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

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          <p>
            <s xml:id="echoid-s5156" xml:space="preserve">
              <pb o="126" file="138" n="138" rhead=""/>
            indagauimus ſinum rectum grad. </s>
            <s xml:id="echoid-s5157" xml:space="preserve">12. </s>
            <s xml:id="echoid-s5158" xml:space="preserve">qui dimidium eſt chordæ arcus grad. </s>
            <s xml:id="echoid-s5159" xml:space="preserve">24.
              <lb/>
            </s>
            <s xml:id="echoid-s5160" xml:space="preserve">quo dicti arcus grad. </s>
            <s xml:id="echoid-s5161" xml:space="preserve">30. </s>
            <s xml:id="echoid-s5162" xml:space="preserve">& </s>
            <s xml:id="echoid-s5163" xml:space="preserve">54. </s>
            <s xml:id="echoid-s5164" xml:space="preserve">inter ſe differunt: </s>
            <s xml:id="echoid-s5165" xml:space="preserve">ita quoque ex ſinubus rectis
              <lb/>
              <note position="left" xlink:label="note-138-01" xlink:href="note-138-01a" xml:space="preserve">Supputatio
                <lb/>
              ſinus grad.
                <lb/>
              26. & grad.
                <lb/>
              64.</note>
            arcus Min. </s>
            <s xml:id="echoid-s5166" xml:space="preserve">30. </s>
            <s xml:id="echoid-s5167" xml:space="preserve">& </s>
            <s xml:id="echoid-s5168" xml:space="preserve">arcus grad. </s>
            <s xml:id="echoid-s5169" xml:space="preserve">52. </s>
            <s xml:id="echoid-s5170" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s5171" xml:space="preserve">30. </s>
            <s xml:id="echoid-s5172" xml:space="preserve">cognitis cognoſeemus ſinum rectum
              <lb/>
            grad. </s>
            <s xml:id="echoid-s5173" xml:space="preserve">26. </s>
            <s xml:id="echoid-s5174" xml:space="preserve">qui dimidium eſt chordæ arcus grad. </s>
            <s xml:id="echoid-s5175" xml:space="preserve">52. </s>
            <s xml:id="echoid-s5176" xml:space="preserve">quo dicti arcus Min. </s>
            <s xml:id="echoid-s5177" xml:space="preserve">30. </s>
            <s xml:id="echoid-s5178" xml:space="preserve">& </s>
            <s xml:id="echoid-s5179" xml:space="preserve">
              <lb/>
            grad. </s>
            <s xml:id="echoid-s5180" xml:space="preserve">52. </s>
            <s xml:id="echoid-s5181" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s5182" xml:space="preserve">30. </s>
            <s xml:id="echoid-s5183" xml:space="preserve">inter ſe differunt, vt ſupra oſtendimus; </s>
            <s xml:id="echoid-s5184" xml:space="preserve">atque ex ſinu grad. </s>
            <s xml:id="echoid-s5185" xml:space="preserve">26.
              <lb/>
            </s>
            <s xml:id="echoid-s5186" xml:space="preserve">ſiet, per propof. </s>
            <s xml:id="echoid-s5187" xml:space="preserve">3. </s>
            <s xml:id="echoid-s5188" xml:space="preserve">notus quoque ſinus complementi, nimirum ſinus grad. </s>
            <s xml:id="echoid-s5189" xml:space="preserve">64.</s>
            <s xml:id="echoid-s5190" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5191" xml:space="preserve">QVOD ſi arcus grad. </s>
            <s xml:id="echoid-s5192" xml:space="preserve">26. </s>
            <s xml:id="echoid-s5193" xml:space="preserve">& </s>
            <s xml:id="echoid-s5194" xml:space="preserve">grad. </s>
            <s xml:id="echoid-s5195" xml:space="preserve">64. </s>
            <s xml:id="echoid-s5196" xml:space="preserve">& </s>
            <s xml:id="echoid-s5197" xml:space="preserve">grad 89. </s>
            <s xml:id="echoid-s5198" xml:space="preserve">& </s>
            <s xml:id="echoid-s5199" xml:space="preserve">grad. </s>
            <s xml:id="echoid-s5200" xml:space="preserve">89. </s>
            <s xml:id="echoid-s5201" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s5202" xml:space="preserve">30. </s>
            <s xml:id="echoid-s5203" xml:space="preserve">quo-
              <lb/>
            rum ſinus inuenti ſunt, ſecemus continue bifariam, quoad poſſumus, accipia-
              <lb/>
              <note position="left" xlink:label="note-138-02" xlink:href="note-138-02a" xml:space="preserve">Supputatio
                <lb/>
              ſinuum ar
                <lb/>
              cuũ Miau-
                <lb/>
              tis 15. ſeſe
                <lb/>
              ſuperãuũ.</note>
            musque medictatum complementa, quę rurſus continue biſariam diuidamus,
              <lb/>
            &</s>
            <s xml:id="echoid-s5204" xml:space="preserve">c. </s>
            <s xml:id="echoid-s5205" xml:space="preserve">adhibeamusq́ue doctrinam illam, qua ex duorum arcuum ſinubus notis
              <lb/>
            cognoſcitur ſinus medietatis differentiæ illorum arcuum, reperiemus ſin us ar
              <lb/>
            cuum numero 240. </s>
            <s xml:id="echoid-s5206" xml:space="preserve">qui in ordinem redacti cum ſinubus arcuum numero 120.
