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

Page concordance

< >
Scan Original
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
151 139
152 140
153 141
154 142
155 143
156 144
157 145
158 146
159 147
160 148
< >
page |< < (128) of 532 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div397" type="section" level="1" n="167">
          <p style="it">
            <s xml:id="echoid-s5400" xml:space="preserve">
              <pb o="128" file="140" n="140" rhead=""/>
            _HL_, _EK_, differentiæ inter ſinus _HI_, _EG_, & </s>
            <s xml:id="echoid-s5401" xml:space="preserve">ſinum _DT_. </s>
            <s xml:id="echoid-s5402" xml:space="preserve">Quoniam vero arcus _DE_,
              <lb/>
            ſi e xiguus fuerit, qualem nos ponimus, nempe Minutorum _45_. </s>
            <s xml:id="echoid-s5403" xml:space="preserve">vel _15_. </s>
            <s xml:id="echoid-s5404" xml:space="preserve">vel _5_. </s>
            <s xml:id="echoid-s5405" xml:space="preserve">(Ex his
              <lb/>
            enim ſolis intermediorum arcuum ſinus inquirimus) à recta linea, quoad ſenſum, non
              <lb/>
              <figure xlink:label="fig-140-01" xlink:href="fig-140-01a" number="133">
                <image file="140-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/140-01"/>
              </figure>
            differt, ac proinde multo minus arcus _DH_; </s>
            <s xml:id="echoid-s5406" xml:space="preserve">erunt trianæ
              <lb/>
            gula _DEK_, _DHL_, quodammodo rectilinea. </s>
            <s xml:id="echoid-s5407" xml:space="preserve">& </s>
            <s xml:id="echoid-s5408" xml:space="preserve">æquian-
              <lb/>
            gula inter ſe. </s>
            <s xml:id="echoid-s5409" xml:space="preserve">Quamobrem erit, vt _DE_, differentia inter
              <lb/>
              <note position="left" xlink:label="note-140-01" xlink:href="note-140-01a" xml:space="preserve">4. fexti.</note>
            arcum _BD_, & </s>
            <s xml:id="echoid-s5410" xml:space="preserve">arcum _BE_, ad _EK_, differentiam inter ſi-
              <lb/>
            num _DF_, & </s>
            <s xml:id="echoid-s5411" xml:space="preserve">ſinum _EG_, ita _DH_, differentia inter ar-
              <lb/>
            cum _BD_, & </s>
            <s xml:id="echoid-s5412" xml:space="preserve">arcum _BH_, ad _HL_, differentiam inter ſi-
              <lb/>
            num _DF_, & </s>
            <s xml:id="echoid-s5413" xml:space="preserve">ſinum _HI_. </s>
            <s xml:id="echoid-s5414" xml:space="preserve">Cum ergo priores tres magnitu-
              <lb/>
            dines ſint cognitæ, (nempe arcus _DE_, quo arcus _BE_, arcũ
              <lb/>
            _BD_, ſuperat; </s>
            <s xml:id="echoid-s5415" xml:space="preserve">& </s>
            <s xml:id="echoid-s5416" xml:space="preserve">recta _EK_, qua ſinus _EG_, ſinum _DF_,
              <lb/>
            excedit; </s>
            <s xml:id="echoid-s5417" xml:space="preserve">nec non arcus _DH_, quo arcus _BH_, cuius ſinus
              <lb/>
            queritur, ſuperat arcum _BD_.) </s>
            <s xml:id="echoid-s5418" xml:space="preserve">cognita etiam erit quarta magnitudo, id eſt, recta _HL_,
              <lb/>
            quæ addenda eſt ſinui _DF_, vt fiat ſinus _HI_. </s>
            <s xml:id="echoid-s5419" xml:space="preserve">Conſtat igitur, ſinus per regulam pro-
              <lb/>
            portionum inuentos ſenſibiliter non differre à veris ſinubus, præſertim quando arcus
              <lb/>
            _DE_, quo arcus cognitorum ſinuuminter ſe differunt, valde exiguus eſt, ita vt à recta
              <lb/>
            linea vix differat.</s>
            <s xml:id="echoid-s5420" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s5421" xml:space="preserve">_MAGNVM_ quoque compendium in hoc negotio nobis afferet propoſitio octaua.
