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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