Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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etiam ſecet communem illam diametrum
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AB
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(ſi opus eſt productam) </
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in
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T
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; ſitque
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SY
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ad hanc rectam, &
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BQ
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ad
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hanc diametrum perpendicularis, atque Figu
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ræ
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RPB
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latus rectum ponatur L. </
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<
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per Cor. </
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<
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linea
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RPB
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circa centrum
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S
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moventis velo
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citas in loco quovis
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P
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ſit ad velocitatem cor
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poris intervallo
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SP
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circa idem centrum Cir
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culum deſcribentis in ſubduplicata ratione rec
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tanguli 1/2 LX
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SP
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ad
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quadratum. </
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<
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tem ex Conicis
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ACB
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ad
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CPq
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ut 2
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AO
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ad L,
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adeoque (2
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CPqXAO/ACB
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) æquale L. </
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<
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locitates illæ ſunt ad invicem in ſubduplicata
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ratione (
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CPqXAOXSP/ACB
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) ad
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SY quad.
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Por
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ro ex Conicis eſt
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CO
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ad
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BO
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ut
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BO
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ad
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TO,
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& compoſite vel diviſim ut
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CB
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ad
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BT.
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Unde vel dividendo vel componendo fit
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BO
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-vel+
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CO
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ad
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BO
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ut
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CT
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ad
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BT,
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id eſt
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AC
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ad
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ut
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CP
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ad
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; indeque (
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CPqXAOXSP/ACB
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) æquale eſt
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(
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BQqXACXSP/AOXBC.
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) Minuatur jam in infinitum Figuræ
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RPB
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latitu
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do
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CP,
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ſic ut punctum
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P
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coeat cum puncto
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C,
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punctumque
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S
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cum
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puncto
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B,
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& linea
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SP
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cum linea
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BC,
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lineaque
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SY
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cum linea
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BQ
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;
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& corporis jam recta deſcendentis in linea
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CB
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velocitas fiet ad
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velocitatem corporis centro
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B
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intervallo
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BC
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Circulum deſcribentis,
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in ſubduplicata ratione ipſius (
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BQqXACXSP/AOXBC
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) ad
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SYq,
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hoc eſt (neg
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lectis æqualitatis rationibus
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SP
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ad
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BC
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&
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BQq
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ad
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SYq
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) in ſub
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duplicata ratione
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AC
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ad
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AO
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ſive 1/2
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AB.
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E. D.
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LIBER
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PRIMUS.</
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Corol.
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1. Punctis
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B
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&
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S
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coeuntibus, fit
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TC
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ad
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TS
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ut
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AC
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ad
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AO.
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Corol.
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2. Corpus ad datam a centro diſtantiam in Circulo quo
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vis revolvens, motu ſuo ſurſum verſo aſcendet ad duplam ſuam a
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centro diſtantiam. </
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