An inscription in the middle of his book records that Gardner lived at Cockerham in Lancashire in 1787; he was quite probably the Robert Gardner who was baptized in that town in August 1765, making him 21 or 22 when most of the book was written. It looks very much as though he was learning mathematics as part of a practical education to get him into a particular trade: surveying or something closely related. The book itself would have served him as a practical tool, with correctly-worked examples covering a range of different plausible types of situation.
Suppose a Gable end to be measured. Breadth at the Bottom 19 feet 6 inches height to the Square 21 feet 9 inches height above the Square 15 feet 6 inches … NB you must multiply the height to the Square into the Bradth at or below the Square And for that above the Square Multiply the hight into the Breadth at or below the Square or 1/2 the Breadth into the height. Then add the Contents togather ….
These two books show how different geometry could appear – in every sense – from different parts of the social spectrum. Gardner would have gone on to one of the trades: quite likely a surveyor or something in the quantity-surveying line, given his book’s emphasis on calculating the sizes not just of fields but of walls, windows, roofs and floors. Porcher more likely lived a gentry life: we’ve no evidence that he was a gentleman of private means, but working in a trade or craft was quite probably not his destination. So one young man would have put his geometry to practical use, while the other used it as the foundation, perhaps, for further polishing of his mental faculties in reasoning and judgement.
Either way, geometry was an important part of an education that would shape the future course of a life, whether in the form of practical skills or mental discipline. And in both cases it left its traces – very different traces – in the form of copy-books laboriously put together over months or years, so that today we can find out, and see, something about what it meant to learn geometry in Georgian England.