DelMonte, Guidubaldo, In duos Archimedis aequeponderantium libros Paraphrasis : scholijs illustrata

Page concordance

< >
Scan Original
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
< >
page |< < of 207 > >|
    <archimedes>
      <text>
        <body>
          <chap id="N10019">
            <p id="N140F0" type="main">
              <s id="N1414A">
                <pb xlink:href="077/01/113.jpg" pagenum="109"/>
                <emph type="italics"/>
              nea OX. dicti autem trapezii centrum gauitatis est etiam in li­
                <lb/>
              nea EF, quare trapezii ABCD centrum grauitatis est punctum
                <lb/>
              P. At verò triangulum BCD ad ABD proportionem habet eam,
                <arrow.to.target n="marg176"/>
                <lb/>
              OP ad P
                <emph.end type="italics"/>
              X. cùm ſint puncta OX triangulorum centla graui
                <lb/>
              tatis, ac punctum P vtrorum〈que〉 commune centrum.
                <emph type="italics"/>
              Sed vt
                <lb/>
              triangulum BDC adtriangulum ABD, ita eſt
                <emph.end type="italics"/>
              quo〈que〉 baſis
                <emph type="italics"/>
              BC
                <emph.end type="italics"/>
                <arrow.to.target n="marg177"/>
                <lb/>
                <emph type="italics"/>
              ad
                <emph.end type="italics"/>
              baſim
                <emph type="italics"/>
              AD.
                <emph.end type="italics"/>
              cùm triangula eandem habeant altitudinem,
                <lb/>
              ſiquidem ſunt in ijsdem parallelis AD BC. quare vt BC ad
                <lb/>
              AD, ita OP ad PX.
                <emph type="italics"/>
              Sed
                <emph.end type="italics"/>
              quoniam anguli RPO SPX
                <arrow.to.target n="marg178"/>
              ver­
                <lb/>
              ticem ſunt ęquales, & angulus PRO ipſi PSX, veluti
                <arrow.to.target n="marg179"/>
                <lb/>
              ROP angulo PXS eſt ęqualis, erit triangulum OPR triangu
                <lb/>
              lo XPS ſimile; quare
                <emph type="italics"/>
              vt OP ad PX, ſic PR ad PS.
                <emph.end type="italics"/>
              eſt
                <arrow.to.target n="marg180"/>
                <lb/>
              BC ad AD, vt OP ad PX
                <emph type="italics"/>
              ; vt igitur BC ad AD, ita RP ad PS.
                <emph.end type="italics"/>
                <arrow.to.target n="marg181"/>
                <lb/>
              & antecedentium dupla, duæ ſcilicet BC ad AD, vt duæ PR
                <lb/>
              ad PS. & componendo duæ BC cum AD ad AD; vt
                <arrow.to.target n="marg182"/>
                <lb/>
              PR cum PS ad PS. & ad conſe〈que〉ntium dupla, vt ſcilicet
                <lb/>
              duæ BC cum AD ad duas AD, ita duæ PR cum PS ad duas
                <lb/>
              PS. dictum eſt autem BC ad AD ita eſſe, vt PR ad PS. quare
                <lb/>
              conuerrendo AD ad BC erit, vt PS ad PR. &
                <arrow.to.target n="marg183"/>
                <lb/>
              dupla. </s>
              <s id="N14232">hoc eſt duæ AD ad BC, vt duæ PS ad PR. Ita〈que〉 in
                <lb/>
              eadem ſunt proportione duç BC cum AD ad duas AD, vt
                <lb/>
              duę PR
                <expan abbr="cũ">cum</expan>
              PS ad duas PS. ſicut verò duę AD ad BC, ita duę
                <lb/>
              PS ad PR. antecedentes igitur ad ſuas ſimul conſe〈que〉ntes
                <arrow.to.target n="marg184"/>
                <lb/>
              eadem erunt proportione.
                <emph type="italics"/>
              Quare ſicut duæ BC cum AD ad duas
                <lb/>
              AD cum BC, ita duæ RP cum PS ad duas P S cum PR,
                <lb/>
              verùm duæ quidem RP cum PS eſt vtra〈que〉 ſimul SR RP.
                <emph.end type="italics"/>
              bis
                <lb/>
              enim aſſumitur PR, ſemel verò PS. Cum autem lineæ DH ES
                <lb/>
              à lineis diuidantur ęquidiſtantibus ED OT HM, erit DK
                <arrow.to.target n="marg185"/>
                <lb/>
              KH, vt ER ad CS; kD verò eſt æqualis KH, erit ER ipſi
                <lb/>
              RS ęqualis. </s>
              <s id="N14258">erit igitur ER cum RP,
                <emph type="italics"/>
              hoc est PE
                <emph.end type="italics"/>
              ipſis SR RP
                <lb/>
              ęqualis.
                <emph type="italics"/>
              duæ verò PS cum PR eſt vtra〈que〉 PS SR.
                <emph.end type="italics"/>
              bis enim aſ­
                <lb/>
              ſumitur PS, ſemel què PR. & quoniam FS eſt ęqualis ipſi SR.
                <lb/>
              quod quidem eodem modo oſtendetur, cùm ſit FS ad SR, vt
                <lb/>
              BH ad Hk. </s>
              <s id="N1426E">erit FS cum SP,
                <emph type="italics"/>
              hoc est PF
                <emph.end type="italics"/>
              ipſis PS SR æqualis.
                <lb/>
              Quare ita ſehabet PE ad PF, vt duæ BC cum AD ad duas
                <lb/>
              AD cum BC. Centrum igitur grauitatis P trapezij ABCD
                <lb/>
              in linea eſt EF, quæ
                <expan abbr="cõiungit">coniungit</expan>
              parallelas AD BC bifariam di </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum