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

Page concordance

< >
Scan Original
121 109
122 110
123 111
124 112
125 113
126 114
127 115
128 116
129 117
130 118
131 119
132 120
133 121
134 122
135 123
136 124
137 125
138 126
139 127
140 128
141 129
142 130
143 131
144 132
145 133
146 134
147 135
148 136
149 137
150 138
< >
page |< < (197) of 532 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div566" type="section" level="1" n="263">
          <p style="it">
            <s xml:id="echoid-s8295" xml:space="preserve">
              <pb o="197" file="209" n="209" rhead=""/>
            tem eiuſdem prioris illius arcus, cuius ſecantem ſubduxiſti Item ſi tangentem cuiuſ@
              <lb/>
            libet arcus ex eiuſdem ſecante detrahas, remanebit tangens ſemiſsis complementi
              <lb/>
            arcus eiuſdem. </s>
            <s xml:id="echoid-s8296" xml:space="preserve">Primum conſtat ex ſcholio propoſ. </s>
            <s xml:id="echoid-s8297" xml:space="preserve">19. </s>
            <s xml:id="echoid-s8298" xml:space="preserve">vbi oſtenſum eſt, ſecantem, & </s>
            <s xml:id="echoid-s8299" xml:space="preserve">
              <lb/>
            tangentem cuiuſuis arcus ſimul æquales eſſe tangenti arcus compoſiti ex illo, & </s>
            <s xml:id="echoid-s8300" xml:space="preserve">ex
              <lb/>
            ſemiſſe complementi eiuſdem. </s>
            <s xml:id="echoid-s8301" xml:space="preserve">H@nc enim fit, vt ſecans ex cõpoſita hac tangente ablata
              <lb/>
            relinquat alteram illá tangentem. </s>
            <s xml:id="echoid-s8302" xml:space="preserve">Secundum vero liquet ex propoſ. </s>
            <s xml:id="echoid-s8303" xml:space="preserve">hac 20. </s>
            <s xml:id="echoid-s8304" xml:space="preserve">vbi de-
              <lb/>
            monſtrauimus, ſeca ntem cuiusuis arcus æqualem eſſe tangenti eiuſdem, vna cum tan-
              <lb/>
            gente ſemiſsis complementi arcus eiuſdem. </s>
            <s xml:id="echoid-s8305" xml:space="preserve">Quare huius ſemiſsis tangens reliqua fiet
              <lb/>
            poſt ſubtractionem alterius illius tangentis ex ſecante. </s>
            <s xml:id="echoid-s8306" xml:space="preserve">V. </s>
            <s xml:id="echoid-s8307" xml:space="preserve">g. </s>
            <s xml:id="echoid-s8308" xml:space="preserve">ſi ſecantem arcus grad.
              <lb/>
            </s>
            <s xml:id="echoid-s8309" xml:space="preserve">20. </s>
            <s xml:id="echoid-s8310" xml:space="preserve">quæ eſt 10641777. </s>
            <s xml:id="echoid-s8311" xml:space="preserve">detrahamus ex 14281480. </s>
            <s xml:id="echoid-s8312" xml:space="preserve">tangente arcus grad. </s>
            <s xml:id="echoid-s8313" xml:space="preserve">55. </s>
            <s xml:id="echoid-s8314" xml:space="preserve">
              <lb/>
            compoſiti ex arcu grad. </s>
            <s xml:id="echoid-s8315" xml:space="preserve">20. </s>
            <s xml:id="echoid-s8316" xml:space="preserve">& </s>
            <s xml:id="echoid-s8317" xml:space="preserve">ſemi
              <unsure/>
            ſſe complementi eiuſdem, relinquetur tangens
              <lb/>
            3639703. </s>
            <s xml:id="echoid-s8318" xml:space="preserve">arcus eiuſdem grad. </s>
            <s xml:id="echoid-s8319" xml:space="preserve">20. </s>
            <s xml:id="echoid-s8320" xml:space="preserve">Item ſi 4244748. </s>
            <s xml:id="echoid-s8321" xml:space="preserve">tangentem arcus grad. </s>
            <s xml:id="echoid-s8322" xml:space="preserve">23. </s>
            <s xml:id="echoid-s8323" xml:space="preserve">
              <lb/>
