Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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16. </
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<
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vſque ad arcum grad. </
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<
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<
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<
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</
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<
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Min. </
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<
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<
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maiorum adhuc arcuum, nempe grad. </
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<
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<
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arcũ gra. </
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<
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<
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78 Min 45 ſemiſſem quadrantis excedit, duplus eſt arcus grad. </
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ius tangens vltimo loco inuenta ſuit. </
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quàm grad. </
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<
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rurſus tangentem, & </
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<
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">illorum, qui minuta numero paria compre-
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hendat, in vnam colligamus ſummá, inueniemus tágentes maiorum adhuc arcuum,
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cuiuſmodi ſunt arcus grad. </
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<
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<
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<
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grad. </
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<
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<
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<
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<
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84. </
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<
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<
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mus eſt eorum, qui minuta numero paria habent, & </
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<
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ſunt. </
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<
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grad. </
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<
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<
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<
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<
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<
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11 quo arcus grad 87 Min 11. </
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<
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84. </
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<
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<
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xml:space
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">Ex his vero repertis conficiemus
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tangentes ſequentium arcuum, vſque ad arcum grad. </
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<
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<
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<
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<
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ius arcus grad. </
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<
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<
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<
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<
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<
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<
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">35. </
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>
<
s
xml:id
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xml:space
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">quadrátis dimidiũ excedit, d@
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plus eſt arcus gra. </
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<
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<
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<
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>
<
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">qui maximus eſt eorũ, qui minuta habent numero paria,
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& </
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>
<
s
xml:id
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">quorum tangentes proxime inuent æ ſunt. </
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>
<
s
xml:id
="
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"
xml:space
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">Per has quoque reperiemus aliorum ar-
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cuum tangentes, vſque ad arcum grad. </
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<
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<
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<
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<
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>
<
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xml:id
="
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">cum huius arcus grad. </
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<
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44. </
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<
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<
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>
<
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">quo arcus grad. </
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<
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s
xml:id
="
echoid-s8211
"
xml:space
="
preserve
">dimidiatum quadrantem excedit, duplus ſit
<
lb
/>
arcus grad. </
s
>
<
s
xml:id
="
echoid-s8212
"
xml:space
="
preserve
">88. </
s
>
<
s
xml:id
="
echoid-s8213
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s8214
"
xml:space
="
preserve
">34. </
