Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

GEOMETRIÆ quibus incidunt ad eundem angulum ex eadem parte, EO, MR, & quę diuidunt ipſas, EO, MR, ſimiliter ad eandem partem exiſten-
tes parallelæ ipſis, BC, GN, ſunt vtipſæ, EO, MR, ad eandem
partem eodem ordine inter ipſas, & circuitum dictarum figurarum
compræhenſæ, quia quæ ſunt ex vna parte ſunt æquales ipſis, BO,
GR, & quæ ex alia ipſis, OC, RN, in triangulis autem ſunt, vt
ipſæ, BO, GR, vel, OC, RN, . i. vt, OE, RM, & ideo, earum
incidentes, & oppoſitarum tangentium dictarum erunt ipſæ, EO,
MR, quę tangentes ſunt regulæ homologarum ſimilium figurarum,
AC, FN, vel, EBC, MGN. Vlterius, quia, BXC, GYN,
ſunt ſemicirculi, erunt figurę planę ſimiles iuxta meam definitionem,
quarum & tangentium, quæ per extrema, BC, GN, ducuntur e-
runt incidentes ipſi diametri, BC, GN, vt probatum fuit, veluti
idem patet de ſemicirculis, B ℟ C, GZN, & de quibuſcumq; alijs,
quæ diuident ipſas, EO, MR, ſimiliter ad eandem partem, & con-
ſequenter diuidunt etiam altitudines eorũdem reſpectu baſium ſum-
ptas ſimiliter ad eandem partem, & deijs, quæ per extrema, E, M,
ducuntur, habemus igitur cylindros, AC, FN, ſiue conos, BEC,
GMN, quorum ducta ſunt plana oppoſita tangentia dictorum ſo-
lidorum homologis figuris parallela, quæ ſunt plana, B ℟ CX, A
D; GYNZ, FH, quibus inciderunt duo plana ad ęquales angulos
ex eadem parte, illa nempè, in quibus ſunt ipſa parallelogramma,
AC, FN, vel triangula, BEC, quia ſunt recta ad baſes . i. ad dicta
tangentia, ipſæ autem ſiguræ . i. parallelogramma, vel triangula in-
uenta ſunt eſſe ſimilia, quarum homologarum regulæ oppoſitę tan-
gentes, AD, BC; FH, GN, quarum ſunt incidentes, EO, MR,
earum autem lineæ homologæ, ſumptæ regulis dictis tangentibus,
repertæ ſunt eſſe incidentes figurarum planarum ſimilium, quæ di-
uidunt altitudines dictorum ſolidorum iam dictas ſimiliter ad ean-
dem partem, & oppoſitarum tangentium, quæ omnes ijs, quæ du-
cuntur per extrema, BC, GN, tangentes circulos, B ℟ CX, GY
NZ, ſunt ęquidiſtantes, vt facilè conſideranti patebit, ergo cylin-
dri, AC, FN, vel coni, BEC, GMN, ſunt ſimiles iuxta meam defi-
nitionem generalem ſimilium ſolidorum, quod oſtendere opus erat.

119.1.

Defin. 11.
Ex. def. 3.
& 4. Cor.
Ex Cor. 5.
& ex 16.
huius.
27. huius.
B. defin.
10.
Ex Lem.
ant.
17. Vnde-
cimi El.
Defin. 11.

120. THEOREMA XXIX. PROPOS. XXXII.

DEfinitio mea ſimilium conicorum, & cylindricorum
concordat cum definitione generali ſimilium ſolido-
rum.

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