Sangaku Problems About Ellipses: Why Primary Sources Matter.

Its base has length HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mfrac><mi>a</mi><mi>v</mi></mfrac><msqrt><mrow><msup><mi>r</mi><mn>2</mn></msup><mo>-</mo><msup><mi>v</mi><mn>2</mn></msup></mrow></msqrt></mrow></math> ht . By similar triangles, HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mfrac><mi>h</mi><mi>u</mi></mfrac><mo>=</mo><mfrac><mi>k</mi><mi>v</mi></mfrac></mrow></math> ht . The images of segments orthogonal to the major axis, like HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math> ht and HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> ht , do not change length. In Figure 5, left, HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="italic">AC</mi></mrow></math> ht is the polar of the point at infinity on HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="italic">BD</mi></mrow></math> ht , and vice versa. [Extracted from the article]