Useful And Fantastic: A Goldfield Schoolmaster - 2
Inspectors who visited the school run by Mr McCombe in Australia in the early years of the 19th Century were astonished by what they discovered there.
Val Yule continues the story of a schoolmaster with very special talents.
Some months later, the five other local teachers asked Brennan if they could accompany him on a visit to McCombe's school. Harrison was especially curious, saying that he “heard McCombe was conceited, and concealed his ignorance by keeping to himself.” Brennan replied that “he appeared to me a perfect gentleman, who had very little to say.”
“Does he know anything of mathematics?” queried Harrison.
“I do not know further than this - that all his flower-beds are geometrical figures.”
Mr McCombe was teaching Latin to his six pupils in the Academy, and after a formal introduction, Brennan intimated that teacher Harrison was a great geometrician. Mr McCombe surveyed him closely and said, “Rara avis in terris nigroque simillima cygno. This line from Juvenal would apply to Mr Harrison were it not that all swans in this country are black.”
Mr Harrison picked up an Eton Latin Grammar and asked the smallest pupil to read a sentence that he pointed out, and then to translate it, which the boy did. “The road to good manners is never too late.”
“Does that assist you in grammar?”
“Yes, sir, it is a part of syntax, and shows that a clause of a sentence may be a nominative case.”
“Where is the clause of that sentence?”
“The way to good manners, sir, is the clause.”
Harrison asked why McCombe taught on Saturdays. McCombe replied that he loved teaching, and Saturdays were the only days when he could give his whole time to his advanced students, whom he was preparing for matriculation with mathematics, classics and the rudiments of science.
Harrison asked if he could ask the pupils some questions in Geometry.
“Certainly, it will doubtless benefit them to be examined by a strange teacher, particularly by one of your high mathematical attainments.”
“Well, then,” said Mr Harrison, “I shall ask the Chinese girl to stand at the blackboard.”
“This child,” interposed Mr McCombe, “is Miss Lee, and I shall be pleased if you address her as such.”
“Well, Miss Lee,” said Harrison, and asked her what was the forty-seventh proposition in the first book of Euclid.
“It is a theorem as distinguished from a problem and its enunciation. In any right-angled triangle, the square described on the side subtending the right angle is equal to the squares described on the sides containing it.”
“Prove it,” said Harrison.
Miss Lee took the chalk and “in a masterly style demonstrated the proposition without using letters, which gained for her the plaudits of the other teachers.''
McCombe asked Harrison to question Miss Lee on the properties of this great proposition. Mr Harrison could not think of any at the present, but teacher Tierney interposed, “Give her the question that we have discussed so long and failed to solve. The question is, in a square, we will assume that the excess of the diagonal above the side is five, or any number, to find the side.”
“I can do it,” returned Miss Lee. “It is an easy quadratic.”
She took the chalk, described a square, drew the diagonal, cut off the excess, which represented five. “Let x equal the side, then x plus 5 will be the diagonal, as the squares of both sides are equal to the square of the diagonal by the forty-seventh proposition; hence we have the equation, 2x squared = (x+5) squared,” which she solved in a few seconds, to the amazement of the teachers.
“To whom are we indebted for this famous proposition?''
“Pythagoras, sir, who offered a hecatomb, or one hundred oxen, as a sacrifice to the Gods of Egypt, on the wonderful discovery. Its importance is said to be of great value in the higher mathematics, involving trigonometry, as all triangles can be reduced to right-angled triangles.''
"Mr Harrison admitted he had thought Mr McCombe knew nothing of mathematics, and was surprised.
“Then,” said Mr McCombe, “you have been misinformed. I have spent many years under the best professors in Great Britain in acquiring a knowledge of the classics and higher mathematics, including conic sections, physics, etc. I presume you are not aware that I am Master of Arts of the Dublin University, or as it is best known, Trinity College.”
Mr Harrison asked for proof. “I could say that I am M.A. of Oxford or Cambridge, and you could not disprove it.”
When McCombe referred Harrison to Professor Woolley of the Sydney University for “irrefragible proof of what I assert,” Harrison had to apologise, and turned to McCombe’s mode of teaching instead.
“I may tell you,” said Mr McCombe, now somewhat excited, “that my system of teaching is altogether different from yours. I teach the pupils principally by lectures on the blackboard, and explain their lessons simply and fully. I also deliver numerous brief lectures to my advanced pupils on all important events, remarkable men of Great Britain and elsewhere, on natural history, natural philosophy, and get them to note in their lecture-books all matters of special interest or importance."
The teachers inspected the school, which was well furnished with desks, maps, blackboards, a terrestrial globe, biological charts, etc. Mr McCombe produced his Latin testamur as proof of his being M.A. The document was vellum, and bore the University seal of Trinity College, Dublin. The masters examined the seal and signatures. Mr McCombe enlightened them by translating the contents. In looking over the lecture-books, the teachers found many extracts of interest, relating to warriors, poets, orators, etc. and one in Miss Lee’s book, under the heading the “Great Tribune”.
“That portly form arrayed in olive green,
That head, on which a scratch peruke is seen;
That countenance of true Milesian mould
Oft waxing warm, but never calmly cold;
And lineaments that forcibly attest
The character in which he stands confess’d.''