Theodosius <Bithynius>; Clavius, Christoph, Theodosii Tripolitae Sphaericorum libri tres

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        <div xml:id="echoid-div363" type="section" level="1" n="159">
          <p>
            <s xml:id="echoid-s4364" xml:space="preserve">
              <pb o="115" file="127" n="127" rhead=""/>
            ponitur ergo AE, (quæ ſinui DM, arcus grad. </s>
            <s xml:id="echoid-s4365" xml:space="preserve">54. </s>
            <s xml:id="echoid-s4366" xml:space="preserve">æqualis eſt.) </s>
            <s xml:id="echoid-s4367" xml:space="preserve">ex AG, me-
              <lb/>
            dietate ſinus totius, & </s>
            <s xml:id="echoid-s4368" xml:space="preserve">GE, quæ æqualis eſt oſtenſa ſinui CI, arcus grad. </s>
            <s xml:id="echoid-s4369" xml:space="preserve">18.
              <lb/>
            </s>
            <s xml:id="echoid-s4370" xml:space="preserve">Quod eſt primum.</s>
            <s xml:id="echoid-s4371" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4372" xml:space="preserve">IAM vero, quoniam KF, ipſi EG; </s>
            <s xml:id="echoid-s4373" xml:space="preserve">& </s>
            <s xml:id="echoid-s4374" xml:space="preserve">EG, ipſi CI, oſtenſa eſt æqualis:
              <lb/>
            </s>
            <s xml:id="echoid-s4375" xml:space="preserve">erit, KF, ſinui recto CI, æqualis: </s>
            <s xml:id="echoid-s4376" xml:space="preserve">Eſt autem KF, ipſi AK, æqualis. </s>
            <s xml:id="echoid-s4377" xml:space="preserve">Igitur
              <lb/>
            erit quoque AK, ipſi CI, æqualis. </s>
            <s xml:id="echoid-s4378" xml:space="preserve">Cum ergo AK, ſinui LN, ſit æqualis, erit
              <lb/>
              <note position="right" xlink:label="note-127-01" xlink:href="note-127-01a" xml:space="preserve">34. primi.</note>
            etiam ſinus LN, ſinui CI, æqualis. </s>
            <s xml:id="echoid-s4379" xml:space="preserve">Eſt autem CI, ſinus arcus grad. </s>
            <s xml:id="echoid-s4380" xml:space="preserve">18. </s>
            <s xml:id="echoid-s4381" xml:space="preserve">Igitur
              <lb/>
            & </s>
            <s xml:id="echoid-s4382" xml:space="preserve">LN, ſinus erit arcus grad. </s>
            <s xml:id="echoid-s4383" xml:space="preserve">18. </s>
            <s xml:id="echoid-s4384" xml:space="preserve">ac proinde arcus BL, cuius ſinus eſt LN,
              <lb/>
            continebit grad. </s>
            <s xml:id="echoid-s4385" xml:space="preserve">18. </s>
            <s xml:id="echoid-s4386" xml:space="preserve">ideoq́ue eius complementum CL; </s>
            <s xml:id="echoid-s4387" xml:space="preserve">continebit grad. </s>
            <s xml:id="echoid-s4388" xml:space="preserve">72.
              <lb/>
            </s>
            <s xml:id="echoid-s4389" xml:space="preserve">cuius ſinus verſus KC, cõponitur ex CG, medietate ſinus totius, & </s>
            <s xml:id="echoid-s4390" xml:space="preserve">ex GK,
              <lb/>
            quæ ſinui verſo EC, arcus CD, grad. </s>
            <s xml:id="echoid-s4391" xml:space="preserve">36. </s>
            <s xml:id="echoid-s4392" xml:space="preserve">oſtenſa eſt æqualis. </s>
            <s xml:id="echoid-s4393" xml:space="preserve">Quod eſt ſecun-
              <lb/>
            dum. </s>
            <s xml:id="echoid-s4394" xml:space="preserve">Itaque Sinus rectus arcus graduum 54. </s>
            <s xml:id="echoid-s4395" xml:space="preserve">componitur, &</s>
            <s xml:id="echoid-s4396" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4397" xml:space="preserve">Quod erat
              <lb/>
            demonſtrandum.</s>
            <s xml:id="echoid-s4398" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div366" type="section" level="1" n="160">
          <head xml:id="echoid-head186" xml:space="preserve">COROLLARIVM.</head>
          <p>
            <s xml:id="echoid-s4399" xml:space="preserve">CONSTAT cx his, triangulum ACD, cuius baſis CD, ſubtẽdit gradus 36. </s>
            <s xml:id="echoid-s4400" xml:space="preserve">verticemq́;
              <lb/>
            </s>
            <s xml:id="echoid-s4401" xml:space="preserve">habet in centro, eſſe Iſoſceles, cuius vterque æqualium angulorum C, D, reliqui anguli ad
              <lb/>
            centrum duplus eſt. </s>
            <s xml:id="echoid-s4402" xml:space="preserve">Nam angulus CAD, oſtenſus eſt continere {2/5}. </s>
            <s xml:id="echoid-s4403" xml:space="preserve">vnius recti, vtrumque
              <lb/>
            vero C, & </s>
            <s xml:id="echoid-s4404" xml:space="preserve">D, {4/5}.</s>
            <s xml:id="echoid-s4405" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div367" type="section" level="1" n="161">
          <head xml:id="echoid-head187" xml:space="preserve">THEOR. 4. PROPOS. 6.</head>
          <p>
            <s xml:id="echoid-s4406" xml:space="preserve">DIFFERENTIA chordarũ duorum arcuũ
              <lb/>
              <note position="right" xlink:label="note-127-02" xlink:href="note-127-02a" xml:space="preserve">Differentia
                <lb/>
              inter chor-
                <lb/>
              das duorũ
                <lb/>
              arcuũ, quo-
                <lb/>
              rũ alter tá
                <lb/>
              to ſit mi-
                <lb/>
              nor arcu
                <lb/>
              grad. 120.
