Angeli, Stefano degli, Miscellaneum hyperbolicum et parabolicum : in quo praecipue agitur de centris grauitatis hyperbolae, partium eiusdem, atque nonnullorum solidorum, de quibus nunquam geometria locuta est, parabola nouiter quadratur dupliciter, ducuntur infinitarum parabolarum tangentes, assignantur maxima inscriptibilia, minimaque circumscriptibilia infinitis parabolis, conoidibus ac semifusis parabolicis aliaque geometrica noua exponuntur scitu digna

Table of contents

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[41.] PROPOSITIO XIX.
Page: 69 (57)
[42.] SCHOLIVM I.
Page: 70 (58)
[43.] SCHOLIVM II.
Page: 71 (59)
[44.] PROPOSITIO XX.
Page: 72 (60)
[45.] SCHOLIVM.
Page: 74 (62)
[46.] PROPOSITIO XXI.
Page: 76 (64)
[47.] PROPOSITIO XXII.
Page: 78 (66)
[48.] SCHOLIVMI.
Page: 80 (68)
[49.] SCHOLIVM II.
Page: 82 (70)
[50.] PROPOSITIO XXIII.
Page: 85 (73)
[51.] PROPOSITIO XXIV.
Page: 86 (74)
[52.] PROPOSITIO XXV.
Page: 86 (74)
[53.] PROPOSITIO XXVI.
Page: 88 (76)
[54.] SCHOLIVM I.
Page: 91 (79)
[55.] SCHOLIVM II.
Page: 93 (81)
[56.] SCHOLIVM III.
Page: 98 (86)
[57.] PROPOSITIO XXVII.
Page: 99 (87)
[58.] ALITER.
Page: 101 (89)
[59.] PROPOSITIO XXVIII.
Page: 102 (90)
[60.] SCHOLIVMI.
Page: 104 (92)
[61.] SCHOLIVM II.
Page: 104 (92)
[62.] PROPOSITIO XXIX.
Page: 107 (95)
[63.] SCHOLIV M.
Page: 109 (97)
[64.] PROPOSITIO XXX.
Page: 125 (113)
[65.] SCHOLIVM I.
Page: 128 (116)
[66.] SCHOLIVM II.
Page: 129 (117)
[67.] PROPOSITIO XXXI. Semifuſi parabolici cuiuſcunque, centrum grauitatis reperire.
Page: 131 (119)
[68.] SCHOLIVM.
Page: 135 (123)
[69.] PROPOSITIO XXXII.
Page: 138 (126)
[70.] SCHOLIV M.
Page: 140 (128)
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page |< < (33) of 232 > >|
4533
SCHOLIVM.
Tria autem, quæ collecta ſunt in quamplurimis
propoſitionibus lib. 3. colligentur etiam nunc. Nam
primò, tam ſuper D E, quam ſupra A B E, intelle-
ctis cylindricis rectis æquealtis reſectis diagonaliter
plano tranſeunte per E B, & per latus oppoſitum ip-
ſi D A, colligentur cubationes amborum truncorum
cylindrici ſuper ſemihyperbola exiſtentis, cumhac
tamen diuerſitate; quod cubatio trunci ſiniſtri dabi-
tur ſemota hyperbolæ quadratura; quia ſine tali qua-
dratura datur ratio D C, cylindri ad conoides
A B C; ſecùs dicendum de cubatione trunci dexte-
ri, quæ non habetur niſi ſuppoſita quadratura. Se-
cundum eſt (quadratura ſuppoſita) ratio cylindri ex
D E, circa D A, ad annulum ſtrictum ex ſemihyper-
bola A B E, circa D A. Tertium eſt ratio conoi-
dis, & prædicti ſolidi ad inuicem, pariter ſuppoſita
quadratura.
Sed antequam vlterius progrediamur, ſicuti plu-
ribus modis patefacta eſt ratio cylindri circumſcri-
pti ad conoides, ſic non erit inutile aſſignare centrum
grauitatis conoidis. Sit ergo.
PROPOSITIO XIII.
Centrum grauitatis conoidis hyperbolici ſic diuidit d uode
cimam partem diametri eiuſdem ordine quartam à

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