            ex 10863603 ſecante eiuſdem arcus ſubducamus, remanebit tangens 6618855. </s>
            <s xml:id="echoid-s8324" xml:space="preserve">ar-
              <lb/>
            cus grad 33. </s>
            <s xml:id="echoid-s8325" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8326" xml:space="preserve">30. </s>
            <s xml:id="echoid-s8327" xml:space="preserve">hoc eſt, ſem ſsis complementi dati arcus grad. </s>
            <s xml:id="echoid-s8328" xml:space="preserve">23. </s>
            <s xml:id="echoid-s8329" xml:space="preserve">Rurſus
              <lb/>
            ſi 11547004. </s>
            <s xml:id="echoid-s8330" xml:space="preserve">ſecantem arcus grad. </s>
            <s xml:id="echoid-s8331" xml:space="preserve">30 ex 17320508. </s>
            <s xml:id="echoid-s8332" xml:space="preserve">tangente arcus grad. </s>
            <s xml:id="echoid-s8333" xml:space="preserve">60. </s>
            <s xml:id="echoid-s8334" xml:space="preserve">
              <lb/>
            qui ex arcu grad. </s>
            <s xml:id="echoid-s8335" xml:space="preserve">30. </s>
            <s xml:id="echoid-s8336" xml:space="preserve">& </s>
            <s xml:id="echoid-s8337" xml:space="preserve">ſemiſſe complementi eiuſdem componitur, auferamus, @elin
              <lb/>
            quetur tangens 5773504. </s>
            <s xml:id="echoid-s8338" xml:space="preserve">arcus grad. </s>
            <s xml:id="echoid-s8339" xml:space="preserve">30. </s>
            <s xml:id="echoid-s8340" xml:space="preserve">Et ſi 1763268. </s>
            <s xml:id="echoid-s8341" xml:space="preserve">tangentem arcus grad. </s>
            <s xml:id="echoid-s8342" xml:space="preserve">10. </s>
            <s xml:id="echoid-s8343" xml:space="preserve">
              <lb/>
            demamus ex 10154264. </s>
            <s xml:id="echoid-s8344" xml:space="preserve">ſecante eiuſdem arcus gra. </s>
            <s xml:id="echoid-s8345" xml:space="preserve">10. </s>
            <s xml:id="echoid-s8346" xml:space="preserve">remanebit tangẽs 8390996. </s>
            <s xml:id="echoid-s8347" xml:space="preserve">
              <lb/>
            arcus grad. </s>
            <s xml:id="echoid-s8348" xml:space="preserve">40. </s>
            <s xml:id="echoid-s8349" xml:space="preserve">qui ſemiſsis eſt complementi dicti arcus grad. </s>
            <s xml:id="echoid-s8350" xml:space="preserve">10.</s>
            <s xml:id="echoid-s8351" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s8352" xml:space="preserve">IAM vero ſi per ea, quæ propoſ. </s>
            <s xml:id="echoid-s8353" xml:space="preserve">18. </s>
            <s xml:id="echoid-s8354" xml:space="preserve">eiusq́; </s>
            <s xml:id="echoid-s8355" xml:space="preserve">ſcholio tradidimus, tangentes om-
              <lb/>
            nium arcuum quadrantis per ſingula Minuta extenſorum inueſtigemus; </s>
            <s xml:id="echoid-s8356" xml:space="preserve">reperiemus
              <lb/>
            earum beneficio per ſolam additionem ſecantes omnium arcuum per bina minuta pro-
              <lb/>
            gredientium, ſi mmirum tangentem cuiuſuis arcus minuta numero paria habentis
              <lb/>
            addamus ad tangentem ſemiſsis complementi arcus eiuſdem: </s>
            <s xml:id="echoid-s8357" xml:space="preserve">propterea quòd Secans
              <lb/>
            cuiuſuis arcus æqualis eſt tangenti eiuſdem, vna cum tangente ſemiſsis complementi
              <lb/>
              <note position="right" xlink:label="note-209-01" xlink:href="note-209-01a" xml:space="preserve">20. huius.</note>
            eiuſdem; </s>
            <s xml:id="echoid-s8358" xml:space="preserve">conſtat autem omnium arcuum minuta numero paria habentium comple-
