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

Scan	Original
41	21
42	22
43	23
44	24
45	25
46	26
47	27
48	28
49	29
50	30
51	31
52	32
53	33
54	34
55	35
56	36
57	37
58	38
59	39
60	40
61	41
62	42
63	43
64	44
65	45
66	46
67	47
68	48
69	49
70	50

4828GEOMETRIÆ ad eandem partem ſecantium planorum exiſtent: Et ſi idem
ſecetur planis parallelis quomodocumq; omnibus eiuſdem
lateribus coincidentibus, conceptæ in cylindrico figuræ e-
runt ſimiles, æquales, & ſimiliter poſitæ.

Conſpiciatur figura Propoſit. 10. in qua iam propoſitas ſectiones
habemus, plana enim, AE, ME, tranſeuntia per cylindrici latera

21[Figure 21] ipſum ſecant, & plana, BNG, COF, omni-
bus eiuſdem lateribus coincidunt, & ſunt paral-
lela. Dico ergo figuras, MZH, EIV, eſſe ſi-
miles, & æquales, & ſimiliter poſitas, quod pa-
tet, nam illæ ſunt cylindrici, MHZI, oppoſi-
tæ baſes; idem eodem modo probabitur de figu-
ris, AMH, DVE, & de, ARH, DXE, &
tandem oſtendemus pariter figuras, BNGK, C
OFL, eſſe ſimiles, æquales, & ſimiliter poſitas,
1111. Huius. quia ſunt cylindrici, BF, oppoſitæ baſes, quod
demonſtrandum erat.

COROLLARIV M.

_H_Inc apparet, quamuis figuram planam ex ſectione plani, oppofi-
tis baſibus cylindrici æquidiſtantis, in eo productam, eiſdem op-
poſitis baſibus eſſe ſimilem, æqualem, & ſimiliter poſitam.

THEOREMA X. PROPOS. XIII.

SI quis cylindricus ſecetur plano per latera, deinde ſece-
tur planis oppoſitis eiuſdem baſibus æquidiſtantibus:
Communes ſectiones plani per latera ducti, & planorum ba-
ſibus æquidiſtantium, erunt lineæ, vellatera homologa fi-
gurarum ſimilium, quæ ex ſectione æquidiſtantium plano-
rum in cylindrico effecta in eodem producuntur.

Sit cylindricus, ADM, cuius oppoſitæ baſes, ABC, TDF, ſe-
cetur autem plano vtcumque per latera ducto, quod in eo producat
parallelogrammum, BF, & alio vtcumque plano oppoſitis baſibus
æquidiſtante, quodin eo producat figuram, YNXO, & in paral-
lelogrammo, BF, rectam, NO. Dicorectas, DF, NO, BC, eſſe
lineas, vellatera homologa figurarum, TDF, YNO, ABC,

Page concordance

Text layer

Text normalization

Search

Scan	Original
41	21
42	22
43	23
44	24
45	25
46	26
47	27
48	28
49	29
50	30
51	31
52	32
53	33
54	34
55	35
56	36
57	37
58	38
59	39
60	40
61	41
62	42
63	43
64	44
65	45
66	46
67	47
68	48
69	49
70	50

Scan	Original
41	21
42	22
43	23
44	24
45	25
46	26
47	27
48	28
49	29
50	30
51	31
52	32
53	33
54	34
55	35
56	36
57	37
58	38
59	39
60	40
61	41
62	42
63	43
64	44
65	45
66	46
67	47
68	48
69	49
70	50

Scan	Original
41	21
42	22
43	23
44	24
45	25
46	26
47	27
48	28
49	29
50	30
51	31
52	32
53	33
54	34
55	35
56	36
57	37
58	38
59	39
60	40
61	41
62	42
63	43
64	44
65	45
66	46
67	47
68	48
69	49
70	50