Calculating Speed of Geometric Progression - Mechanics

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The discussion centers on the calculation of the speed of a geometric progression as presented in a specific text. The author derives the derivative of the function, noting the use of a minus sign in the expression for speed, which is intended to yield a positive quantity. Participants question whether this negative sign has any significance related to the motion of the particle described in the geometric progression. Additionally, there is a request for a working link to the referenced document, as the original link leads to a "Not Found" error. Understanding the implications of the negative sign in the context of motion is a key focus of the conversation.
LagrangeEuler
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One question. In the text

http://locomat.loria.fr/napier/napier1619construction.pdf

author calculate

##y′_β=−10^7a^t lna##
for
##y_β=10^7a^t##
(see pages 4 and 5)
why minus sign in derivative? ##y_{\beta}'## is speed. And they use minus sign as I see just to obtain positive quantity for ##y′_β=10^7a^t lna##. Is there any relation between that sign and motion of the particle? Particle moves in the some law of geometric progression.
 
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LagrangeEuler said:
http://locomat.loria.fr/napier/napie...nstruction.pdf

This link is not complete. It gives me a "Not Found" error in my Web browser. Could you please post a correct version of it?
 
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