              <lb/>
            </s>
            <s xml:id="echoid-s5207" xml:space="preserve">prius inuentis, conſtituent ſinus arcuum numero 360. </s>
            <s xml:id="echoid-s5208" xml:space="preserve">ſeſe ordine ſuperantium
              <lb/>
            Minutis 15.</s>
            <s xml:id="echoid-s5209" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5210" xml:space="preserve">VERVM quia laborioſum eſt, atque moleſtum tot ſinus ea ratione in-
              <lb/>
              <note position="left" xlink:label="note-138-03" xlink:href="note-138-03a" xml:space="preserve">Alia ſuppu
                <lb/>
              tatio ſinuũ
                <lb/>
              arcuũ ſeſe
                <lb/>
              Minutis 15
                <lb/>
              ſuperantiũ</note>
            dagare, ſatis erit, tanta difficultate inueniſſe ſinus illos arcuum ſuperiorum
              <lb/>
            numero 120. </s>
            <s xml:id="echoid-s5211" xml:space="preserve">ſeſe ordine ſuperantium Minutis 45. </s>
            <s xml:id="echoid-s5212" xml:space="preserve">Ex illis enim ſacile per re-
              <lb/>
            gulam proportionum reperiemus ſinus arcuum ſe ordine ſuperantium Minu-
              <lb/>
            tis 15. </s>
            <s xml:id="echoid-s5213" xml:space="preserve">Deinde ex his ſinus arcuum, qui ordine ſe ſuperant Minutis 5. </s>
            <s xml:id="echoid-s5214" xml:space="preserve">Acdeni-
              <lb/>
            que ex iſtis ſinus arcuum per ſingula Minuta extenſorum; </s>
            <s xml:id="echoid-s5215" xml:space="preserve">neque vnquàm in
              <lb/>
            hac ſupputatione error ſenſibilis continget. </s>
            <s xml:id="echoid-s5216" xml:space="preserve">Cum enim ſinum totum poſue-
              <lb/>
            rimus centies maiorem, quàm 100000. </s>
            <s xml:id="echoid-s5217" xml:space="preserve">ſit vt abiectis primis duabus figuris ad
              <lb/>
            dexteram, vt ſupra dictum eſt, exquiſitiſsimi relinquantur ſinus reſpectu ſinus
              <lb/>
            totius 100000. </s>
            <s xml:id="echoid-s5218" xml:space="preserve">quod totus error, qui in hac ſupputatione contingere poteſt,
              <lb/>
            conſiſtat in prima figura ad dexterá, vel ad ſummum in duabus primis. </s>
            <s xml:id="echoid-s5219" xml:space="preserve">Qua-
              <lb/>
            re abiectis duabus primis figuris, remanebunt omnic ijdem ſinus, qui inuen-
              <lb/>
            ti eſſent priori illo modo Geometrico reſpectu eiuſdem ſinus totius 100000.
              <lb/>
            </s>
            <s xml:id="echoid-s5220" xml:space="preserve">ſi in ſupputatione poneretur ſinus totus centies etiam maior, nempe partium
              <lb/>
            10000000. </s>
            <s xml:id="echoid-s5221" xml:space="preserve">& </s>
            <s xml:id="echoid-s5222" xml:space="preserve">ex inuentis ſinubus duæ figuræ reijcerentur: </s>
            <s xml:id="echoid-s5223" xml:space="preserve">Id quod experien-
              <lb/>
            tia docebit. </s>
            <s xml:id="echoid-s5224" xml:space="preserve">Ita autem rem exequemur. </s>
            <s xml:id="echoid-s5225" xml:space="preserve">Statuátur ordine illi arcus cum ſinu-
              <lb/>
            bus, & </s>
            <s xml:id="echoid-s5226" xml:space="preserve">ad dexteram cuiuſque ſinus aſcribatur differentia, qua à præcedenti ſi-
              <lb/>
              <note position="right" xlink:label="note-138-04" xlink:href="note-138-04a" xml:space="preserve">
                <lb/>
              ## Arcus # Sinus # Differentiæ
                <lb/>
              G # M
                <lb/>
              0 # 0 # 000000
                <lb/>
              0 # 45 # 130896 # 130896
                <lb/>
              1 # 30 # 261769 # 130873
                <lb/>
              2 # 15 # 392598 # 130829
                <lb/>
              3 # 0 # 523360 # 130762
                <lb/>
              3 # 45 # 654031 # 130671
                <lb/>
              </note>
            nu differt; </s>
            <s xml:id="echoid-s5227" xml:space="preserve">vt hic factum eſſe vides in quin
              <lb/>
            que arcubus. </s>
            <s xml:id="echoid-s5228" xml:space="preserve">Deinde dic. </s>
            <s xml:id="echoid-s5229" xml:space="preserve">Si Minuta 45. </s>
            <s xml:id="echoid-s5230" xml:space="preserve">re-
              <lb/>
            quirunt differentiam 130896. </s>
            <s xml:id="echoid-s5231" xml:space="preserve">addendam ad
              <lb/>
            ſinum Minuti. </s>
            <s xml:id="echoid-s5232" xml:space="preserve">0. </s>
            <s xml:id="echoid-s5233" xml:space="preserve">vt ſiat ſinus Minutorum
              <lb/>
            45. </s>
            <s xml:id="echoid-s5234" xml:space="preserve">Minuta 15. </s>
            <s xml:id="echoid-s5235" xml:space="preserve">quantam poſtulant diffe-
              <lb/>
            rentiam addendam eidem ſinui Minur. </s>
            <s xml:id="echoid-s5236" xml:space="preserve">0.