              <lb/>
            </s>
            <s xml:id="echoid-s5422" xml:space="preserve">
              <note position="left" xlink:label="note-140-02" xlink:href="note-140-02a" xml:space="preserve">Compédiũ
                <lb/>
              miri ficum
                <lb/>
              pro inuen-
                <lb/>
              rione pluti
                <lb/>
              morum ſi-
                <lb/>
              nuum.</note>
            Ex ea enim plurimos ſinus ex alijs inuentis per ſolam additionem, ſubtractionemue
              <lb/>
            nanciſcemur. </s>
            <s xml:id="echoid-s5423" xml:space="preserve">_N_am ſi ſinum cuiuſuis arcus, qui maior non ſit, quàm grad. </s>
            <s xml:id="echoid-s5424" xml:space="preserve">_30_. </s>
            <s xml:id="echoid-s5425" xml:space="preserve">addamus
              <lb/>
            ſinui arcus, qui ab arcugrad. </s>
            <s xml:id="echoid-s5426" xml:space="preserve">_60_. </s>
            <s xml:id="echoid-s5427" xml:space="preserve">ſuperatur ſumpto illo arcu, componemus ſinum arcus
              <lb/>
            qui eodemillo arcu aſſumpto arcũgrad. </s>
            <s xml:id="echoid-s5428" xml:space="preserve">_30_. </s>
            <s xml:id="echoid-s5429" xml:space="preserve">ſuperat: </s>
            <s xml:id="echoid-s5430" xml:space="preserve">propterea quod differentia inter
              <lb/>
            ſinus duorum horum arcuum maiorum æqualis eſt ſinui arcus illius aſſumpti, qui ma
              <lb/>
            ior nõ ponitur, quàm grad. </s>
            <s xml:id="echoid-s5431" xml:space="preserve">_30_. </s>
            <s xml:id="echoid-s5432" xml:space="preserve">vt ibi demonſtrauimus. </s>
            <s xml:id="echoid-s5433" xml:space="preserve">Vt ſi _3461171_. </s>
            <s xml:id="echoid-s5434" xml:space="preserve">ſinũ arcus grad.
              <lb/>
            </s>
            <s xml:id="echoid-s5435" xml:space="preserve">_20_. </s>
            <s xml:id="echoid-s5436" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s5437" xml:space="preserve">_15_. </s>
            <s xml:id="echoid-s5438" xml:space="preserve">adijciamus ad _6394390_. </s>
            <s xml:id="echoid-s5439" xml:space="preserve">ſinum arcus grad. </s>
            <s xml:id="echoid-s5440" xml:space="preserve">_39_. </s>
            <s xml:id="echoid-s5441" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s5442" xml:space="preserve">_45._</s>
            <s xml:id="echoid-s5443" xml:space="preserve">. </s>
            <s xml:id="echoid-s5444" xml:space="preserve">qui abarcu grad. </s>
            <s xml:id="echoid-s5445" xml:space="preserve">
              <lb/>
            _60_. </s>
            <s xml:id="echoid-s5446" xml:space="preserve">ſuperatur dicto arcu grad. </s>
            <s xml:id="echoid-s5447" xml:space="preserve">_20_. </s>
            <s xml:id="echoid-s5448" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s5449" xml:space="preserve">_15_. </s>
            <s xml:id="echoid-s5450" xml:space="preserve">conficiemus _9855561_. </s>
            <s xml:id="echoid-s5451" xml:space="preserve">ſinum arcus grad. </s>
            <s xml:id="echoid-s5452" xml:space="preserve">
              <lb/>
            _80_. </s>
            <s xml:id="echoid-s5453" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s5454" xml:space="preserve">_15_. </s>
            <s xml:id="echoid-s5455" xml:space="preserve">qui arcum gra. </s>
            <s xml:id="echoid-s5456" xml:space="preserve">_60_. </s>
            <s xml:id="echoid-s5457" xml:space="preserve">eodem arcu grad. </s>
