Newton, Isaac, Philosophia naturalis principia mathematica, 1713

Page concordance

< >
Scan Original
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
< >
page |< < of 524 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <subchap1>
              <subchap2>
                <pb xlink:href="039/01/053.jpg" pagenum="25"/>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  LEMMA II.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Si in Figura quavis
                    <emph.end type="italics"/>
                  AacE,
                    <emph type="italics"/>
                  rectis
                    <emph.end type="italics"/>
                  Aa, AE
                    <emph type="italics"/>
                  & curva
                    <emph.end type="italics"/>
                  acE
                    <emph type="italics"/>
                  com
                    <lb/>
                  prehenſa, inſcribantur parallelogramma quotcunque
                    <emph.end type="italics"/>
                  Ab, Bc, Cd
                    <lb/>
                  &c.
                    <emph type="italics"/>
                  ſub baſibus
                    <emph.end type="italics"/>
                  AB, BC, CD, &c.
                    <emph type="italics"/>
                  æqualibus, & lateribuſ
                    <emph.end type="italics"/>
                    <lb/>
                  Bb, Cc, Dd, &c.
                    <emph type="italics"/>
                  Figuræ lateri
                    <emph.end type="italics"/>
                  Aa
                    <emph type="italics"/>
                  pa­
                    <lb/>
                  rallelis contenta; & compleantur paral-
                    <emph.end type="italics"/>
                    <lb/>
                    <figure id="id.039.01.053.1.jpg" xlink:href="039/01/053/1.jpg" number="6"/>
                    <lb/>
                    <emph type="italics"/>
                  lelogramma
                    <emph.end type="italics"/>
                  aKbl, bLcm, cMdn, &c.
                    <lb/>
                    <emph type="italics"/>
                  Dein horum parallelogrammorum lati­
                    <lb/>
                  tudo minuatur, & numerus augeatur
                    <lb/>
                  in infinitum: dico quod ultimæ rationes,
                    <lb/>
                  quas habent ad ſe invicem Figura in­
                    <lb/>
                  ſcripta
                    <emph.end type="italics"/>
                  AKbLcMdD,
                    <emph type="italics"/>
                  circumſcripta
                    <emph.end type="italics"/>
                    <lb/>
                  AalbmcndoE,
                    <emph type="italics"/>
                  & curvilinea
                    <emph.end type="italics"/>
                  AbcdE,
                    <lb/>
                    <emph type="italics"/>
                  ſunt rationes æqualitatis.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Nam Figuræ inſcriptæ & circumſcriptæ differentia eſt ſumma pa­
                    <lb/>
                  rallelogrammorum
                    <emph type="italics"/>
                  Kl, Lm, Mn, Do,
                    <emph.end type="italics"/>
                  hoc eſt (ob æquales om­
                    <lb/>
                  nium baſes) rectangulum ſub unius baſi
                    <emph type="italics"/>
                  Kb
                    <emph.end type="italics"/>
                  & altitudinum ſumma
                    <lb/>
                    <emph type="italics"/>
                  Aa,
                    <emph.end type="italics"/>
                  id eſt, rectangulum
                    <emph type="italics"/>
                  ABla.
                    <emph.end type="italics"/>
                  Sed hoc rectangulum, eo quod
                    <lb/>
                  latitudo ejus
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  in infinitum minuitur, fit minus quovis dato. </s>
                  <s>Er­
                    <lb/>
                  go (per Lemma 1) Figura inſcripta & circumſcripta & multo magis
                    <lb/>
                  Figura curvilinea intermedia fiunt ultimo æquales.
                    <emph type="italics"/>
                  Q.E.D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  LEMMA III.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Eædem rationes ultimæ ſunt etiam rationes æqualitatis, ubi paral­
                    <lb/>
                  lelogrammorum latitudines
                    <emph.end type="italics"/>
                  AB, BC, CD, &c.
                    <emph type="italics"/>
                  ſunt inæquales,
                    <lb/>
                  & omnes minuuntur in infinitum.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Sit enim
                    <emph type="italics"/>
                  AF
                    <emph.end type="italics"/>
                  æqualis latitudini maximæ, & compleatur paralle­
                    <lb/>
                  logrammum
                    <emph type="italics"/>
                  FAaf.
                    <emph.end type="italics"/>
                  Hoc erit majus quam differentia Figuræ in­
                    <lb/>
                  ſcriptæ & Figuræ circumſcriptæ; at latitudine ſua
                    <emph type="italics"/>
                  AF
                    <emph.end type="italics"/>
                  in infinitum
                    <lb/>
                  diminuta, minus fiet quam datum quodvis rectangulum.
                    <emph type="italics"/>
                    <expan abbr="q.">que</expan>
                  E. D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  1. Hinc ſumma ultima parallelogrammorum evaneſcentium
                    <lb/>
                  coincidit omni ex parte cum Figura curvilinea. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  2. Et multo magis Figura rectilinea, quæ chordis evaneſ-</s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum