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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 446, page id 1041163592:0480
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PHTLOSOPHLA NATVRALIS
L E MI M A V.
Trvenire lineam curvam generis Parabolici, quae per data
quotcunque puncta transibit.
Sunto puHcCa AIIa , B, C, D, E, F, ecc. e ab iisdem ad rectam
quamris positione datam fTN demitre perpendicula quoccunque
AL BB CR, DE EM, FN.
Cas. T. Si punctorum F, F, K, L, M, N aequalia sunE inter-
valla IB IK, KL, _c. collige perpendiculorum AFI, BL
CK, dec. ditterentias primas b, 2b, 3b, 4b, 5b, ecc. Cccundas c, 26.
3C34C, _C. tertias d, 2d, 3d, ecc. id cA, ita ut AE AII - BY =- b
BF-CK = 2b, CK DL. = 36, DL + F M = 4b, = FM + FN = 5b.
_c. dein b - 2b = c, _C.
de sic persatur ad disse-
rentiam ulcimam quae hic
est f. Deinde crecta qua-
cunque perpendiculari
RS, quae fuerit ordina-
tim applicaca ad curram
quaelitam: ut inveniaeur
hujus longitudo, Done
incervalla AI, TK, RL,
L. M, _cC. unitates eAC,
ec dic ATI = a, TIS = p.
2p in - 15 = g, 39 in
ad usque penultimum perpendiculum ML, ec praeponendo signa
negatira terminis FTS, I5, etc. qui jacent ad partes puncti Sver-
TuS A. et hona afirmatira terminis SR, SF, _C. qui jacene
ad alceras partes puncti S. Et sienis probe obserratis, Cxit
RS = a + bp + cg + dr + e5 +ft, ecc.
Cas. 2. Ouod s punctorum LL, T, K, L, ecc. inaequalia sinE inter
valla TTL, TK, ecc collise perpendiculorum AH, BI, CK, &c.
differentias primas per incerralla perpendiculorum divitas b, 2b)
3b, 4b, 5b; sccundas per interralla bina dirilaS C, 26, 363 46, _c.
cerrias per incerralla cerna diritas dn 2d3 3 c _C. QuartaS Per
inter-
.C
1dc
DE NONDK
YBTEMATE
FSR = r, Zr in F SF = 5, Z5 in + SM = +; pergendo videlicet