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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
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PRINOTPTA MATHEMATICA.
Exempl. T. Si vis centripeca ad singulas Sphaerae particulaS Cen- PRIAVS
dens sic reciproce ur dictantia; pro V Ccribe dictanciam P F; dein
2FSXL D PrO PFg, _ ACE D N uE SF - EY 7
Ponc D N equalem duplo ejus 25F -F D - AF B
ED
LB
: ordinate
pars data 2 SF. ducta in longitudinem B describet aream rectan-
Sulam 2SL. X AB; ec pars indetinita L. D ducta normaliter in
eandem lonsitudinem per motum continuum, ca lese ut inter mo-
vendum crescendo vel decrescendo aequetur semper lonsitudini
E. D, deleribet arcam L. B9 - L a9
t
L IdCC, aream SL X AB; Oux
subducta de area priore 2SL. X AB relinquit arcam SI. X AB.
Pars aurem certia  L 
licer in eandem longitudinem, describet
arcam Hyperbolicam; quae subducta de
area SL. X AB relinquet aream quaesitam
ABNA. Onde talis emergie Proble-
matis constructio. Ad puncta L A, B
erise pervendicula L I, Aa, Bb, quorum
Aa ipS L. B, _ Bb ipA L.  aequetuT.
ACMPEOtIS L. B,L. B, per puncta a b de-
scribatur IIpperbola ab. Et acta chor.
da ba claudet aream ab a arex quaelIEX
ABN A aequalem.
i.
ENempl. 2. Si ris centripeta ad lingulas Sphoerae particulas ten-
dens sic reciproce ut cubus distantia, vel (quod perinde cst) ut cubus
ille applicatus ad planum quodvis datum; seribe  L. cub
2 ASq PrOV.
dein 2F SX L D DrO P F g; _E ACE D N uSL X ASq AS 9
AL BX ASg
2PSXL. D
S
SXF
2et
id eAt (ob continue proportionales PS, S, SF)
D = = SI -AL BXSI
2L. Dg. Si ducaneur hujus partes ereS
in lonsitudinem AB, prima
3b
5I
D Generabie arcam IIyPCr-
2
bolicam;
LTBEL
e+