Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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LIBER
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TERTIUS.</
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DE MUNDI
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SYSTEMATE</
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>Quoniam Figura orbis Lunaris ignoratur, hujus vice aſſuma
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mus Ellipſin
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DBCA,
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in cujus centro
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T
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Terra collocetur, & cu
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jus axis major
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DC
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Quadraturis, minor
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AB
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Syzygiis interja
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ceat. </
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>Cum autem planum Ellipſeos hujus motu angulari circa
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Terram revolvatur, & Trajectoria cujus curvaturam conſideramus,
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deſcribi debet in plano quod omni motu angulari omnino deſti
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tuitur: conſideranda erit Figura, quam Luna in Ellipſi illa revol
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vendo deſcribit in hoc plano, hoc eſt Figura
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Cpa,
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cujus puncta
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ſingula
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p
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inveniuntur capiendo punctum quodvis
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P
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in Ellipſi,
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quod locum Lunæ repreſentet, & ducendo
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Tp
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æqualem
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TP,
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ea
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lege ut angulus
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PTp
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æqualis ſit motui apparenti Solis a tem
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pore Quadraturæ
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C
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confecto; vel (quod eodem fere recidit) ut
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angulus
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CTp
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ſit ad angulum
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CTP
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ut tempus revolutio
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nis Synodicæ Lunaris ad tem
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pus revolutionis Periodicæ
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ſeu 29
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d.
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12
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h.
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44′, ad 27
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d.
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7
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h.
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43′. </
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Capiatur igitur angulus
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CTa
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in eadem ratione ad angu
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lum rectum
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CTA,
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& ſit
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longitudo
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Ta
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æqualis lon
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gitudini
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TA
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; & erit
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a
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Apſis ima &
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C
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Apſis ſum
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ma Orbis hujus
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Cpa.
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Ra
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tiones autem ineundo inve
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nio quod differentia inter
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curvaturam Orbis
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Cpa
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in
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vertice
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a,
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& curvaturam Cir
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culi centro
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T
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intervallo
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TA
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deſcripti, ſit ad differentiam
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inter curvaturam Ellipſeos in
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vertice
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A
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& curvaturam ejuſdem Circuli, in duplicata ratione an
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guli
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CTP
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ad angulum
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CTp
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; & quod curvatura Ellipſeos in
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A
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ſit ad curvaturam Circuli illius, in duplicata ratione
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TA
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ad
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TC
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;
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& curvatura Circuli illius ad curvaturam Circuli centro
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T
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in
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tervallo
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TC
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deſcripti, ut
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TC
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ad
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TA
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; hujus autem curvatura ad
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curvaturam Ellipſeos in
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C,
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in duplicata ratione
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TA
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ad
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TC
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; &
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differentia inter curvaturam Ellipſeos in vertice
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C
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& curvaturam
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Circuli noviſſimi, ad differentiam inter curvaturam Figuræ
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Tpa
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in vertice
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C
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& curvaturam ejuſdem Circuli, in duplicata ratione </
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