              <lb/>
            menta ſemiſſes habere, Exempli cauſa, ſi deſideretur ſecans arcus Min. </s>
            <s xml:id="echoid-s8359" xml:space="preserve">2. </s>
            <s xml:id="echoid-s8360" xml:space="preserve">addemus eius
              <lb/>
            tangentem 5818. </s>
            <s xml:id="echoid-s8361" xml:space="preserve">ad 9994184. </s>
            <s xml:id="echoid-s8362" xml:space="preserve">tangentem arcus grad. </s>
            <s xml:id="echoid-s8363" xml:space="preserve">44. </s>
            <s xml:id="echoid-s8364" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8365" xml:space="preserve">59. </s>
            <s xml:id="echoid-s8366" xml:space="preserve">qui ſemiſsis eſt com
              <lb/>
            plementi arcus dati Min. </s>
            <s xml:id="echoid-s8367" xml:space="preserve">2. </s>
            <s xml:id="echoid-s8368" xml:space="preserve">Numerus enim compoſitus 10000002. </s>
            <s xml:id="echoid-s8369" xml:space="preserve">erit ſecans arcus
              <lb/>
            Min. </s>
            <s xml:id="echoid-s8370" xml:space="preserve">2. </s>
            <s xml:id="echoid-s8371" xml:space="preserve">sic etiam ſi quæratur ſecans arcus grad. </s>
            <s xml:id="echoid-s8372" xml:space="preserve">89. </s>
            <s xml:id="echoid-s8373" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8374" xml:space="preserve">58. </s>
            <s xml:id="echoid-s8375" xml:space="preserve">addemus eius tangentem
              <lb/>
            17188033689. </s>
            <s xml:id="echoid-s8376" xml:space="preserve">ad 2909 tangentem arcus Min. </s>
            <s xml:id="echoid-s8377" xml:space="preserve">1. </s>
            <s xml:id="echoid-s8378" xml:space="preserve">qui ſemiſsis eſt complementi arcus
              <lb/>
            dati grad. </s>
            <s xml:id="echoid-s8379" xml:space="preserve">89. </s>
            <s xml:id="echoid-s8380" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8381" xml:space="preserve">58. </s>
            <s xml:id="echoid-s8382" xml:space="preserve">Ná numerus conflatus 17188036598. </s>
            <s xml:id="echoid-s8383" xml:space="preserve">erit ſecans arcus grad.
              <lb/>
            </s>
            <s xml:id="echoid-s8384" xml:space="preserve">89 Min. </s>
            <s xml:id="echoid-s8385" xml:space="preserve">58. </s>
            <s xml:id="echoid-s8386" xml:space="preserve">Hac ratione conficietur dimidiata pars tabulæ Tangentium: </s>
            <s xml:id="echoid-s8387" xml:space="preserve">at Tangen-
              <lb/>
            tes arcuum minuta numero imparia habentium, quoniam eorum complementa ſemiſ-
              <lb/>
            ſes non habent, niſi ad Secunda venire velimus, inueſtigandæ erunt, vt propoſ. </s>
            <s xml:id="echoid-s8388" xml:space="preserve">18. </s>
            <s xml:id="echoid-s8389" xml:space="preserve">
              <lb/>
            eiuſq; </s>
            <s xml:id="echoid-s8390" xml:space="preserve">ſcholio præcepimus.</s>
            <s xml:id="echoid-s8391" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s8392" xml:space="preserve">RVRSVS ſecantem cuiuſuis arcus inueniemus, ſi eius tangentem demamus ex
              <lb/>
            tangente arcus compoſiti ex ar cu illo, & </s>
            <s xml:id="echoid-s8393" xml:space="preserve">ſemiſſe complementi eiuſdem arcus. </s>
            <s xml:id="echoid-s8394" xml:space="preserve">Nam cũ,
              <lb/>
            vt demonſtrauimu, ſecans cuiuſuis arcus, vnà cum tangente eiuſdem æqualis ſit tan-
              <lb/>
              <note position="right" xlink:label="note-209-02" xlink:href="note-209-02a" xml:space="preserve">Schol. 19.
