Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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ferrentur ex chordis omnium arcuũ maiorũ, quàm grad. </
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<
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<
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mnium arcuum à principio ſemicirculi vſque ad arcum grad. </
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<
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<
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<
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nium arcuum à principio ſemicirculi vſque ad arcum grad. </
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<
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<
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<
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chordæ omnium arcuum minorum, quàm 60. </
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<
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<
s
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quàm grad. </
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<
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<
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xml:space
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quàm grad. </
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<
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<
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ſinus oium
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a@cuum ex
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cho@dis in-
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ueniantur.</
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dæ omnium arcuum, qui ſecontinuè Minutis 2. </
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<
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erunt ſinus omnium arcuum per ſingula Minuta progredientiũ, vt ex defin. </
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<
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<
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Ptolemæum & </
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<
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<
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xml:space
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<
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">Rectiꝰ face
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re eos, ꝗ @a
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bulã ſinuũ
<
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cõſtruunt,
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quàm qu@
<
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chordarũ.</
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ſi Quadrans circuli per ſingula Minuta extendatur: </
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<
s
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xml:space
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">at pro chordis neceſſe eſt totum
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ſemicir culum per Minuia ſingula extendere: </
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<
s
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xml:space
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quàm tabula ſinuum. </
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<
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">Taceo, multo expeditiorem, breuiorem, fac@ lioremq́; </
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<
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vjum in rebus Aſtronomicis, & </
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<
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xml:space
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">Geometricis, quàm chordarum: </
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<
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qui ſeſe in bu@@ ſmodi vſu exercue; </
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<
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<
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xml:space
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">QVEMADMODVM autem ſinuũ differentiæ ſenſim decreſcunt à principie
<
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<
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xlink:label
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">Differẽ@iæ
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chordarũ à
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prin c@pio
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ſemici@culi
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vſq; ad e@@s
<
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finé ſen ſim
<
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decreſcunt@
<
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ita vt chor-
<
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dæ minorũ
<
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arcuũmaio
<
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res habeant
<
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differentias
<
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quàm chor
<
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dæ arcuum
<
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maiorũ dũ
<
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modo arcꝰ
<
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habeãt dif-
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ferentias æ
<
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quales.</
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quad@antis vſque ad eius finem; </
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<
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">ita vt, poſitis pluribus arcubus æqualiter ſeſe exc@-
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dentibus, minorum ſinus habeani maiores differentias, quàm ſinus maiorum, vt in co-
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roll. </
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<
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<
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">1 oſtendimus@ ita quoque chordarum differentiæ paulatim decreſcunt à
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principio ſemicirculiad eius finem vſq. </
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<
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">Nam poſitis pluribus arcubus, quorum æqua-
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les ſint differentiæ, minorum chordæ maiores habent differentias, quàm chordæ ma-
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iorum. </
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<
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, arcus AB, AC,
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AD, quorum differentiæ
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C, CD, æquales ſint,
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198-01
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/198-01
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chordæ autem eorundem AB, AC, AD: </
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turq; </
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<
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, chordæ AB, æqualis; </
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">& </
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<
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chordæ AC, æqualis. </
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<
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<
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chordas AB, AC, maiorem eſſe, quàm GD, diffe-
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rentiam inter chordas AC, AD. </
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<
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cta AH, æquali ipſi AF, vel ipſi AB, iunctiſque re-
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ctis BC, CD, CG, CH: </
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<
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lateribus HA, AC, æqualia ſunt, angulosq́; </
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<
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tinent æquales ad A, propter æquales arcus BC, CD; </
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<
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<
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<
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les. </
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<
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<
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<
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tur & </
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<
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">recta CH, rectæ CD, æqualis erit. </
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<
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">Anguli ergo CHD, CDH, æquales quo-
<
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<
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xlink:label
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que erunt: </
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<
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">qui cum ſint duobus rectis minores; </
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<
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<
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<
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<
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xlink:label
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">17.primi.</
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cto erit vterque angulorum ACG,
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, acutus: </
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<
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æqu@les ſunt ob æquales rectas AC, AG. </
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<
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">Quia igitur in triangulo CGH, anguli
<
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<
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xlink:label
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">5.primi.</
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ad G, H, acuti ſunt; </
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<
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">fit, vt CI, ducta ad DH, perpendicularis cadat intra triangu-
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lum in r@ctam GH, vt in ſeholio propoſ. </
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<
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<
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<
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<
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<
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duo anguli CHI, CIH, trianguli CHI, duobus angulis CDI, CID, æquales
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ſunt, ſuntq; </
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<
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xml:space
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">duo latera CH, CD, æqualibus rectis angulis oppoſita æqualia, vel
<
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certe latus CI, commune eſt; </
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<
s
xml:id
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xml:space
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">erunt quoque latera IH, ID, æqualia. </
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<
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xml:space
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">Cum ergo ID,
<
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<
note
position
="
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xlink:label
="
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xlink:href
="
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xml:space
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">26.primi.</
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maior ſit, quàm GD, erit quoq; </
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<
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">HI, & </
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<
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">à fortiori
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style
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, maior, quam GD. </
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<
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xml:id
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">Eſt au-
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tem HG, ipſi FC, æqualis, propterea quòd & </
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<
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xml:id
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xml:space
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">rectæ AC, AG, inter ſe, & </
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<
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">rectæ
<
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style
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">Af</
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>
,
<
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AH, inter ſe æquales ſunt. </
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<
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">Igitur & </
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<
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">FC, differentia chordarum AB, AC, maior
<
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erit, quàm GD, differentia chordarum AC, AD. </
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>
<
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">Quod eſt propoſitum.</
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