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

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180160GEOMETRIÆ omnium quadratorum, CMH, & quadrupla omnium quadrato-
rum, CMH, vel, CBM, & , MEF, ſunt autem omnia quadrata
trianguli, CEG, æqualia omnibus quadratis, AF, cum omnibus
quadratis triangulorum, CBM, MEF, ergo hæc erunt quadrupla
omnium quadratorum triangulorum, CBM, MEF, & diuidendo

103[Figure 103] omnia quadrata, AF, eruntillorum tripla,
119. huius. ſunt autem omnia quadrata, AG, ad om-
nia quadrata, AF, vt quadratum, GE, ad
quadratum, EF, ideſt quadrupla . i. vt 12.
ad 3. & omnia quadrata, AF, ſunt omnium
quadratorum triangulorum, BMC, ME
F, tripla, ergo omnia quadrata, AG, e-
runt duodecupla omnium quadratorum
triangulorum, BMC, MEF, & ſunt ad
omnia quadrata, AF, vt 12. ad 3. ergo om-
nia quadrata, AG, ad omnia quadrata, A
F, cum omnibus quadratis triangulorum, CBM, MEF, erunt vt
12. ad 4. ſunt autem omnia quadrata, AF. cum omnibus quadra-
tis triangulorum, CBM, MEF, æqualia omnibus quadratis trian-
guli, CEG, vel, AEC, vt oſtenſum eſt, ergo omnia quadrata, A
G, ad omnia quadrata trianguli, CEG, vel, AEC, ſunt vt 12.
ad 4. . i. ſunt eorum tripla. quod oſtendendum erat.

COROLLARIVM.

_H_Inc patet, ſi ducamus intra parallelogrammum, AG, æquidiftan-
tem ipſi, EG, vtcunque, RV, ſec antem, CE, in, T, & , BF,
in, S, quod veluti oſtendimus, RV, æquari vni maximarum abſciſſarum.
CG, dum, EG, eſt æqualis ipſi, GC, ita namc oſtendemus quadratum,
RV, æquari quadrato vnius maxim trum abſciſſarum, CG, & quadra-
tum, TV, æquari quadrato vnius omnium abſciſſarum, CG, ideſt qua-
drato, VC; quadratum verò, RT, æquari quadrato @nius reſiduarum
omnium abſciſſirum, CG, ideſt quadrato, VG, vnde concludemus om-
nia quadrata, AG, regula, EG, æquari quadratis maximarum abſciſ-
ſarum, CG, & omnia quadrata triangult, CEG, æquari quadratis om-
nium abſciſſarum, CG, & omnia quadrata trianguli, AEC, æquari
quadratis reſiduarum omnium abſciſſarum, CG, & rectangula ſub tri-
angulis, AEC, CEG, æquari rectangu is ſub omnibus abſctſſis, & re-
ſiduis omnium abſciſſarum, CG, ita ſumptis, vt quoduts rectangulum
intelligatur ſub vna abſciſſirum, & eius reſidua: Vnde veluti oſtendi-
mus omnia quadrata, AG, tripla eſſe omnium quadratorum

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Scan	Original
101	81
102	82
103	83
104	84
105	85
106	86
107	87
108	88
109	89
110	90
111	91
112	92
113	93
114	94
115	95
116	96
117	97
118	98
119	99
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121	101
122	102
123	103
124	104
125	105
126	106
127	107
128	108
129	109
130	110

Scan	Original
101	81
102	82
103	83
104	84
105	85
106	86
107	87
108	88
109	89
110	90
111	91
112	92
113	93
114	94
115	95
116	96
117	97
118	98
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