Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

LIBER V. quadrato, SO, & {1/3}. quadrati, Sk, ergo omnia quadrata, SV, ad
omnia quadrata figuræ, SIQVY, demptis omnibus quadratis ſe-
mihyperbolæ, YON, vel horũ quadrupla . ſ. omnia quadrata, GV,
ad omnia quadrata figuræ, FIQVRH, demptis omnibus quadratis
hyperbolę, MON, vel horum dupla . i. omnia quadrata, TV, ad om-
nia quad. rigurę, XPIQVRHFBT, dẽptis omnibus quadratis op-
poſitarum hyperbolarũ, AEC, MON, erunt vt cubus, YS, vel, ZV,
ad parallelepipedum ſub, kY, & quadrato, YS, vel ſub, QV, & qua-
drato, VZ, vna cum parallelepipedo ſub, kS, & compoſito ex qua-
drato, SO, & {1/3}. quadrati, Sk, vel vna cum parallelepipedo ſub, Z
Q, & compoſito ex quadrato, SO, & {1/3}. quadrati, ZQ, ab his ta-
men dempto parallelepipedo ſub, SO, & quadrato, OY, quę, eſt
reliqua ad ipſam, SY, vel, ZV, vna cum {1/3}. cubi eiuſdem reliquę, N
Y, quę eſt diameter alterutrius hyperbolarum dictarum, quod, & c.

569.1.

0428-01
Defin, 12.
11.
10. l. 2,
21. huius.
10. l. 2.
24. l. 2.
9. huius.

570. COROLLARIVM.

_H_Inc habetur omnia quadrata, TV, ad omnia quadrata fig. ianz
dictæ, quæ comprehenditur terminis, quiſunt, TX, RV, TB,
HR, VQ, PX, & ſectionibus oppoſitis, BFH, PIQ eſſe vt cubus RS,
ad parallelepipedum, ſub, KY, & quadrato. YS, Vna cum parallele-
pipedo ſub, KS, & compoſito ex quadrato, SO, & {1/3}. quadrati, SK, Vt
ſuperius oſtenſum eſt.

571. THEOREMA XXVIII. PROPOS. XXIX.

INeadem anteced. figura ſi aliud parallelogrammum de-
ſcribatur vtcunque, conditionibus tamen, quo, TV, de-
ſcriptum eſt, cuius latera ſectiones coniugatas diuidant,
quod ſit parallelogrammum, βΩ, cuius latera ſectiones cõ-
iugatas diuidant in punctis, L, Γ, Φ, Λ, 3, Σ, 7, 9, & axes,
vel diametros coniugatas, & , Y, GZ, in punctis, ℟, 8, 6, 4,
regula alterutro axium, vel diametrorum coniugatarum, V
T, FI: Oſtendemus omnia quadrata figuræ, quæ remanet
demptis oppoſitis hyperbolis, BFH, PIQ à parallelogram-
mo, TV, ablatis ab ijſdem omnibus quadratis oppoſitarum
hyperbolarum, AEC, MON, (quæ figura breuitatis cau-
ſa dicatur, figura parallelogrammi, TV,) ad omnia qua-
drata figuræ, quæ remanet, demptis oppoſitis hyperbolis,

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