Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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tem arcus
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. </
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<
s
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<
s
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">proportio ſecantis arcus CF, ad ſecantem arcus
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F,
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componatur ex proportione ſecantis arcus CF, ad ſinum totum, & </
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<
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ſinus totius ad ſecantem arcus
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; </
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<
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">quòd ſinus totus ſit medius inter has ſecãtes: </
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vt ſinus arcus
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, ad ſinum arcus
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, ita ſecans arcus CF, ad ſecantem arcus
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;
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</
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<
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xml:space
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">& </
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<
s
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xml:space
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">permutando, vt ſinus arcus
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, ad ſecantem arcus CF, ita ſinus arcus AC, ad
<
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ſecantem arcus
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. </
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<
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">Quoniam eſt, vt ſinus arcus
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, ad ſinum arcus
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D, ita ſinus ar-
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<
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xlink:label
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xml:space
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">40. huius.</
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cus
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, ad ſinum arcus
<
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; </
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<
s
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xml:space
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">hoc eſt, permutando, vt ſinus arcus
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, ad ſinum ar-
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cus
<
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, ita ſinus arcus
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D, ad ſinum arcus
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: </
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ſt autemita ſecans arcus
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,
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<
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">22. Sinuũ.</
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ad ſecantem arcus
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F, vt ſinus
<
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D, qui complementum eſt poſterioris arcus
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, ad
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ſinum arcus
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, qui complementum eſt arcus prioris
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; </
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<
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">erit quoque, vt ſinus ar-
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cus
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, ad ſinum arcus
<
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, ita ſecans arcus CF, ad ſecantem arcus
<
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. </
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<
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<
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t per-
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mutando, vt ſinus arcus
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, ad ſecantem arcus CF, ita ſinus arcus
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, ad ſecan-
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tem arcus
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. </
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<
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<
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">EADEM hæc demonſtratio locum etiam habet, licet duo puncta aſſumpta ſint ad
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diuerſas partes puncti ſectionis. </
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<
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">Secent enim rurſum ſeſe duo circuli maximi
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,
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in D; </
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<
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<
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">à punctis
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, arcus
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, ducantur ad
<
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, arcus perpendiculares
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.
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</
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D, ad ſecantem complementi
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arcus
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, vt est ſinus arcus DF, ad ſecantem comple-
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<
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420-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/420-01
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menti arcus
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. </
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<
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">Nam quoniam eſt, vt ſinus arcus ED,
<
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<
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">40. huius.</
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ad ſinum arcus
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, ita ſinus arcus DF, ad ſinum arcus
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<
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; </
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<
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<
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">permutando, vt ſinus arcus
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D, ad ſinum arcus
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DF, ita ſinus arcus
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, ad ſinum arcus
<
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; </
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<
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ſinus arcus
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, ad ſinum arcus
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, ita eſt ſecans com-
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<
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plementi arcus
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, ad ſecantem complementi arcus
<
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:
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</
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<
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">erit quoque, vt ſinus arcus
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D, ad ſinum arcus DF, ita
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ſecans complementi arcus
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, ad ſecantem complementi
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arcus
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; </
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<
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<
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">permutando, vt ſinus arcus
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D, ad ſecantem complementi arcus
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,
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ita ſinus arcus DF, ad ſecantem complementi arcus
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. </
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<
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CF, nulla fiat mentio, ne nouam figuram cogeremur extruere.</
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<
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<
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">IN omni triangulo ſphærico, ſinus cuiuſlibet
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arcus ad ſinum anguli, quem ſubtendit, eandem
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habet proportionem, quam ſinus vtriuſque reli-
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quorum arcuum ad ſinũ anguli, quem ſubtendit.</
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<
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<
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<
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cus AB, ad ſinum anguli C, quem ſubtendit, vt eſt ſinus arcus AC, ad ſinum
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auguli B, quem ſubtendit, & </
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<
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">vt ſinus arcus BC, ad ſinum anguli A, quem
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ſubtendit. </
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<
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<
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">eruntq́ue propterea
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<
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huius.</
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omnes arcus quadrantes. </
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<
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