By Albertus W. Grootendorst, M. Bakker

This ebook is an English translation of the 1st textbook on Analytic Geometry, written in Latin by way of the Dutch statesman and mathematician Jan de Witt quickly after Descartes invented the topic. De Witt (1625-1672) is healthier recognized for his paintings in actuarial arithmetic ("Calculation of the Values of Annuities as Proportions of the Rents") and for his contributions to analytic geometry, together with the focus-directrix definition of conics and using the discriminant to differentiate between them. as well as the interpretation and annotations, this quantity includes an advent and observation, together with a dialogue of the function of conics in Greek arithmetic.

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Additional info for Jan de Witt’s Elementa Curvarum Linearum, Liber Primus : Text, Translation, Introduction, and Commentary by Albert W. Grootendorst

Example text

COROLLARY 4. A straight line passing through the endpoint of a transverse diameter parallel to the corresponding second diameter is the tangent to the ellipse at this point and has no other point in common with the ellipse. Theorem XIV. A chord connecting two points on an ellipse and bisected by a diameter either passes through the center or is ordinate-wise applied to this diameter. COROLLARY 1. A diameter in an ellipse that bisects a chord (not passing through the center) will also bisect all chords parallel to that chord.

23): the point A is the origin of an orthogonal coordinate system. ABC is a triangle whose (mutually equal) sides AC and AB lie on the positive x-axis and the positive y-axis, respectively. The hypotenuse BC always moves parallel to itself and drags along a straight line passing through C and parallel to the y-axis. The point B drags along a line segment BK of constant length p, always parallel to the x-axis. A straight line rotates about the origin A and always passes through the moving endpoint of BK.

F H G, E H G anguli ad direClric~m, B Poills. B D interval/flm. B H crlls patiens. B G crNS efficiens. P G linea efficiens. D K deJcri6ens in ftatjone prima, five aefcri/mJJ limpliciter. D Be, DBA anguli mobiles in patione prima. ttiolte prima, live eJJiciens fimpliciter. ue a"gulos mohiles D Be, DBA. THEOREMA Propojitio I. I. lt qurevis recta a quolibct curvre puncro ad ~eflribelltemcffi;' ciellti :equidifians applicata poffit recrangulum, fub in. lure intcr PO/11m& applicatam intercipitur, contentum.

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