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

Page concordance

< >
Scan Original
401 389
402 390
403 391
404 392
405 393
406 394
407 395
408 396
409 397
410 398
411 399
412 400
413 401
414 402
415 403
416 404
417 405
418 406
419 407
420 408
421 409
422 410
423 411
424 412
425 413
426 414
427 415
428 416
429 417
430 418
< >
page |< < (398) of 532 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div1092" type="section" level="1" n="538">
          <pb o="398" file="410" n="410" rhead=""/>
        </div>
        <div xml:id="echoid-div1094" type="section" level="1" n="539">
          <head xml:id="echoid-head574" xml:space="preserve">THEOR. 38. PROPOS. 40.</head>
          <p>
            <s xml:id="echoid-s13730" xml:space="preserve">SI duo circuli maximi in ſphæra ſe mutuo ſe-
              <lb/>
            cent, & </s>
            <s xml:id="echoid-s13731" xml:space="preserve">in eorum peripherijs duo puncta ſignen-
              <lb/>
            tur, quorum vtrumque vel in eodem ſemicirculo
              <lb/>
            ſumatur; </s>
            <s xml:id="echoid-s13732" xml:space="preserve">vel in vno ſemicirculo vnum, & </s>
            <s xml:id="echoid-s13733" xml:space="preserve">alterum
              <lb/>
            in altero eiuſdem circuli; </s>
            <s xml:id="echoid-s13734" xml:space="preserve">vel vnum in ſemicircu-
              <lb/>
            lo vno vnius circuli, & </s>
            <s xml:id="echoid-s13735" xml:space="preserve">alterum in ſemicirculo
              <lb/>
            vtrolibet alterius circuli; </s>
            <s xml:id="echoid-s13736" xml:space="preserve">atque per vtrumque ho-
              <lb/>
            rum punctorum arcus maximi circuli ducatur fa-
              <lb/>
            ciẽs cum peripheria alterius circuli, ad quamcum-
              <lb/>
            que partem, angulum rectum: </s>
            <s xml:id="echoid-s13737" xml:space="preserve">habebit ſinus arcus
              <lb/>
            intercepti inter vnum illorum punctorum, & </s>
            <s xml:id="echoid-s13738" xml:space="preserve">al-
              <lb/>
            terutram ſectionem circulorum, ad ſinum arcus,
              <lb/>
            qui per illud punctũ ductus rectum cum periphe-
              <lb/>
            ria alterius circuli angulum facit, eandem propor-
              <lb/>
            tionem, quam habet ſinus arcus inter punctum al
              <lb/>
            terum, & </s>
            <s xml:id="echoid-s13739" xml:space="preserve">alterutram circulortum ſectionem inter-
              <lb/>
            iecti, ad ſinum arcus, qui per illud punctum de-
              <lb/>
            ſcriptus cum alterius circuli peripheria rectũ con-
              <lb/>
            ſtituit angulum.</s>
            <s xml:id="echoid-s13740" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13741" xml:space="preserve">IN ſphęra duo circuli maximi ABCD, AECF, ſe mutuo ſecentin A, & </s>
            <s xml:id="echoid-s13742" xml:space="preserve">
              <lb/>
            C, & </s>
            <s xml:id="echoid-s13743" xml:space="preserve">primum ad angulos non rectos; </s>
            <s xml:id="echoid-s13744" xml:space="preserve">ſignenturq́ue primum in eodem ſemicir-
              <lb/>
            culo ABC, duo puncta vtcũque B, G; </s>
            <s xml:id="echoid-s13745" xml:space="preserve">per quę, & </s>
            <s xml:id="echoid-s13746" xml:space="preserve">polum circuli AECF, qui ſit
              <lb/>
            H, circuli maximi ducantur IBHK, LGHM; </s>
            <s xml:id="echoid-s13747" xml:space="preserve">eruntq́ue anguli ad I, L, K, M,
              <lb/>
              <note position="left" xlink:label="note-410-01" xlink:href="note-410-01a" xml:space="preserve">20. 1 Theod.</note>
            recti. </s>
            <s xml:id="echoid-s13748" xml:space="preserve">Dico eãdem habere proportionẽ ſinum arcus AB, vel CB, ad ſinũ arcus
              <lb/>
              <note position="left" xlink:label="note-410-02" xlink:href="note-410-02a" xml:space="preserve">15. 1. Theod.</note>
            BI, vel BK, quam habet ſinus arcus AG, vel CG, ad ſinũ arcus GL, vel GM.
              <lb/>
            </s>
            <s xml:id="echoid-s13749" xml:space="preserve">Sit enim cõmunis ſectio circulorum recta AC, ad quam ex B, G, perpẽdiculares
              <lb/>
              <note position="left" xlink:label="note-410-03" xlink:href="note-410-03a" xml:space="preserve">3. vndee.</note>
            agátur BN, GO, in plano circuli ABCD; </s>
            <s xml:id="echoid-s13750" xml:space="preserve">eritq; </s>
            <s xml:id="echoid-s13751" xml:space="preserve">BN, ſinus rectus tam arcus
              <lb/>
              <note position="left" xlink:label="note-410-04" xlink:href="note-410-04a" xml:space="preserve">12. primi.</note>
            AB, quam arcus CB, ex definitione ſinus recti; </s>
            <s xml:id="echoid-s13752" xml:space="preserve">& </s>
            <s xml:id="echoid-s13753" xml:space="preserve">eodem modo GO, ſinus
              <lb/>
            vtriuſque arcus AG, CG. </s>
            <s xml:id="echoid-s13754" xml:space="preserve">Demittantur ab eiſdem punctis B, G, ad planum
              <lb/>
              <note position="left" xlink:label="note-410-05" xlink:href="note-410-05a" xml:space="preserve">31. vndee.</note>
            </s>
          </p>
        </div>
      </text>
    </echo>
Impressum