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Page 365 - As soon as I understood the principles, I relinquished for ever the pursuit of the mathematics; nor can I lament that I desisted, before my mind was hardened by the habit of rigid demonstration, so destructive of the finer feelings of moral evidence, which must, however, determine the actions and opinions of our lives.
Page 461 - Simple cases of the construction of circles from sufficient data. Construction of a fourth proportional to three given straight lines and a mean proportional to two given straight lines. Construction of regular figures of 3, 4, 6 or 8 sides in or about a given circle. Construction of a square equal in area to a given polygon. SCHEDULE B Angles at a Point If a straight line stands on another straight line, the sum of the two angles so formed is equal to two right angles ; and the converse.
Page 461 - Any proof of a proposition shall be accepted which appears to the examiners to form part of a systematic treatment of the subject...
Page 364 - It was now a long time, says Baillet, since he had been convinced of the small utility of the mathematics, especially when studied on their own account, and not applied to other things. There was nothing, in truth, which appeared to him more futile than to occupy ourselves with simple numbers and imaginary figures, as if it were proper to confine ourselves to these trifles (bagatelles) without carrying our view beyond.
Page 461 - Geometry will be set on the constructions contained in the annexed Schedule A, together with easy extensions of them. In cases where the validity of a construction is not obvious, the reasoning by which it is justified may be required.
Page 365 - ... of all reasoning, it must of course enable us to correct this the most dangerous and prevalent of our intellectual failings. But, among all our rational pursuits, mathematics stand distinguished, not merely as affording us no aid toward alleviating the evil, but as actually inflaming the disease. The mathematician, as already noticed, is exclusively engrossed with the deduction of inevitable conclusions, from data passively received ; while the cultivators of the other departments of knowledge,...
Page 470 - The study of foreign systems is also having a great influence on the present discussion. The continual stream of young men to German universities, the extensive study of European schools on the part of our educational leaders, the critical studies of curricula from all parts of the world that...
Page 446 - Geschäft, das Nachdenken erfordert, wenn es nicht unmittelbar durch jene leichte Verbindung von Zeichen geschehen kann, die mehr das Werk der Routine, als des Denkens sind.
Page 364 - In a letter to Mersenne, written in 1630, M. Descartes recalled to him that he had renounced the study of mathematics for many years: and that he was anxious not to lose any more of his time in the barren operations of geometry and arithmetic, studies which never lead to anything important.
Page 461 - Bisection of angles and of straight lines. Construction of perpendiculars to straight lines. Construction of an angle equal to a given angle. Construction of parallels to a given straight line. Simple cases of the construction from sufficient data of triangles and quadrilaterals. Division of straight lines into a given number of equal parts or into parts in any given proportions. Construction of a triangle equal in area to a given polygon. Construction of tangents to a circle and of common tangents...