s
>
<
s
xml:id
="
echoid-s8215
"
xml:space
="
preserve
">vtpote maximus eorum, qui minuta numero paria continent,
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s8216
"
xml:space
="
preserve
">quorum iam tangentes ſunt cognitæ. </
s
>
<
s
xml:id
="
echoid-s8217
"
xml:space
="
preserve
">Beneficio deinde harum tangentium inuen-
<
lb
/>
tarum eliciemus tangentes aliorum arcuum, vſque ad arcum grad. </
s
>
<
s
xml:id
="
echoid-s8218
"
xml:space
="
preserve
">89. </
s
>
<
s
xml:id
="
echoid-s8219
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s8220
"
xml:space
="
preserve
">38. </
s
>
<
s
xml:id
="
echoid-s8221
"
xml:space
="
preserve
">in-
<
lb
/>
cluſiue; </
s
>
<
s
xml:id
="
echoid-s8222
"
xml:space
="
preserve
">eo quod huius arcus grad. </
s
>
<
s
xml:id
="
echoid-s8223
"
xml:space
="
preserve
">44. </
s
>
<
s
xml:id
="
echoid-s8224
"
xml:space
="
preserve
">Min 38. </
s
>
<
s
xml:id
="
echoid-s8225
"
xml:space
="
preserve
">quo arcus grad. </
s
>
<
s
xml:id
="
echoid-s8226
"
xml:space
="
preserve
">89. </
s
>
<
s
xml:id
="
echoid-s8227
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s8228
"
xml:space
="
preserve
">38. </
s
>
<
s
xml:id
="
echoid-s8229
"
xml:space
="
preserve
">ſemiſſem
<
lb
/>
quadrantis ſuperat, duplus eſt arcus grad. </
s
>
<
s
xml:id
="
echoid-s8230
"
xml:space
="
preserve
">89. </
s
>
<
s
xml:id
="
echoid-s8231
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s8232
"
xml:space
="
preserve
">16. </
s
>
<
s
xml:id
="
echoid-s8233
"
xml:space
="
preserve
">qui maximus eſt eorum, qui
<
lb
/>
minuta numero habent paria, & </
s
>
<
s
xml:id
="
echoid-s8234
"
xml:space
="
preserve
">quorũ tangentes iam factæ ſunt notæ; </
s
>
<
s
xml:id
="
echoid-s8235
"
xml:space
="
preserve
">Hinc aliorum
<
lb
/>
arcuũ tãgentes inquiremus, vſq; </
s
>
<
s
xml:id
="
echoid-s8236
"
xml:space
="
preserve
">ad arcũ gra. </
s
>
<
s
xml:id
="
echoid-s8237
"
xml:space
="
preserve
">89. </
s
>
<
s
xml:id
="
echoid-s8238
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s8239
"
xml:space
="
preserve
">49. </
s
>
<
s
xml:id
="
echoid-s8240
"
xml:space
="
preserve
">quippe qui ſuperet quadrã
<
lb
/>
tis dimidiũ drcugrad. </
s
>
<
s
xml:id
="
echoid-s8241
"
xml:space
="
preserve
">44. </
s
>
<
s
xml:id
="
echoid-s8242
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s8243
"
xml:space
="
preserve
">49 cuius duplus eſt arcus grad. </
s
>
<
s
xml:id
="
echoid-s8244
"
xml:space
="
preserve
">89. </
s
>
<
s
xml:id
="
echoid-s8245
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s8246
"
xml:space
="
preserve
">38. </
s
>
<
s
xml:id
="
echoid-s8247
"
xml:space
="
preserve
">ad quẽ pro-
<
lb
/>
xime peruenimus. </
s
>
<
s
xml:id
="
echoid-s8248
"
xml:space
="
preserve
">At ex his inueſtigabimus tangentes ſequentium arcuum vſq; </
s
>
<
s
xml:id
="
echoid-s8249
"
xml:space
="
preserve
">ad ar-
<
lb
/>
cum grad. </
s
>
<
s
xml:id
="
echoid-s8250
"
xml:space
="
preserve
">89. </
s
>
<
s
xml:id
="
echoid-s8251
"
xml:space
="
preserve
">Min 54 quippe qui quadran
<
unsure
/>
tis medietatẽ ſuperet arcu grad. </
s
>
<
s
xml:id
="
echoid-s8252
"
xml:space
="
preserve
">44. </
s
>
<
s
xml:id
="
echoid-s8253
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s8254
"
xml:space
="
preserve
">
<
lb
/>
54. </
s
>
<
s
xml:id
="
echoid-s8255
"
xml:space
="
preserve
">cuius duplus ſt arcus grad. </
s
>
<
s
xml:id
="
echoid-s8256
"
xml:space
="
preserve
">89. </
s
>
<
s
xml:id
="
echoid-s8257
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s8258
"
xml:space
="
preserve
">48. </
s
>
<
s
xml:id
="
echoid-s8259
"
xml:space
="
preserve
">qui maximus eſt eorum, qui minuta ha-
<
lb
/>
bent numero paria, & </
s
>
<
s
xml:id
="
echoid-s8260
"
xml:space
="
preserve
">quorum tangentes iam ſunt inuentæ. </
s
>
<
s
xml:id
="
echoid-s8261
"
xml:space
="
preserve
">Eadẽ ratione ex his in-
<
lb
/>
ueniemus tangentes ſequentium arcuum vſq@ ad arcum grad. </
s
>
<
s
xml:id
="
echoid-s8262
"
xml:space
="
preserve
">89. </
s
>
<
s
xml:id
="
echoid-s8263
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s8264
"
xml:space
="
preserve
">57 Quia hu-
<
lb
/>
ius arcus grad. </
s
>
<
s
xml:id
="
echoid-s8265
"
xml:space
="
preserve
">44. </
s
>
<
s
xml:id
="
echoid-s8266
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s8267
"
xml:space
="
preserve
">57. </
s
>
<
s
xml:id
="
echoid-s8268
"
xml:space
="
preserve
">quo arcus grad. </
s
>
<
s
xml:id
="
echoid-s8269
"
xml:space
="
preserve
">89. </
s
>
<
s
xml:id
="
echoid-s8270
"
xml:space
="
preserve
">Min 57 quadrantis dimidium ſupe-
<
lb
/>
rat, duplus eſt arcus grad. </
s
>
<
s
xml:id
="
echoid-s8271
"
xml:space
="
preserve
">89. </
s
>
<
s
xml:id
="
echoid-s8272
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s8273
"
xml:space
="
preserve
">54. </
s
>
<
s
xml:id
="
echoid-s8274
"
xml:space
="
preserve
">ad quem proxime peruentum fuit. </
s
>
<
s
xml:id
="
echoid-s8275
"
xml:space
="
preserve
">Denique ex
<
lb
/>
tangente, & </
s
>
<
s
xml:id
="
echoid-s8276
"
xml:space
="
preserve
">ſecante arcus grad. </
s
>
<
s
xml:id
="
echoid-s8277
"
xml:space
="
preserve
">89. </
s
>
<
s
xml:id
="
echoid-s8278
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s8279
"
xml:space
="
preserve
">56. </
s
>
<
s
xml:id
="
echoid-s8280
"
xml:space
="
preserve
">conficiemus tangentem arcus grad. </
s
>
<
s
xml:id
="
echoid-s8281
"
xml:space
="
preserve
">89. </
s
>
<
s
xml:id
="
echoid-s8282
"
xml:space
="
preserve
">
<
lb
/>
Min. </
s
>
<
s
xml:id
="
echoid-s8283
"
xml:space
="
preserve
">58. </
s
>
<
s
xml:id
="
echoid-s8284
"
xml:space
="
preserve
">Et hinc tangentem explor abimus arcus grad. </
s
>
<
s
xml:id
="
echoid-s8285
"
xml:space
="
preserve
">89. </
s
>
<
s
xml:id
="
echoid-s8286
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s8287
"
xml:space
="
preserve
">59. </
s
>
<
s
xml:id
="
echoid-s8288
"
xml:space
="
preserve
">Atq; </
s
>
<
s
xml:id
="
echoid-s8289
"
xml:space
="
preserve
">ita, vt vides,
<
lb
/>
ex tangentibus arcuum vſque ad grad. </
s
>
<
s
xml:id
="
echoid-s8290
"
xml:space
="
preserve
">45. </
s
>
<
s
xml:id
="
echoid-s8291
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s8292
"
xml:space
="
preserve
">ex ſecantibus omnium arcuum qua-
<
lb
/>
drantis perficitur integra tabula tangentium.</
s
>
<
s
xml:id
="
echoid-s8293
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s8294
"
xml:space
="
preserve
">QVOD ſi ſecantem cuiuſcunq; </
s
>
<
s
xml:id
="
echoid-s8295
"
xml:space
="
preserve
">arcus ſubducas ex tangente alterius arcus, qui
<
lb
/>
ex priore illo, ac ſemiſſe complementi eiuſdem componitur, reliquam facies tangen-
<
lb
/>
<
lb
/>
</
s
>
</
p
>
</
div
>
</
text
>
</
echo
>