Cavalieri, Buonaventura - Geometria indivisibilibvs continvorvm : noua quadam ratione promota

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10181LIBER I. terminans in ambientem ſuperficiem bifariam diuidetur ab ipſa, BD,
11Ex antec. vtin, N; Sie oſtendemus, BD, diuidere cæteras omnes ipfi, EM,
æquidiſtantes in ſuperficiem ambientem hinc inde terminatas, &
quia, BD, ſecat, EM, adangulos rectos, cæteras omnes iam di-
ctas bifariam, & ad angulos rectos ſecabit, igitur tunc figura, BED
M, erit circa axem, BD, ſiue in ſolido rotundo, ſiue in cono: Siau-
tem triangulus, APQ, non tranſeat per ductam ipſi plano perpen-
dicularem, tunc eodem modo, quoſupra oſtendemus, BD, ſecare
omnes ęquidiſtantes ipſi, EM, bifariam, & quia triangulus, APQ,
non tranſit per perpendicularem baſi, neque erit erectus ipſi baſi, P
EQM, ergo angulus, EDB, non erit rectus, nam ſi eſſet rectus,
cum ſit etiam rectus, EDP, planum circuli, PEQM, eſſet erectum
triangulo, APQ, & ille huic, quod eſt contra ſuppoſitum, igitur,
224. Vndec.
Elem. BD, ſecabit, EM, & conſequenter cæteras iam dictas illi æquidi-
ſtantes bifariam, & ad angulos non rectos, igitur figura, EBM, tunc
erit circa diametrum, & erit diameter ipſa, BD, ſiue axis, in ſupra-
dicto caſu tum in cono, tum etiam in ſolido rotundo, quod erat oſten-
dendum.

COROLLARIVM.

_H_Inc colligitur in cono, ſi triangulus per axem ductus ſit erectus
baſi, fieri dictam figuram circa axem; ſi verò non ſit erectus, ſed
inclinatus eidem, fieri figuram circa diametrum; in ſolido rotundo au-
tem fieri ſemper figuram circa axem.

THEOREMA XXXV. PROPOS. XXXVIII.

SI conus ſecetur plano per axem, ſecetur deinde altero pla-
no ſecante baſim coni ſecundum rectam lineam, quę ad
baſim trianguli per axem ſit perpendicularis, cuius & trian-
guli per axem cõmunis ſectio ſit parallela vni laterum trian-
guli per axem; quadrata ordinatim applicatarum ad axim,
vel diametrum figurę in cono ſecundo plano productę, æqui-
diſtantium eiuſdem, & baſis communi ſe ctioni erunt inter fe,
vt abíciſſæ per eaidem ordinatim applicatas verſus verticem
ſumptæ ab eiſdem axibus, vel diametris iam dictis.

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Scan	Original
101	81
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105	85
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130	110

Scan	Original
101	81
102	82
103	83
104	84
105	85
106	86
107	87
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109	89
110	90
111	91
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113	93
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