Salusbury, Thomas, Mathematical collections and translations (Tome I), 1667
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              <s>THEOR.
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              XXI.
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              PROP.
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              XXXII.
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              <s>If two points be taken in the Horizon, and any
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              Line ſhould be inclined from one of them to­
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              wards the other, out of which a Right-Line is
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              drawn unto the Inclined Line, cutting off a
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              part thereof equal to that which is included
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              between the points of the Horizon, the De­
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              ſcent along this laſt drawn ſhall be ſooner per­
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              formed, than along any other Right Lines pro­
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              duced from the ſame point unto the ſaid Incli­
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              ned Line. </s>
              <s>And along other Lines which are
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              on each hand of this by equal Angles a De­
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              ſcent ſhall be made in equal Times.</s>
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              In the Horizon let there be two points A and B, and from B incline
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              the Right Line B C, in which from the Term B take B D equal to
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              the ſaid B A, and draw a Line from A to D. </s>
              <s>I ſay, that the De­
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              ſcent along A D is more ſwiftly made, than along any other whatſoever
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              drawn from the point A unto the inclined Line B C. </s>
              <s>For out of the
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              points A and D unto B A and
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              B D draw the Perpendiculars
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              A E and D E, interſecting one
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              another in E: and foraſmuch as
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              in the equicrural Triangle A B D
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              the Angles B A D and B D A
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              are equal, the remainders to the
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              Right-Angles D A E and E D A
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              ſhall be equal. </s>
              <s>Therefore a Circle
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              deſcribed about the Center E at
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              the diſtance A E ſhall alſo paſſe
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              by D; and the Lines B A and
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              B D will touch it in the points A
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              and D. </s>
              <s>And ſince A is the end of the Perpendicular A E, the Deſcent
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              along A D ſhall be ſooner performed, than along any other produced from
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              the ſame Term A unto the Line B C beyond the Circumference of the
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              Circle: Which was firſt to be proved.
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              But if in the Perpendicular A E being prolonged any Center be taken as
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              F, and at the diſtance F A the Circle A G C be deſcribed cutting the
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              Tangent Line in the points G and C; drawing A G and A C they ſhall
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              make equal Angles with the middle Line A D by what hath been afore
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