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Sir, I have found you an argument. I am not obliged to find you an understanding.
J. Boswell, The Life of Samuel Johnson, 1784.
Learning Geometry in Georgian England
Robert Gardner's 'Book of Accompts'
Robert Gardner compiled what he called his ‘Book of Accompts’ during the 1780s, in Lancashire. It covered a period in his mathematical education when he was doing some advanced arithmetic and also – despite the title – learning some geometry. It was a larger book than Thomas Porcher’s – nearly a foot tall, giving lots of room on the page for diagrams and illustrations – but a slimmer one: just fifty pages or so.
The geometrical parts were thoroughly practical in character.
(We’ll come back to that slightly surprising Westmoreland rood.)
Other topics were measuring pavements, measuring boards and boarded floors, and measuring land. There was a section, for instance, devoted to measuring trapezoidal pieces of land: presumably a response to the shape of local fields.
Figure 5. Robert Gardner’s trapezoidal field
The geometric and trigonometrical problems to be solved were not always very far removed from what we saw in Thomas Porcher’s case. But Gardner solved his problems by pre-learned rules, and was unconcerned with such abstractions as theorems and proofs. His questions demanded not elegant methods but practicable answers, and space was given to such minutiae as the different systems of measurement one might come across:
Figure 6. Robert Gardner measures ceilings and paintwork.
Wardhaugh, Benjamin, "Learning Geometry in Georgian England," Loci (August 2012), DOI: 10.4169/loci003930