Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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gentes alias quaſvis duas
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GCD, FDE
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in
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L
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&
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K.
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Per harum
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tangentium non parallelarum
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CL, FK
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cum parallelis
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CF, KL
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concurſus
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C
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&
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K, F
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&
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L
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age
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CK, FL
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concurrentes in
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R,
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& rec
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ta
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OR
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ducta & producta ſecabit tangentes parallelas
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CF, KL
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in
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punctis contactuum. </
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<
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>Patet hoc per Corol. </
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<
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>2. Lem. </
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<
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>XXIV. </
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>Ea
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dem methodo invenire licet alia contactuum puncta, & tum de
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mum per Probl. </
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<
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>XIV. &c. </
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<
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>Trajectoriam deſcribere.
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q.E.F.
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LIBER
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PRIMUS.</
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Scholium.
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<
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>Problemata, ubi dantur Trajectoriarum vel centra vel Aſymp
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toti, includuntnr in præcedentibus. </
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<
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>Nam datis punctis & tangen
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tibus una cum centro, dantur alia totidem puncta aliæque tangen
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tes a centro ex altera ejus parte æqualiter diſtantes. </
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<
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>Aſymptotos
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autem pro tangente habenda eſt, & ejus terminus infinite diſtans
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(ſi ita loqui fas ſit) pro puncto contactus. </
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<
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>Concipe tangentis cu
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juſvis punctum contactus abire in infinitum, & tangens vertetur in
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Aſymptoton, atque conſtructiones Problematis XIV & Caſus pri
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mi Problematis XV vertentur in conſtructiones Problematum ubi
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Aſymptoti dantur. </
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<
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>Poſtquam Trajectoria deſcripta eſt, invenire licet axes & umbi
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licos ejus hac methodo. </
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<
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>In conſtructione & figura Lemmatis XXI,
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fac ut angulorum mobi
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lium
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PBN, PCN
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cru
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ra
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BP, CP,
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quorum
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concurſu Trajectoria de
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ſcribebatur, ſint ſibi invi
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cem parallela, eumque
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ſervantia ſitum revolvan
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tur circa polos ſuos
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B, C
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in figura illa. </
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<
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>Interea ve
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ro deſcribant altera an
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gulorum illorum crura
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CN, BN,
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concurſu
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ſuo
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K
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vel
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k,
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Circulum
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IBKGC.
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Sit Circuli
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hujus centrum
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O.
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Ab
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hoc centro ad Regulam
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MN,
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ad quam altera illa crura
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CN, BN
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interea concurrebant </
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