From the line-pair we pass through an infinity of hyperbolas to the parabola, and thence through an infinity of ellipses to the circle.
It is easily seen that the curves traced by the shadow of the point P arehyperbolas whose convexity is turned toward A B.
H E the summits of the hyperbolas corresponding to the winter and summer solstices.
Consequently, anything coming to the Sun from a great distance must have one exact amount of proper motion to produce a parabola: all other amounts would give hyperbolas or ellipses.
Ellipses and hyperbolas have countless varieties of forms, but there is only one form of parabola; or, to speak literally, all parabolas are similar, while there are infinitely numerous dissimilar ellipses and dissimilar hyperbolas.
When Barrow wrote, quadratures were familiar and differentiation unfamiliar, just as hyperbolas were trusted while logarithms were strange.
Fermat did not use fractional or negative indices, but he regarded his problems as the quadratures of parabolas andhyperbolas of various orders.
The above list will hopefully give you a few useful examples demonstrating the appropriate usage of "hyperbolas" in a variety of sentences. We hope that you will now be able to make sentences using this word.