            <s xml:id="echoid-s5458" xml:space="preserve">_20_. </s>
            <s xml:id="echoid-s5459" xml:space="preserve">Min _15_. </s>
            <s xml:id="echoid-s5460" xml:space="preserve">ſuperat. </s>
            <s xml:id="echoid-s5461" xml:space="preserve">Sic ſi _5000000_. </s>
            <s xml:id="echoid-s5462" xml:space="preserve">
              <lb/>
            ſinum arcus grad. </s>
            <s xml:id="echoid-s5463" xml:space="preserve">_30_. </s>
            <s xml:id="echoid-s5464" xml:space="preserve">addamus ſinui _5000000_. </s>
            <s xml:id="echoid-s5465" xml:space="preserve">arcus grad _30_. </s>
            <s xml:id="echoid-s5466" xml:space="preserve">quem arcus grad. </s>
            <s xml:id="echoid-s5467" xml:space="preserve">_60_. </s>
            <s xml:id="echoid-s5468" xml:space="preserve">
              <lb/>
            fuperat dicto illo arcu grad. </s>
            <s xml:id="echoid-s5469" xml:space="preserve">_30_. </s>
            <s xml:id="echoid-s5470" xml:space="preserve">componemus _10000000_. </s>
            <s xml:id="echoid-s5471" xml:space="preserve">ſinum arcus grad. </s>
            <s xml:id="echoid-s5472" xml:space="preserve">_90_. </s>
            <s xml:id="echoid-s5473" xml:space="preserve">qui
              <lb/>
            arcum grad. </s>
            <s xml:id="echoid-s5474" xml:space="preserve">_60_. </s>
            <s xml:id="echoid-s5475" xml:space="preserve">eodem illo arcu aſſumpto grad. </s>
            <s xml:id="echoid-s5476" xml:space="preserve">_30_. </s>
            <s xml:id="echoid-s5477" xml:space="preserve">ſuperat.</s>
            <s xml:id="echoid-s5478" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s5479" xml:space="preserve">_ITEM_ ſi ſinum cuiuslibet arcus, qui arcu grad. </s>
            <s xml:id="echoid-s5480" xml:space="preserve">_30_. </s>
            <s xml:id="echoid-s5481" xml:space="preserve">maior non ſit, ſubducamus ex
              <lb/>
            ſinu arcus, qui arcum grad _60_. </s>
            <s xml:id="echoid-s5482" xml:space="preserve">ſumpto illo arcu ſuperat, relinquetur ſinus arcus, qui
              <lb/>
            eodem illo arcu aſſumpto ab arcu grad. </s>
            <s xml:id="echoid-s5483" xml:space="preserve">_60_. </s>
            <s xml:id="echoid-s5484" xml:space="preserve">ſuperatur. </s>
            <s xml:id="echoid-s5485" xml:space="preserve">Vt ſi _3502075_. </s>
            <s xml:id="echoid-s5486" xml:space="preserve">ſinum arcus
              <lb/>
            grad. </s>
            <s xml:id="echoid-s5487" xml:space="preserve">_20_. </s>
            <s xml:id="echoid-s5488" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s5489" xml:space="preserve">_30_ detrahamus ex _9862856_. </s>
            <s xml:id="echoid-s5490" xml:space="preserve">ſinu arcus grad _80_. </s>
            <s xml:id="echoid-s5491" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s5492" xml:space="preserve">_30_. </s>
            <s xml:id="echoid-s5493" xml:space="preserve">qui arcum
              <lb/>
            grad. </s>
            <s xml:id="echoid-s5494" xml:space="preserve">_60_. </s>
            <s xml:id="echoid-s5495" xml:space="preserve">dicto arcu grad. </s>
            <s xml:id="echoid-s5496" xml:space="preserve">_20_. </s>
            <s xml:id="echoid-s5497" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s5498" xml:space="preserve">_30_. </s>
            <s xml:id="echoid-s5499" xml:space="preserve">ſuperat, reliquus erit _6360781_. </s>
            <s xml:id="echoid-s5500" xml:space="preserve">ſinus arcus gra.