                <lb/>
              huius.</note>
            genti arcus compoſiti ex dato arcu, & </s>
            <s xml:id="echoid-s8395" xml:space="preserve">ſemiſſe complementi eiuſdem; </s>
            <s xml:id="echoid-s8396" xml:space="preserve">efficitur, vt tan
              <lb/>
            gens dati arcus ex tangente arcus ex eo, & </s>
            <s xml:id="echoid-s8397" xml:space="preserve">ſemiſſe complementi compoſiti ablata re-
              <lb/>
            linquat ſecantem eiuſdem dati arcus. </s>
            <s xml:id="echoid-s8398" xml:space="preserve">Vt ſi cupiamus ſecantem arcus Min. </s>
            <s xml:id="echoid-s8399" xml:space="preserve">2. </s>
            <s xml:id="echoid-s8400" xml:space="preserve">aufere-
              <lb/>
            mus 5818. </s>
            <s xml:id="echoid-s8401" xml:space="preserve">tangentem ipſius ex 10005820. </s>
            <s xml:id="echoid-s8402" xml:space="preserve">tangente arcus grad. </s>
            <s xml:id="echoid-s8403" xml:space="preserve">45. </s>
            <s xml:id="echoid-s8404" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8405" xml:space="preserve">1 cõpoſiti ex
              <lb/>
            arcu Min. </s>
            <s xml:id="echoid-s8406" xml:space="preserve">2. </s>
            <s xml:id="echoid-s8407" xml:space="preserve">& </s>
            <s xml:id="echoid-s8408" xml:space="preserve">ex arcu grad. </s>
            <s xml:id="echoid-s8409" xml:space="preserve">44. </s>
            <s xml:id="echoid-s8410" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8411" xml:space="preserve">59. </s>
            <s xml:id="echoid-s8412" xml:space="preserve">qui ſemiſsis eſt complementi arcus dati
              <lb/>
            Min. </s>
            <s xml:id="echoid-s8413" xml:space="preserve">2 Relictus namque numerus 10000002 erit ſecans arcus dati Min. </s>
            <s xml:id="echoid-s8414" xml:space="preserve">2. </s>
            <s xml:id="echoid-s8415" xml:space="preserve">Ita quoq;
              <lb/>
            </s>
            <s xml:id="echoid-s8416" xml:space="preserve">ſi velimus habere ſecantem arcus grad. </s>
            <s xml:id="echoid-s8417" xml:space="preserve">60. </s>
            <s xml:id="echoid-s8418" xml:space="preserve">ſubducemus 17320508. </s>
            <s xml:id="echoid-s8419" xml:space="preserve">eius tangentem
              <lb/>
            ex 37320514. </s>
            <s xml:id="echoid-s8420" xml:space="preserve">tangente arcus grad. </s>
            <s xml:id="echoid-s8421" xml:space="preserve">75. </s>
            <s xml:id="echoid-s8422" xml:space="preserve">compoſiti ex dato arcu grad. </s>
            <s xml:id="echoid-s8423" xml:space="preserve">60. </s>
            <s xml:id="echoid-s8424" xml:space="preserve">& </s>
            <s xml:id="echoid-s8425" xml:space="preserve">ex </s>
          </p>
        </div>
      </text>
    </echo>
Impressum