
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in orbem
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redeant; deinde com
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pleantur hæc ſegmenta
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in circulos integros. </
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cent circuli duo prio
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res ſe mutuo in
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G,
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ſint
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que centra eorum
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P
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&
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<
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Junctis
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GP, PQ,
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cape
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Ga
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ad
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AB
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ut eſt
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GP
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ad
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PQ,
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& cen
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tro
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G,
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intervallo
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Ga
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deſcribe circulum, qui ſecet circulum primum
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DGE
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in
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a.
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Jungatur
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tum
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aD
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ſecans circulum ſecundum
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DFG
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in
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b,
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tum
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aE
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ſecans cir-</
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