Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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pagenum
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64
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ad
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MA
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ut eſt
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MN
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ad
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AB,
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& erecta
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PR
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perpendiculari ad
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AB,
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demiſſaque
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ZR
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perpendiculari ad
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PR
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; erit, ex natura hujus Hy
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perbolæ,
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ZR
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ad
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AZ
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ut eſt
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MN
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ad
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AB.
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Simili diſcurſu punctum
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Z
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locabitur in alia Hyperbola, cujus umbilici ſunt
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A, C
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& princi
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palis axis differentia inter
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AZ
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&
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CZ,
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ducique poteſt
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QS
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ipſi
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AC
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perpendicularis, ad quam ſi ab Hyperbolæ hujus puncto quovis
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Z
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demittatur normalis
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ZS,
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hæc fuerit ad
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AZ
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ut eſt differentia inter
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<
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AZ
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&
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CZ
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ad
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AC.
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Dantur ergo rationes ipſarum
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ZR
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&
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ZS
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<
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ad
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AZ,
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& idcirco datur earun
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<
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dem
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ZR
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&
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ZS
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ratio ad invicem;
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ideoque ſi rectæ
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RP, SQ
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concur
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rant in
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T,
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& agatur
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TZ,
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figura
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TRZS,
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dabitur ſpecie, & recta
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TZ
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in qua punctum
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Z
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alicubi lo
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catur, dabitur poſitione. </
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<
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>Eadem
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methodo per Hyperbolam ter
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tiam, cujus umbilici ſunt
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B
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&
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C
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& axis principalis differentia re
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ctarum
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BZ, CZ,
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inveniri poteſt
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alia recta in qua
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expan
abbr
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pũctum
">punctum</
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Z
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locatur. </
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Habitis autem duobus Locis recti
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lineis, habetur punctum quæſitum
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Z
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in eorum interſectione.
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Q.E.I.
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DE MOTU
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CORPORUM</
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Cas.
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2. Si duæ ex tribus lineis, puta
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AZ
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&
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BZ
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æquantur, pun
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ctum
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Z
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locabitur in perpendiculo biſecante diſtantiam
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AB,
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& lo
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cus alius rectilineus invenietur ut ſupra.
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Q.E.I.
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Cas.
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3. Si omnes tres æquantur, locabitur punctum
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Z
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in centro
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Circuli per puncta
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A, B, C
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tranſeuntis.
<
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Q.E.I.
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<
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>Solvitur etiam hoc Lemma problematicum per Librum Tactio
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num
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Apollonii
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a
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Vieta
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reſtitutum. </
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PROPOSITIO XXI. PROBLEMA XIII.
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Trajectoriam circa datum umbilicum deſcribere, quæ tranſibit per
<
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puncta data & rectas poſitione datas continget.
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<
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>Detur umbilicus
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S,
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punctum
<
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P,
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& tangens
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TR,
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& invenien
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dus ſit umbilicus alter
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H.
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Ad tangentem demitte perpendiculum
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<
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ST,
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& produc idem ad
<
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Y,
<
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"/>
ut ſit
<
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type
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TY
<
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="
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"/>
æqualis
<
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type
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ST,
<
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type
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"/>
& erit
<
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type
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YH
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æ
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qualis axi principali. </
s
>
<
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>Junge
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SP, HP,
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& erit
<
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SP
<
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differentia inter
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<
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HP
<
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& axem principalem. </
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>
<
s
>Hoc modo ſi dentur plures tangen-</
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