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Euclid Looked On Beauty Bare

I am amateur geometer with an interest in tangent line constructions using a compass and straightedge only. There are many well known tangent line constructions for the conic sections, but I have found it is also possible to construct true tangent lines for a certain set of cubic and quartic curves.

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Reading of poem on youtube:

The opinions of two notable thinkers from the first half of 19th century...

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In this 30 minute video (link below), Dr. Laura Kotevska discusses how Euclid's geometry was regarded during the renaissance.

quotation from video:

  • ... scholars and practitioners of mathematics advocated a knowledge of mathematics for the extra-mathematical value it possessed. That is the value of math lay outside what it is that mathematics taught us in mathematical terms. Its value was in what it taught us about ourselves as beings of reason. ... More precisely early modern practitioners ascribed The Elements a role in cultivating a slew of intellectual virtues. Euclid’s mathematics could train a love of truth, attentiveness, the habits of being governed by reason, and among others epistemic humility. For Antoine Arnauld ... geometry could accustom an individual to the love of truth and to taste it and his words to ‘feel its beauty’. On his view there was no study more appropriate than geometry to help practitioners to discern truth from falsity and encourage a firm grasp of what one knows. Crucial to this apprehension of difficult truths was attentiveness. Only by being attentive could an early modern agent be certain about the knowledge they were in pursuit of acquiring. There are philosophical reasons for this being their view but what it boils down to is the idea that without paying attention it would be impossible to have any certainty about the knowledge of the world that one was in pursuit of. For the renaissance and early modern thinker strict attention to thoughts and judgments could inoculate an individual from assenting to obscure and uncertain principles or failing prey to skepticism. Now why is this? On their view by being attentive ‘one would not be mislead by false glimmers when one does not pay enough attention.’ Geometry was best at training attentiveness many thought since it required following complex trains of reasoning and drawing conclusions on the basis of these.
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