Harriot, Thomas, Mss. 6784

List of thumbnails

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611
611 (306) 		612
612 (306v)
613
613 (307) 		614
614 (307v)
615
615 (308) 		616
616 (308v)
617
617 (309) 		618
618 (309v)
619
619 (310) 		620
620 (310v)
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              <s xml:space="preserve">[
                <emph style="bf">Commentary:</emph>
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            <p>
              <s xml:space="preserve"> On this page Harriot investigates Proposition 17 from
                <emph style="it">Supplementum geometriæ</emph>
                <ref id="Viete_1593c" target="http://www.e-rara.ch/zut/content/pageview/2684119"> (Viète 1593c, Prop </ref>
              . </s>
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              <quote xml:lang="lat">
                <s xml:space="preserve"> Proposition XVII.
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                Si duo triangula fuerint aequicrura singula, & ipsa alterumalteria cruribus aequalia, angulus autem, quem is qui est ad basin secundi relinquit e duobus rectis, sit triplus anguli qui est ad basin primi: solidum triplum sub base primi & cruris communis quadrato, minus cubo e base primi, aequale est solido sub base secundi & cruris communis </s>
              </quote>
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              <quote>
                <s xml:space="preserve"> If two triangles are each isosceles, both with equal legs, and moreover the angle at the base of the second subtracted from two right angles is three times the angle at the base of the first, then three times the product of the base of the first and the square of the common side, minus the cube of the first base, is equal to the product of the second base and the square of the common </s>
              </quote>
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              <s xml:space="preserve"> The working contains reference to three propositions from Euclid's
                <emph style="it">Elements</emph>
              . </s>
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              <quote>
                <s xml:space="preserve">
                  <ref target="http://aleph0.clarku.edu/~djoyce/java/elements/bookII/propII6.html"/>
                If a straight line be bisected and produced to any point, the rectangle contained by the whole line so increased, and the part produced, together with the square of half the line, is equal to the square of the line made up of the half, and the produced part. </s>
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              <quote>
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                  <ref target="http://aleph0.clarku.edu/~djoyce/java/elements/bookIII/propIII36.html"/>
                If from a point outside a circle two straight lines be drawn to it, one of which is a tangent to the circle, and the other cuts it; the rectangle under the whole cutting line and the external segment is equal to the square of the tangent. </s>
              </quote>
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              <quote>
                <s xml:space="preserve">
                  <ref target="http://aleph0.clarku.edu/~djoyce/java/elements/bookI/propI47.html"/>
                In a right-angled triangle, the square on the side opposite the right angle is equal to the sum of the squares on the sides containing the right angle. </s>
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              <s xml:space="preserve">]</s>
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          <head xml:space="preserve"> prop. 17.
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          [
            <emph style="bf">Translation: </emph>
          Proposition 17 from the ]</head>
          <p xml:lang="lat">
            <s xml:space="preserve"> Si duo triangula fuerint aequicrura singula,
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            et ipsa alterumalteria cruribus aequalia; angulus
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            autem, quem is qui est ad basin secundi relinquit
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            e duobus rectis, sit triplus anguli qui est ad basin
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              <emph style="st">secundi</emph>
              <emph style="super">primi</emph>
            . Solidum triplum sub base primi et cruris
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            communis quadrato, minus cubo e base primi: aequale
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            est solido sub base secundiet cruris communis
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            [
              <emph style="bf">Translation: </emph>
            If two triangles are each isosceles, the legs of one equal to the legs of the other, and moreover the angle at the base of the second is three times the angle at the base of the first, then the cube of the first base, minus three times the product of the base of the first and the square of the common side, is equal to the product of the second base and the square of the same side.</s>
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          <p xml:lang="lat">
            <s xml:space="preserve"> per 6,2 el.
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            per 36,3 el.
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            per 47,1 el.
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            […]
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            quia parallogramma æquialta
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            et sunt ut bases.
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            […]
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            vel per notas
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            simplices
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            Hæque Resoluatur Analogia, erit:
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              <lb/>
            [
              <emph style="bf">Translation: </emph>
            by Elements II.6
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            by Elements III.35
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            by Elements I.47
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            because the parallelograms are of equal height and are as the bases.
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            or in simple notation
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            And this ratio is resolved, hence the ]</s>
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Impressum