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On this page, Harriot outlines the first six problems in
<emph style="it">Apollonius Gallus</emph>
<ref id="Viete_1600a" target="http://www.e-rara.ch/zut/content/pageview/2684195">
(Viete 1600a, Probs 1 to </ref>
. Each problem requires the construction of a circle passing through given points and/or touching given lines or circles. The sketches next to the problem numbers, down the left-hand side of the page, offer a brief summary of each problem. Problem 2, for example, is to describe a circle through two given points touching a given line. On the right-hand side of the page, Harriot attempts to enumerate the different cases, according to the relative positions of points and lines and whether the lines are inclined to each other or parallel. </s>
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Problema I.
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Datis tribus punctis per eadem circulum describere:
oportet autem data puncta non existere tria in eadem linea recta.
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Problema II.
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Datis duobus punctis, & linea recta, per data puncta circulum describere,
quem data linea recta contingat.
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Problema III.
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Datis tribus lineis rectis, describere circulum quem harum unaquæque contingat.
Oportet autem datas lineas rectas non esse parallelas.
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Problema IV.
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Datis duabus lineis rectis, & puncto, per datum punctum circulum describere,
quem datae duae lineae rectae contingat.
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Problema V.
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Dato circulo, & duabus lineis describere circulum quem datus & datae duae lineæ rectæ contingat.
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Problema VI.
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Datis puncto, linea recta, & circulo, per datum punctam describere circulum,
quem data linea recta & datus circulus </s>
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I. Given three points, describe a circle thorugh them;
moreover it must be the case that the three fiven points are not in a straight line.
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II. Given two points and a line, through the given points describe a circle
that touches the given line.
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III. Given three lines, describe a circle that touches each of them.
Moroever it must be the case that the three lines are not parallel.
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IV. Given two lines and point, through the given point describe a circle
that touches the two lines.
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V. Given a curcle and two lines, describe a cricle that touches the given circle and the two lines.
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VI. Given a point, a line, and a circle, through the given point describe a circle
that touches the given line and the given circle.</s>
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It is very difficult to transcribe this page in a meaningful way,
and the reader is strongly advised to examine the layout of the original.</s>
