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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 75, page id 1041163592:0109
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d
F Puncts aaeS JaISC MIa GMLVIo A, D, C, Cc circum duo eorum
B, C ceu polos, rotando angulos magnitudine datos Abl.
ACB, applicenEur CFU-
ra B A. C. Aprimo ad
punctum D, deinde
2d punctum P, ec no-
centur puncta N, N in
quibus altera crura
BL, CF casu utroque
SC decuManE. AGatUE
recta infinita NN, e
rotentur anguliillimo
biles circum polos suos
B, C, ca lege ut cru-
rum BL, CF vel
BMI, C M intersectio
quae jam sic m incidae
semper in rectam illam
intinitam M N ec cru-
rum B A, C A, vel BD, CD interlectio, quae jam Sit a Trajecto-
riam quaesitam P AD aB delincabit. Nam punctum a, per Lem.
XXF, continget sectionem Conicam per puncta B, C transeuntem; ee
ubi punctum m accedit ad puncta L. M, N, punctum d (Per con-
Aructionem) accedet ad puncta , D, P. Delcribetur itaque sec.
tio Conica transiens per puncta quinque , B, C3 P, D. Q. F. P.
Corol. 2. Hlinc recta expedite duci porest qux Trajectoriam quae
litam, in puncto quoris dato B, continset. Accedat punctum a ad
punctum B, de recta B d cradet tangens quaesIta.
Corol. 2. Inde etiam Trajectoriarum Cenera, Diametri de Latera
recta inveniri poltunt, ut in Corollario secundo Lemmatis XIX.
Scholium.
Constructio prior cradet paulo simplicior junsendo B P, ec in cas
S opus cA, producta capiendo Bp ad B P uc CA P R ad P T; e
per p asendo rectam intinitam p d ipsi S P F Parallelam, inque ca
capiendo semper pd aequalem Pr; ec agendo rectas Bd, Cr con-
currences in d. Nam cum SInE P r ad PF, F R ad PT, pB adZB,
ed 2d PF in eadem ratione: CrUnE P et Dr semiper aqua-
1C5.
PRINCIPTA MATHEMATICA.
Idem aliter.
LIBER
PRrUVS