Clavius, Christoph
,
Geometria practica
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LIBER OCTAVVS.
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1. </
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les. </
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<
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demptis OE, NE, æqualibus ex æqualibus OH, NI, reliquæ re-
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ctæ EH, EI, æquales ſunt: </
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<
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cti, cum HEI, ſit rectus; </
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<
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<
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<
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I, in Iſoſcele KIH, æquales. </
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in pentagono æquales ſunt.</
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<
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<
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cũ latera EL, EI, lateribus EL,
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E H, ſintæqualia, contineantque angulos æquales
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ſemirectos; </
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<
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<
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<
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guli ad L, ideoque recti. </
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<
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">Ex quo efficitur, rectas AB, HI, eſſe parallelas: </
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<
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"> quod etiam conſtat ex
<
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quod alterni anguli INA, NIH, æquales ſint, nimi-
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">27. primi.</
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rum ſemirecti. </
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<
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">Hinc etiam ſequitur, rectam C D L,
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productam cadere in angulum K, diuidereque eum
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bifariam. </
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<
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">Si enim dicatur non cadere in K, diuidet perpendicularis ex K, ad HI, demiſſa baſem Iſoſce-
<
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<
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primi.</
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lis KIH, bifariam in alio puncto, quam in L, quod eſt abſurdum. </
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<
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tera KI, KL, lateribus KH, KL, æqualia ſunt, & </
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<
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lis: </
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<
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</
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<
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<
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ita præmiſsis, demonſtrabimusiam pentagonum ABHKI, non eſſe æ-
<
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primi.</
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quiangulum, hocmodo. </
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<
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<
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">anguli in pentagono quolibet, ſiue ſit ę- quilaterum, & </
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<
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<
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">rectis, hoc eſt, gra. </
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<
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</
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<
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">quibus diuiſis per 5. </
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<
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">efficitur vnus angulus pentagoni æquilateri, & </
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<
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grad. </
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<
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<
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quam grad. </
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<
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<
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">& </
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<
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">vterlibet duorum H, I, minor, & </
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<
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">angulus K, maior quolibet
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reliquorum quatuor. </
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<
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">vt oſtendemus. </
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<
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gulum. </
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<
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<
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<
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poſito ſinu toto AB, 10000000. </
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<
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">eius ſemiſsis BM, ſinus vide-
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licet grad. </
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<
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<
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">eſt 5000000. </
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<
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">cui ſi addatur MO, id eſt, ME, ſinus verſus grad. </
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<
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</
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<
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<
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">fiet tota BO, 6339746. </
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<
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">Quia ergo in triangulo BHO, duo la-
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tera dantur BH, 10000000. </
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<
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">& </
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<
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">BO, 6339746. </
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>
<
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">vna cum angulo O, grad. </
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<
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<
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">15. triang. re-
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ctil.</
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>
non cum ſpecie anguli H, qui ſupra oſtenſus fuit recto minor: </
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<
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Vt lat{us} B H, \\ 10000000. # ad 707 068. ſinum an- \\ guli O, g ad. 45. # Italat{us} B O, \\ 6339746. # ad aliud,
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<
s
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">inuenietur ſinus anguli BHO, 4482877 {1/2}. </
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<
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ipſum angulum 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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>
<
s
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ma angulorum H, O, grad. </
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<
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<
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<
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<
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">quæ ſumma dempta ex duobusrectis, id
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eſt, ex 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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gulus A, B, in pentagono maior eſt verò angulo pentagoni 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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ducta BP, ad HI, perpendiculari, ſi iterum ſtatuatur BH, finus to-
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tus 10000000. </
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>
<
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">erit HP, 3150970. </
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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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">quirelin quitur, ſi
<
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rectus angulus A B P, grad 90. </
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>
<
s
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xml:space
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">detrahatur ex angulo A B H, inuento 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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">Si igitur addatur PL. </
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>
<
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">5000000. </
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>
<
s
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"> cum ſit æqualis ipſi BM, ſemiſsi
<
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xml:space
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">34. primi.</
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>
totius, fiet tota HL, ſinus anguli HKL, 8150970. </
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<
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xml:space
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">Ac propterea angulus ipſe erit
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grad. </
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<
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<
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<
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>
<
s
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">qui duplicatus dabit totum angulum H K I, 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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"
xml:space
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">maiore verò angulo pentagoni grad. </
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>
<
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">108.</
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>
<
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