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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 83, page id 1041163592:0117
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PRINCIPLA MATTIEMATICA.
83
ea, e eadem pro radio ordinato primo adhibica, cran(mutetUE A- LIDLE
Dura (per L. em. XXIL) in figuram novam, et tangentes binas quae 2d Pucuvo
radium ordinatum primum concurrebant, jam cradent parallelae. Sun-
eo illae hi ee kI, ik ec hl continences parallelosrammum hikl. Sit-
que p punctum in hac nova figura, puncto in Rgura prima dato
relpondens. Per Agurx centrum O agaeur p9 ee existemte Oq X
quali Op, erit q punctum alterum per quod sectio Conica in hac
figura nova transire debet. Per Lemmatis xxir operationem in-
verlam transteratur hoc punctum in tisuram primam, ee ibi habe.
buntur puncta duo per quae Prajectoria describenda cAt. Per Ca-
dem vero describi porest Prajectoria illa per Prob. XVTI. 9. F.. L.
L. F MI M A XXIII.
Si rectae duae positione datae AC, BD ad data puncta A, B, ter
minentur, datamque habeant rationem ad invicem,  recta
CD, qua puncta indeterminata C, D junsuntur, secetur in ra-
tione data in K: dico quod punctum K locabitur in recta posi
tione data.
Concurrane enim rectae AC.
BD in F, ec in BF capiatur BC
ad AF uC est B D ad AC, SIE-
que F D semper aequalis datx
LC; ee erie ex constructione
FC ad G D, hoc CA, ad F F uE
AC ad BD, adeoque inratione
data, et propterca dabitur specie
criangulum P FC. SCCCTE CF
in L UE SIE CL. ad C F in P2
ne CR ad C D; ex, ob datam il
lam rationem, dabitur etiam specie triangulum P. FL; proindeque
punctum P. locabitur in recta P. L positione data. Junge L. K, ex
similia crune criangula CL R, CF D; X, ob datam P D ee datam
rationem L R ad F D, dabitur L HI. Huic aequalis capiatur P. IL,
eE CrIt semper P L. K II parallelogrammum. Locatur isieur punc-
cum K in parallelogrammi illius latere politione dato LIR. 8. F. D.
N
Ta L MI.