In Gulliver's Travels by Jonathan Swift, how does Gulliver understand that the Lilliputians are excellent mathematicians?

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Gulliver decides that the Lilliputians are good mathematicians because of their ability to accurately calculate his size, clothing needs, and food requirements.  

I would tend to agree with Gulliver because the Lilliputians used only a single instrument and measurement to calculate Gulliver's overall size and calorie intake needs.  The tool that they used was a quadrant, which historically has been used to measure altitude angles of stars.  The mathematicians took a quadrant reading of Gulliver's height, and they compared that to their own height.  The mathematicians determined that the difference was a twelve to one ratio.  From that ratio, they determined that Gulliver's overall body size was 1,724 Lilliputian bodies; therefore, Gulliver needed enough food to feed that many Lilliputian people.  

Some time after, asking a friend at court how they came to fix on that determinate number, he told me that his majesty's mathematicians, having taken the height of my body by the help of a quadrant, and finding it to exceed theirs in the proportion of twelve to one, they concluded from the similarity of their bodies, that mine must contain at least 1724 of theirs, and consequently would require as much food as was necessary to support that number of Lilliputians.

Gulliver is equally amazed at their ability to make him proper clothes by taking rudimentary measurements and calculating everything based on ratios.  

Then they measured my right thumb, and desired no more; for by a mathematical computation, that twice round the thumb is once round the wrist, and so on to the neck and the waist, and by the help of my old shirt, which I displayed on the ground before them for a pattern, they fitted me exactly.

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