Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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Corol.
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1. Eſt igitur
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Rr
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æqualis (
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DRXAB
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/N)-(
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RDGT
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/N), ideoque
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ſi producatur
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RT
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ad
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X
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ut ſit
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RX
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æqualis (
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DRXAB
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/N), (id eſt, ſi
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compleatur parallelogrammum
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ACPY,
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jungatur
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DY
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ſecans
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CP
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in
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Z,
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& producatur
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RT
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donec occurrat
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DY
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in
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X
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;) erit
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Xr
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æqua
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lis (
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RDGT
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/N), & propterea tempori proportionalis. </
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LIBER
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SECUNDUS.</
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Corol.
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2. Unde ſi capiantur innumeræ
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CR
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vel, quod perinde eſt,
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innumeræ Z
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X,
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in progreſſione Geometrica; erunt totidem
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Xr
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in
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progreſſione Arithmetica. </
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<
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>Et hinc Curva
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DraF
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per tabulam Lo
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garithmorum facile delineatur. </
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Corol.
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3. Si vertice
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D,
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diametro
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DE
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deorſum producta, & La
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tere recto quod ſit ad 2
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DP
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ut reſiſtentia tota, ipſo motus initio,
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ad vim gravitatis, Parabola conſtruatur: velocitas quacum corpus
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exire debet de loco
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D
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ſecundum rectam
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DP,
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ut in Medio uNI
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formi reſiſtente deſcribat Curvam
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DraF,
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ea ipſa erit quacum ex
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ire debet de eodem loco
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D,
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ſecundum eandem rectam
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DP,
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ut
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in ſpatio non reſiſtente deſcribat Parabolam. </
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<
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>Nam Latus re
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ctum Parabolæ hujus, ipſo motus initio, eſt (
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DVquad./Vr
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) &
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Vr
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eſt (
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tGT
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/N) ſeu (
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DRXTt
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/2N). Recta autem quæ, ſi duceretur, Hy
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perbolam
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GTB
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tangeret in
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G,
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parallela eſt ipſi
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DK,
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ideoque
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Tt
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eſt (
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CKXDR/DC
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) & N erat (
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QBXDC/CP
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). Et propterea
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Vr
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eſt
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(
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DRqXCKXCP/2DCqXQB
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), id eſt, (ob proportionales
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DR
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&
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DC, DV
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&
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DP
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) (
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DVqXCKXCP/2DPqXQB
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), & Latus rectum (
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DVquad./Vr
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) prodit
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(2
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DPqXQB/CKXCP
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), id eſt (ob proportionales
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QB
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&
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CK, DA
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&
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AC
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)
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(2
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DPqXDA/ACXCP
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), adeoque ad 2
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DP,
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ut
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DPXDA
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ad
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CPXAC
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; hoc
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eſt, ut reſiſtentia ad gravitatem.
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Q.E.D.
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Corol.
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4. Unde ſi corpus de loco quovis
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D,
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data cum velocitate,
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ſecundum rectam quamvis poſitione datam
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DP
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projiciatur; & re
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ſiſtentia Medii ipſo motus initio detur: inveniri poteſt Curva
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<
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DraF,
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quam corpus idem deſcribet. </
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<
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