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

Scan	Original
131	111
132	112
133	113
134	114
135	115
136	116
137	117
138	118
139	119
140	120
141	121
142	122
143	123
144	124
145	125
146	126
147	127
148	128
149	129
150	130
151	131
152	132
153	133
154	134
155	135
156	136
157	137
158	138
159	139
160	140

134114GEOMETRIÆ nes lineas figurę, D, tunc enim comparare continuum ad continuum
non eſſet niſi ipſa indiuiſibilia comparare; ſed eſto, quod hoc ſit fal-
ſum, vel quod, etiamſi verum ſit, tamen legitima ratione ad hoc pro-
bandum nondum peruenerimus; nihilominus adhuc dico ipſa indi-
uiſibilia. ſ. omnes lineas figurę, A, ad omnes lineas figuræ, D, eſſe
vt figuram, A, ad figuram, D. Quoniam ergo aſſumpſimus figu-
ras, B, C, ſingulas æquales figuræ, A, & , E, æqualem figuræ, D,
omnes lineæ ſingularum figurarum, A, B, C, erunt æquales omni-
11Perante-
ctd. bus lineis figuræ, A, ſumptis iuxta dictam regulam (quacunque re-
gula dictæ omnes lineæ ſint aſſumptæ) & ideò quotuplex erit com-
poſitum ex figuris, ABC, figuræ, A, totuplex erit compoſitum ex
omnibus lineis figurarum, ABC, omnium linearum figuræ, A, &
ideò habebimus æquè multiplicia primæ, & tertiæ vtcunq; ſumpta;
ſimiliter oſtendemus compoſitum ex figuris, E, D, æquè multiplex

74[Figure 74] eſſe figuræ, D, ac compoſitum ex omnibus li-
neis figurarum, E, D, multiplex eſt omnium
linearum figuræ, D, quæ ſunt æquè multipli-
cia ſecundæ, & quartę vtcunque ſumpta, quia
ergo ſi multiplex primę. ſ. compoſitum ex figu
ris, ABC, ſuperauerit multiplex ſecundę, ſci-
licet compoſitum ex figuris, DE, etiam mul-
tiplex tertiæ. ſ. compoſitum ex omnibus lineis
figurarum, ABC, ſuperabit multiplex quartæ
. ſ. compoſitum ex omnibus lineis figurarum, DE, & ſi multiplex pri-
22Elicitur
ex antec. mæ fuerit æquale multiplici ſecundæ, etiam multiplex tertię erit æ-
quale multiplici quarte, ſcilicet ſi compoſitum ex figuris, ABC,
fuerit æquale compoſito ex figuris, DE, etiam eorundem compo-
ſitorum omnes lineæ erunt æquales, & ſi minus, minus, ideò prima
33Defin. 5.
Qui. El. ad ſecundam erit, vt tertia ad quartam, ſcilicet figura, A, ad figu-
ram, D, erit vt omnes lineæ figuræ, A, ad omnes lineas figuræ, D,
ſumptas iuxta datas regulas. ſ. iuxta quaſcunq; regulas, quod in fig.
44Coroll. I.
huius. planis erat oſtendendum.

Verum ſi intellexerimus, A, D, eſſe figuras ſolidas, aſſumentes,
C, B, ſingulas æquales ipſi, A, & , E, ipſi, D, oſtendemus com-
poſitum ex figuris, ABC, tam multiplex eſſe figurę, A, ac compo-
ſitum ex omnibus planis figurarum, A, B, C, multiplex eſt omnium
planorum figurę, A, & ſic compoſitum ex figuris, D, E, tam mul-
tiplex eſſe figuræ, D, ac compoſitum ex omnibus planis figurarum,
DE, multiplex eſt omnium planorum figuræ, D, & tandem per
antecedentem Propoſitionem oſtendemus, ſi multiplex primæ ſupe-
rauerit multiplex ſecundę, etiam multiplex tertiæ ſuperaturum mul-
tiplex quartæ, & ſi minus, minus, vel ſi æquale, & ęquale fore,

Page concordance

Text layer

Text normalization

Search

Scan	Original
131	111
132	112
133	113
134	114
135	115
136	116
137	117
138	118
139	119
140	120
141	121
142	122
143	123
144	124
145	125
146	126
147	127
148	128
149	129
150	130
151	131
152	132
153	133
154	134
155	135
156	136
157	137
158	138
159	139
160	140

Scan	Original
131	111
132	112
133	113
134	114
135	115
136	116
137	117
138	118
139	119
140	120
141	121
142	122
143	123
144	124
145	125
146	126
147	127
148	128
149	129
150	130
151	131
152	132
153	133
154	134
155	135
156	136
157	137
158	138
159	139
160	140

Scan	Original
131	111
132	112
133	113
134	114
135	115
136	116
137	117
138	118
139	119
140	120
141	121
142	122
143	123
144	124
145	125
146	126
147	127
148	128
149	129
150	130
151	131
152	132
153	133
154	134
155	135
156	136
157	137
158	138
159	139
160	140