bob012345's latest activity

If you define segments ##b##, ##h## and ##a## using the drawing on the right, it has been shown here that...

For Descartes, yes. In post #1 I mentioned this was a variation of Descartes’ original problem. His case is when ##a## is taken as...

I agree wholeheartedly, however one needs to be careful. Writing ##b+1## mixes apples and oranges. Having reached ##h^2=ab##, I would...

In my mind all these quantities are lengths representing pure numbers. We can say ##3=\sqrt{9}## without saying ##9## has different...

I think we need to remember we are talking about geometric constructions here. We can define a line segment as 1 unit then construct...

I had an overnight revelation about this. It should resonate with any person who has been sensitized to the importance of units. Here it...

Regarding the use of the word computer, I think he’s basically correct. Digital devices have exploded everywhere but we don’t call them...

Let D be the point where the perpendicular meets AB. Then: $$\triangle ADC \sim \triangle CDB \implies \frac{h}{b}=\frac{a}{h} $$

Very tactfully put by Descartes! Nicolaus Copernicus in a header page of De Revolutionibus Orbium Coelestium writes somewhat more...

in polar coordinates a circle whose center is on the x-axis is given by the graph ##r=2R \cos \theta## ##r = 2R \cos \theta =...

I would think that Descartes used similar triangles to finish this purely geometric that can be constructed with ruler and straight edge...

I think inventing the geometric construction was the big accomplishment. We are left merely with the pleasure of showing that it works...

Yes, I had that one also and that is why I labeled sides ##h_1## and ##h_2##. However, I dropped it after seeing @renormalize's, more...

From the book I gather Descartes starts with line segment we call ##b## then extends it by ##a## which he takes as 1. His goal is to...

@kuruman's construction can also be solved using Pythagoras on the three right angled triangles: $$\begin{eqnarray} h_1^2&=&b^2+h^2\\...