By Albert W. Grootendorst à , Jan Aarts (auth.), Albert W. Grootendorst, Jan Aarts, Miente Bakker, Reinie Erné (eds.)

- Following on from the 2000 version of Jan De Witt’s Elementa Curvarum Linearum, Liber Primus, this publication offers the accompanying translation of the second one quantity of Elementa Curvarum Linearum (Foundations of Curved Lines). one of many first books to be released on Analytic Geometry, it used to be initially written in Latin by way of the Dutch statesman and mathematician Jan de Witt, quickly after Descartes’ invention of the topic.

- Born in 1625, Jan de Witt served with contrast as Grand Pensionary of Holland for a lot of his grownup lifestyles. In arithmetic, he's most sensible identified for his paintings in actuarial arithmetic in addition to large contributions to analytic geometry.

- Elementa Curvarum Linearum, Liber Secondus strikes ahead from the development of the commonplace conic sections lined within the Liber Primus, with a dialogue of difficulties hooked up with their type; given an equation, it covers how you can get well the normal shape, and also how you can locate the equation's geometric homes.

- This quantity, started by way of Albert Grootendorst (1924-2004) and accomplished after his loss of life through Jan Aarts, Reinie Erné and Miente Bakker, is supplemented by:

- annotation explaining finer issues of the translation;

- broad remark at the mathematics

those positive factors make the paintings of Jan de Witt largely obtainable to today’s mathematicians.

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Additional resources for Jan de Witt’s Elementa Curvarum Linearum: Liber Secundus

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In an obvious way this gives rise to the new forms. For example the form a2 x2 + b2 y2 =1 gives rise to a 2 x 2 + b 2 z 2 = 1, a 2 v 2 + b 2 y 2 = 1 , and a 2 v 2 + b 2 z 2 = 1, where z and v are as above. The form xy = c gives rise to xz = c, vy = c and vz = c, but in this case Jan de Witt restricts himself to z = y + h and v = x + k. The third Regula Universalis states that the general quadratic equation in two variables can be reduced to one of the forms in (ii)−(iv) or to one of the forms deduced from these as above.

The length 2d of the conjugate diameter then follows from the definition of the latus rectum using the proportion 2 f : 2d = 2d : p . In our further explanation and proof of the correctness of the construction we restrict ourselves to the second equation that was mentioned; Jan de Witt of course treats both equations. The point B on the curve is chosen as the intersection point of the curve with the line through B that makes the given angle with the abscissa-axis AE. Jan de Witt now refers to the characteristic property of the hyperbola that he mentioned in Liber Primus as Theorem IX, Proposition 10, p.

Z 2 = dx • f 2 , where z = y ± (bx / a) Again one chooses AM as in Case V, but next one draws the lines FL through the points F and L (see II and IV for the definitions). These lines meet the lines AM at the points N. The following cases are distinguished with respect to the position of the parabola: 1. z 2 = dx + f 2 and z = y + (bx / a) – the line AM with equation y = −(bx / a) is the transverse axis, the corresponding vertex N has abscissa AF = − f 2 / d 2. z 2 = dx − f 2 and z = y + (bx / a) – the line AM with equation y = −(bx / a) is the transverse axis, the corresponding vertex N has abscissa AF = f 2 / d 3.

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