              <lb/>
            </s>
            <s xml:id="echoid-s5501" xml:space="preserve">_39_. </s>
            <s xml:id="echoid-s5502" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s5503" xml:space="preserve">_30_. </s>
            <s xml:id="echoid-s5504" xml:space="preserve">quem arcus grad. </s>
            <s xml:id="echoid-s5505" xml:space="preserve">_60_. </s>
            <s xml:id="echoid-s5506" xml:space="preserve">eodemillo arcu grad. </s>
            <s xml:id="echoid-s5507" xml:space="preserve">_20_. </s>
            <s xml:id="echoid-s5508" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s5509" xml:space="preserve">_30_ ſuperat.</s>
            <s xml:id="echoid-s5510" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s5511" xml:space="preserve">_RVRSVS_, ſi ex ſinu cuiuſuis arcus, qui maior ſit arcu grad. </s>
            <s xml:id="echoid-s5512" xml:space="preserve">_60_. </s>
            <s xml:id="echoid-s5513" xml:space="preserve">detrahatur ſinus
              <lb/>
            arcus, quitanto minor ſit arcu grad. </s>
            <s xml:id="echoid-s5514" xml:space="preserve">_60_. </s>
            <s xml:id="echoid-s5515" xml:space="preserve">quanto ille maior eſt, relinquetur ſinus ar-
              <lb/>
            cus, quo vteruis illorũ ab arcu grad. </s>
            <s xml:id="echoid-s5516" xml:space="preserve">_60_. </s>
            <s xml:id="echoid-s5517" xml:space="preserve">differt. </s>
            <s xml:id="echoid-s5518" xml:space="preserve">Vt ſi ex _9781476_. </s>
            <s xml:id="echoid-s5519" xml:space="preserve">ſinu arcus gra. </s>
            <s xml:id="echoid-s5520" xml:space="preserve">_78_.
              <lb/>
            </s>
            <s xml:id="echoid-s5521" xml:space="preserve">auferatur _6691306_. </s>
            <s xml:id="echoid-s5522" xml:space="preserve">ſinus arcus gra. </s>
            <s xml:id="echoid-s5523" xml:space="preserve">_42_. </s>
            <s xml:id="echoid-s5524" xml:space="preserve">reliquus erit _3090170_. </s>
            <s xml:id="echoid-s5525" xml:space="preserve">ſinus arcus grad. </s>
            <s xml:id="echoid-s5526" xml:space="preserve">_18_. </s>
            <s xml:id="echoid-s5527" xml:space="preserve">
              <lb/>
            quo vterq; </s>
            <s xml:id="echoid-s5528" xml:space="preserve">illorũ ab arcu grad. </s>
            <s xml:id="echoid-s5529" xml:space="preserve">_60_. </s>
            <s xml:id="echoid-s5530" xml:space="preserve">differt. </s>
            <s xml:id="echoid-s5531" xml:space="preserve">Quæ omnia ex dicta propeſ. </s>
            <s xml:id="echoid-s5532" xml:space="preserve">_8_. </s>
            <s xml:id="echoid-s5533" xml:space="preserve">colliguntur.</s>
            <s xml:id="echoid-s5534" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s5535" xml:space="preserve">_ITAQVE_ ſatis eſt, vt inueniantur per regulam proportionum ſinus ommum ar-
              <lb/>
            cuum à principio quadrantis vſque ad arcum grad. </s>
            <s xml:id="echoid-s5536" xml:space="preserve">_30_. </s>
            <s xml:id="echoid-s5537" xml:space="preserve">Si enim ex his eliciantur ſinus
              <lb/>
            complementorum, & </s>
            <s xml:id="echoid-s5538" xml:space="preserve">ex his inuentis detrahãtur priores illi ſinus, reli qui erunt ſinus
              <lb/>
            omnium arcuum inter arcum grad. </s>
            <s xml:id="echoid-s5539" xml:space="preserve">_30_ & </s>
            <s xml:id="echoid-s5540" xml:space="preserve">arcum grad. </s>
            <s xml:id="echoid-s5541" xml:space="preserve">_90_. </s>
            <s xml:id="echoid-s5542" xml:space="preserve">Item ſicogniti eſſent ſinus
              <lb/>
            arcuũ omniũ ab arcu grad. </s>
            <s xml:id="echoid-s5543" xml:space="preserve">_30_. </s>
            <s xml:id="echoid-s5544" xml:space="preserve">vſq; </s>
            <s xml:id="echoid-s5545" xml:space="preserve">ad finem quadrantis, & </s>
            <s xml:id="echoid-s5546" xml:space="preserve">ſinus omniũ arcuum, </s>
          </p>
        </div>
      </text>
    </echo>
Impressum