Salusbury, Thomas, Mathematical collections and translations (Tome I), 1667
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              <s>
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              But the curve-line A C B, is greater than the two right-lines A C,
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              and C B; therefore,
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              à fortiori,
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              the curve-line A C B, is much
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              greater than the right line A B, which was to be
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            <p type="margin">
              <s>
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              The
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              tion of a
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              tick, to prove the
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              right line to be the
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              ſhorteſt of all lines.
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              <s>
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              The Paralogiſm
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              of the ſame
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              tetick, which
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              veth
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              ignotum per
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              ignotius.</s>
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              <s>SALV. </s>
              <s>I do not think that if one ſhould ranſack all the
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              logiſms of the world, there could be found one more commodious
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              than this, to give an example of the moſt ſolemn fallacy of all
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              fallacies, namely, than that which proveth
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              ignotum per ignotius.
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              <s>SIMP. </s>
              <s>How ſo?</s>
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              <s>SALV. </s>
              <s>Do you ask me how ſo? </s>
              <s>The unknown concluſion
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              which you deſire to prove, is it not, that the curved line A C B, is
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              longer than the right line A B; the middle term which is taken
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              for known, is that the curve-line A C B, is greater than the two
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              lines A C and C B, the which are known to be greater than A B;
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              And if it be unknown whether the curve-line be greater than the
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              ſingle right-line A B, ſhall it not be much more unknown whether
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              it be greater than the two right lines A C & C B, which are known
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              to be greater than the ſole line A B, & yet you aſſume it as known?</s>
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              <s>SIMP. </s>
              <s>I do not yet very well perceive wherein lyeth the
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              lacy.</s>
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            <p type="main">
              <s>SALV. </s>
              <s>As the two right lines are greater than A B, (as may be
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              known by
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              Euclid
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              ) and in as much as the curve line is longer than
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              the two right lines A C and B C, ſhall it not not be much greater
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              than the ſole right line A B?</s>
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              <s>SIMP. </s>
              <s>It ſhall ſo.</s>
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            <p type="main">
              <s>SALV. </s>
              <s>That the curve-line A C B, is greater than the right
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              line A B, is the concluſion more known than the middle term,
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              which is, that the ſame curve-line is greater than the two
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              lines A C and C B. </s>
              <s>Now when the middle term is leſs known
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              than the concluſion, it is called a proving
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              ignotum per ignotius.
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              But to return to our purpoſe, it is ſufficient that you know the
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              right line to be the ſhorteſt of all the lines that can be drawn
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              tween two points. </s>
              <s>And as to the principal concluſion, you ſay,
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              that the material ſphere doth not touch the ſphere in one ſole
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              point. </s>
              <s>What then is its contact?</s>
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              <s>SIMP. </s>
              <s>It ſhall be a part of its ſuperficies.</s>
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            <p type="main">
              <s>SALV. </s>
              <s>And the contact likewiſe of another ſphere equal to the
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              firſt, ſhall be alſo a like particle of its ſuperficies?</s>
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            <p type="main">
              <s>SIMP. </s>
              <s>There is no reaſon vvhy it ſhould be othervviſe.</s>
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            <p type="main">
              <s>SALV. </s>
              <s>Then the tvvo ſpheres vvhich touch each other, ſhall
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              touch vvith the tvvo ſame particles of a ſuperficies, for each of them
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              agreeing to one and the ſame plane, they muſt of neceſſity agree
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              in like manner to each other. </s>
              <s>Imagine now that the two ſpheres </s>
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              <s>
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              [
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              in Fig.
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              6.] whoſe centres are A and B, do touch one another:
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              and let their centres be conjoyned by the right line A B, which
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              paſſeth through the contact. </s>
              <s>It paſſeth thorow the point C, and </s>
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