              <lb/>
            </s>
            <s xml:id="echoid-s5237" xml:space="preserve">vt fiat ſinus Minutorum 15? </s>
            <s xml:id="echoid-s5238" xml:space="preserve">Inuenies enim
              <lb/>
            requiri differentiã 43632. </s>
            <s xml:id="echoid-s5239" xml:space="preserve">quæ addita ſinui
              <lb/>
            Minuti. </s>
            <s xml:id="echoid-s5240" xml:space="preserve">0. </s>
            <s xml:id="echoid-s5241" xml:space="preserve">conſtituet ſinũ Minutorum 15. </s>
            <s xml:id="echoid-s5242" xml:space="preserve">
              <lb/>
            partium 43632. </s>
            <s xml:id="echoid-s5243" xml:space="preserve">Rurſus dic. </s>
            <s xml:id="echoid-s5244" xml:space="preserve">Poſitis ijſdem,
              <lb/>
            quantam differẽtiam exigune Minuta 30. </s>
            <s xml:id="echoid-s5245" xml:space="preserve">
              <lb/>
            addendam eidem ſinui Minuti 0. </s>
            <s xml:id="echoid-s5246" xml:space="preserve">vt ſiat ſi-
              <lb/>
            nus Minutorum 30? </s>
            <s xml:id="echoid-s5247" xml:space="preserve">Reperies enim differentiam 87264. </s>
            <s xml:id="echoid-s5248" xml:space="preserve">quæ addita ſinui Minu
              <lb/>
            tio. </s>
            <s xml:id="echoid-s5249" xml:space="preserve">faciet 87264. </s>
            <s xml:id="echoid-s5250" xml:space="preserve">ſinum Min 30. </s>
            <s xml:id="echoid-s5251" xml:space="preserve">Item dic. </s>
            <s xml:id="echoid-s5252" xml:space="preserve">Si Minuta 45. </s>
            <s xml:id="echoid-s5253" xml:space="preserve">quibus arcus Min. </s>
            <s xml:id="echoid-s5254" xml:space="preserve">45. </s>
            <s xml:id="echoid-s5255" xml:space="preserve">
              <lb/>
            ab arcu ſequenti grad. </s>
            <s xml:id="echoid-s5256" xml:space="preserve">1. </s>
            <s xml:id="echoid-s5257" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s5258" xml:space="preserve">30. </s>
            <s xml:id="echoid-s5259" xml:space="preserve">differt, requirunt differentiam 130873. </s>
            <s xml:id="echoid-s5260" xml:space="preserve">ad-
              <lb/>
            dendam ſinui Min. </s>
            <s xml:id="echoid-s5261" xml:space="preserve">45. </s>
            <s xml:id="echoid-s5262" xml:space="preserve">vt ſiat ſinus grad. </s>
            <s xml:id="echoid-s5263" xml:space="preserve">1. </s>
            <s xml:id="echoid-s5264" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s5265" xml:space="preserve">30. </s>
            <s xml:id="echoid-s5266" xml:space="preserve">quantam differentiam po-
              <lb/>
            ſtulant Minuta 15. </s>
            <s xml:id="echoid-s5267" xml:space="preserve">addédam eidem ſinui Min. </s>
            <s xml:id="echoid-s5268" xml:space="preserve">45. </s>
            <s xml:id="echoid-s5269" xml:space="preserve">vt fiat ſinus Min. </s>
            <s xml:id="echoid-s5270" xml:space="preserve">60. </s>
            <s xml:id="echoid-s5271" xml:space="preserve">hoc </s>
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