Origin of scientific 'secular' - meaning long lasting

'Secular', as mplungjan or another good dictionary will tell you, comes from the Latin saecula. There is no perfect translation for this, but 'age' , as in 'spirit of the age' is fairly close.

And that is the cause of the opposite meanings. To an economist or a journalist who is used to thinking of a decade as long enough for entire theories to rise and fall, an age is the longest period imaginable; durable ideas can be age-old and this age is synonymous with 'this world' or 'everything'. But to a theologian, who naturally contrasts 'time' with 'eternity' (hence temporal as both 'time-related' and 'not related to the church') an age is a fleeting moment. Isaac Watts wrote "A thousand ages in Thy sight/ Are as an evening gone"; the mediaeval Dies Irae has the line "Solvit saeclum in favilla", 'he dissolves the age into ashes'. Nineteenth century freethinkers, looking for a term to reflect a philosophy with no belief in eternity, reasonably chose secularism.

It's the other way around

https://google.com/search?q=secular+etymology

http://en.wikipedia.org/wiki/Secularism

The term "secularism" was first used by the British writer George Jacob Holyoake in 1851.[5] Although the term was new, the general notions of freethought on which it was based had existed throughout history. In particular, early secular ideas involving the separation of philosophy and religion can be traced back to Ibn Rushd (Averroes) and the Averroism school of philosophy.[6][7]

In researching the question of scientific 'secular' it appears to have two origins depending on one's own preference which best defines the word as long lasting. The earliest is from John Donne, a poet, lawyer & cleric, from Oxford who in 1629 gave a sermon which in part he said, "If I had a secular glass, a glass that would run an age.., it would not be enough to tell the godly man what his treasure is." The second originated from Pierre-Simon marquis de Laplace in 1801 who... "found the secular equation of the moon to be due to the action of the sun on the moon." Source: Oxford English Dictionary,1989, Vol. XIV, page 849.

I have no proof of this theiry, but it's possible that secular picked up its meaning of "lack of religious significance" because of the word "regular":

http://www.etymonline.com/index.php?term=regular

late 14c., from Old French reguler "ecclesiastical" (Modern French régulier), from Late Latin regularis "containing rules for guidance," from Latin regula "rule," from PIE reg- "move in a straight line" (see regal).

Earliest sense was of religious orders (the opposite of secular). Extended from late 16c. to shapes, etc., that followed predictable or uniform patterns; sense of "normal" is from 1630s; meaning "real, genuine" is from 1821. Old English borrowed Latin regula and nativized it as regol "rule, regulation, canon, law, standard, pattern;" hence regolsticca "ruler" (instrument); regollic (adj.) "canonical, regular."

When "regular" began to mean "appearing repeatedly, on pattern", perhaps that's when people started using "secular" (meaning "appearing only once") to contrast with it. Then "secular", being in contrast with "regular", could have picked up the opposite of the other meaning of "regular" as well.

Or that could be a complete coincidence.