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Updated: May 15, 2025
At the age of sixteen he wrote a treatise on conic sections, which was followed by several important discoveries in arithmetic and geometry. His experiments in natural science added to his fame, and he was recognized as one of the most eminent geometricians of modern times.
Speaking generally, society in Germany during the Saxon line of its princes, was always improving. State of Literature during the Saxon Dynasty. "In the school of Paderborn," says the biographer of Meinwert, as he is cited by Schmidt, "there are famous musicians, dialecticians, orators, grammarians, mathematicians, astronomers and geometricians.
I am not addressing geometricians, who are generally indifferent to questions of instinct, nor entomological collectors, who, as such, take no interest in mathematical theorems; I write for any one with sufficient intelligence to enjoy the lessons which the insect teaches. What am I to do?
Practical arithmetic extends further than is usually supposed if you would attain exact precision. There are operations of extreme length in which I have sometimes seen good geometricians lose themselves.
Geometricians have always sought to found their science on the most logical basis possible, and thus have carefully and critically inquired into its foundations. The new geometry which has thus arisen is of two closely related yet distinct forms. One of these is called NON-EUCLIDIAN, because Euclid's axiom of parallels, which we shall presently explain, is ignored.
The geometricians tell us that the figure which has most angles bears the nearest resemblance to that which has no angles at all; so here at Leghorn, where you can hardly find forty men of a mind, dispute and contention grow vain, a comfortable though temporary union takes place, while nature and opinion bend to interest and necessity.
To this man Varro proposed the task of finding the day and hour of Romulus's birth, basing his calculations on the influence which the stars were said to have had upon his life, just as geometricians solve their problems by the analytic method; for it belongs, he argued, to the same science to predict the life of a man from the time of his birth, and to find the date of a man's birth if the incidents of his life are given.
It proved that if a republic fails in unity and centralisation, it is unable to defend a continental nationality. Waves and mountains are the frontiers of the weak men are the frontiers of a people. Let us then have done with geography. It is not geometricians but statesmen who form social constitutions.
No priestly dogmas, invented on purpose to tame and subdue the rebellious reason of mankind, ever shocked common sense more than the doctrine of the infinitive divisibility of extension, with its consequences; as they are pompously displayed by all geometricians and metaphysicians, with a kind of triumph and exultation.
With me the act of contemplation makes the thing contemplated, as the geometricians contemplating describe lines correspondent; but I not describing lines, but simply contemplating, the representative forms of things rise up into existence. And this at once practically and speculatively.
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