Salusbury, Thomas, Mathematical collections and translations (Tome I), 1667

Table of figures

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              <s>
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              the leſſer Poligon, exceeding it only the quantity of b B. </s>
              <s>Here
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              then, without the leaſt repugnance the cauſe is ſeen, why the grea­
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              ter Poligon paſſeth or moveth not (being carried by the leſs)
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              with its Sides a greater Line than that paſſed by the leſs; that is,
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              becauſe that one part of each of them falleth upon its next coter­
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              minal and precedent.</s>
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              <s>But if we ſhould conſider the two Circles about the Center A,
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              reſting upon their Parallels, the leſſer touching his in the point B,
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              and the greater his in the
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              point C; here, in begin­
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              ning to make the Revolu­
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              tion of the leſs, it ſhall not
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              occur as before, that the
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              point B reſt for ſome time
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              immoveable, ſo that the
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              Line B C giving back,
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              carry with it the point C,
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              as it befell in the Poligons,
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              which reſting fixed in the
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              point I till that the Side
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              K I falling upon the Line
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              I M, the Line I B carried
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              back B, the term of the
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              Side C B, as far as b, by
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              which means the Side B C
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              fell on b c, ſuper-poſing or
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              reſting the part B b upon
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              the Line B A, and advancing forwards only the part
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              B
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              c, equal to
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              I M, that is to one Side of the leſſer Poligon: by which ſuperpoſi­
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              tions, which are the exceſſes of the greater Sides above the leſs, the
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              advancements which remain equal to the Sides of the leſſer Poli­
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              gon come to compoſe in the whole Revolution the Right-line
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              equal to that traced, and meaſured by the leſſer Poligon. </s>
              <s>But
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              now, I ſay, that if we would apply this ſame diſcourſe to the ef­
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              fect of the Circles, it will be requiſite to confeſs, that whereas the
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              Sides of whatſoever Poligon are comprehended by ſome Number,
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              the Sides of the Circle are infinite; thoſe are quantitative and di­
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              viſible, theſe non-quantitative and Indiviſible: the terms of the
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              Sides of a Poligon in the Revolution ſtand ſtill for ſome time, that
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              is, each ſuch part of the time of an entire Converſion, as it is of
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              the whole Perimeter: in the Circles likewiſe the ſtay oſ the terms
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              of its infinite Sides are momentary, for a Moment is ſuch part of a
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              limited Time, as a Point is of a Line, which containeth infinite of
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              them; the regreſſions made by the Sides of the greater Poligon, are
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              not of the whole Side, but only of its exceſs above the Side of the </s>
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