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

Scan	Original
81	61
82	62
83	63
84	64
85	65
86	66
87	67
88	68
89	69
90	70
91	71
92	72
93	73
94	74
95	75
96	76
97	77
98	78
99	79
100	80
101	81
102	82
103	83
104	84
105	85
106	86
107	87
108	88
109	89
110	90

10787LIBERI.

THEOREMA XLII. PROPOS. XLV.

SI ſphæroides, vel conoides parabolicum, ſeu hyperboli-
cum ſecentur quomodocumq; planis parallelis ad axem
rectis, ſiue inclinatis, communes ſectiones ſimiles erunt, &
diametri eiuſdem rationis erunt omnes in eadem figura per
axem tranſeunte, rectè eaſdem ſecante.

Hæc colliguntur in Coroll. 2. Prop. 15. lib. Arch. de Conoidibus,
& Sphæroidibus, & ibidem etiam à Federico Commandino in ſuis in
Arch. Comment. demonſtrantur. Hęc verò circa ipſas ſectionum fi-
guras verificari pariter manifeſtum eſt, hoc autem dico, vtor enim
ijſdem ſectionum nominibus tamquam figuras ſub ipſis comprehen-
fas ſignificantibus.

THEOREMA XLIII. PROPOS. XLVI.

EXpoſitis prædictis coni ſectionibus, circulo nempè, El-
lipſi, Parabola, & Hyperbola, ſi, quę ad earundem axes
ordinatim applicantur, diametri eſſe intelligantur circulo-
rum ab ipſis deſcriptorum, qui ſint erecti pianis ipſarum figu-
rarum, periphærię deſcriptorum circulorum in ſectione, quę
eſt circulus, erunt omnes in ſuperficie ſphęrę, in Ellipſi verò
in ſuperficie ſphæroidis, in Parab. in ſuperficie conoidis pa-
rabolici, & in Hyperbola in ſuperficie conoidis Hyperbolici.

Sint prædictę ſectiones figurę

60[Figure 60] ſcilicet, ipſæ, ABCD, earum
axes, AC, vna ex ordinatim ad
axim applicatis, BD, quæ in-
telligatur eſſe diameter ab ea
deſcripti circuli, BNDE. Di-
co circumferentiam, BNDE,
eſſe in dicta ſuperficie. Intelli-
gantur dictę figuræ reuolui circa
ſuos axes, vt ex circulo fiat ſphę-
ra, ex ellipſi ſphæroides, ex pa-
rabola conoides parabolicum,
& ex hyperbola hyperbolicum,
ſecentur autem planis ad axem
rectis, eundem axem ſecantibus in eodem puncto, in quo

Page concordance

Text layer

Text normalization

Search

Scan	Original
81	61
82	62
83	63
84	64
85	65
86	66
87	67
88	68
89	69
90	70
91	71
92	72
93	73
94	74
95	75
96	76
97	77
98	78
99	79
100	80
101	81
102	82
103	83
104	84
105	85
106	86
107	87
108	88
109	89
110	90

Scan	Original
81	61
82	62
83	63
84	64
85	65
86	66
87	67
88	68
89	69
90	70
91	71
92	72
93	73
94	74
95	75
96	76
97	77
98	78
99	79
100	80
101	81
102	82
103	83
104	84
105	85
106	86
107	87
108	88
109	89
110	90

Scan	Original
81	61
82	62
83	63
84	64
85	65
86	66
87	67
88	68
89	69
90	70
91	71
92	72
93	73
94	74
95	75
96	76
97	77
98	78
99	79
100	80
101	81
102	82
103	83
104	84
105	85
106	86
107	87
108	88
109	89
110	90