                <lb/>
              quáto alter
                <lb/>
              maior eſt,
                <lb/>
              ęquat chot
                <lb/>
              dæ arcus,
                <lb/>
              quo alteru-
                <lb/>
              ter dictorũ
                <lb/>
              arcuũ dif-
                <lb/>
              fert ab arcu
                <lb/>
              grad. 120.</note>
            ſemicirculi, quorum alter tãto minor ſit arcu grad.
              <lb/>
            </s>
            <s xml:id="echoid-s4407" xml:space="preserve">120. </s>
            <s xml:id="echoid-s4408" xml:space="preserve">quanto alter maior eſt, æqualis eſt chordæ ar-
              <lb/>
            cus, quo alteruter dictorum arcuum ab arcu grad. </s>
            <s xml:id="echoid-s4409" xml:space="preserve">
              <lb/>
            120. </s>
            <s xml:id="echoid-s4410" xml:space="preserve">differt.</s>
            <s xml:id="echoid-s4411" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4412" xml:space="preserve">IN ſemicirculo ABC, ſit arcus BA, grad. </s>
            <s xml:id="echoid-s4413" xml:space="preserve">120. </s>
            <s xml:id="echoid-s4414" xml:space="preserve">arcus vero BD, eo tan-
              <lb/>
            to minor, quanto arcus BE, maior eſt; </s>
            <s xml:id="echoid-s4415" xml:space="preserve">quorum chordæ BD, BE: </s>
            <s xml:id="echoid-s4416" xml:space="preserve">abſcin-
              <lb/>
            daturq́ue BF, ipſi BD, æqualis, & </s>
            <s xml:id="echoid-s4417" xml:space="preserve">iungantur rectæ AD, AE, AF. </s>
            <s xml:id="echoid-s4418" xml:space="preserve">Dico EF,
              <lb/>
            differentiã duarũ chor
              <lb/>
              <figure xlink:label="fig-127-01" xlink:href="fig-127-01a" number="124">
                <image file="127-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/127-01"/>
              </figure>
            darum BD, BE, æqua-
              <lb/>
            lem eſſe chordæ AE,
              <lb/>
            vel AD. </s>
            <s xml:id="echoid-s4419" xml:space="preserve">Cõpleto enim
              <lb/>
            circulo, & </s>
            <s xml:id="echoid-s4420" xml:space="preserve">inſcriptotriã
              <lb/>
            gulo æquilatero ABG,
              <lb/>
            cuius vnum latus eſt
              <lb/>
            AB, chorda arcus grad.
              <lb/>
            </s>
            <s xml:id="echoid-s4421" xml:space="preserve">120. </s>
            <s xml:id="echoid-s4422" xml:space="preserve">cum ſubtendat ter
              <lb/>
            tiã circunferentiæ par-
              <lb/>
            tem; </s>
            <s xml:id="echoid-s4423" xml:space="preserve">erit angulus AGB,
              <lb/>
            tertia pars duorum re-
              <lb/>
              <note position="right" xlink:label="note-127-03" xlink:href="note-127-03a" xml:space="preserve">32. primi.
                <lb/>
              21. tertij.</note>
            ctorum. </s>
            <s xml:id="echoid-s4424" xml:space="preserve">Cum ergo ei æqualis ſit angulus AEB, in eodem cum illo </s>
          </p>
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