Benedetti, Giovanni Battista de, Io. Baptistae Benedicti ... Diversarvm specvlationvm mathematicarum, et physicarum liber : quarum seriem sequens pagina indicabit ; [annotated and critiqued by Guidobaldo Del Monte]

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167155DE MECHAN.
CAP. XIIII.
Incipiens autem à prima dico dubium non eſſe, quin tangente corpore aliquo ro
tundo
aliquod planum mediante ſolo quodam puncto contingat, quemadmodum
probat
Theodoſius in .3. lib. primi & Vitellio in .71. lib. primi, & ducendo per centrum
ſphæræ
lineam vſque ad punctum contactus, ipſa erit perpendicularis plano contin-
genti
ſphęram dictam, vt probat idem Thęodoſius in .4. lib. primi Alhazem in .25. quar-
ti
, & Vitellio in .7. primi.
Verum etiam eſt omnem inclinationem ponderoſam huiuſ
modi
corporis homogęnei totam hanc lineam æqualiter omni ex parte circundare;
cuius quidem rei exemplum in carta deſcribere poſſumus mediante figura circulari
hîc
ſubſcripta .a.n.e.u. contigua lineæ rectæ .b.d. in puncto .a. vnde .e.o.a. perpendicu
laris
erit ipſi .b.d. ex .17. lib. 3. Eucli. & tantum ponderis habebimus à parte .a.u.e. quan
tum
ab ipſa .a.n.e.
Nuncigitur ſi imaginabimur ductum eſſe centrum verſus .u. per
lineam
.o.u. parallelam ipſi .a.d. clarum nobis
erit
, quod abſque; vlla difficultate aut reſiſtentia idem
225[Figure 225] ducemus, quia huiuſmodi centrum ab inferiori
parte
ad ſuperiorem, nunquam mutabit ſitum
reſpectu
diſtantiæ ſeu interualli, quę inter ipſum
lineamq́ue
.a.d. intercedit, quod quidem centrum
in
ſe colligittotum pondus figurę .a.n.e.u. & be
neficio
lineæ .e.o.a. illud ipſum puncto .a. in li-
nea
.b.a.d. committit, productum .a. nil refert,
vt
magis, aut minus verſus ipſum .d. aut verſus
b
. dirigatur;
ita vt cum non oporteat vt huius figuræ
pondus, vna vice, magis eleuetur, quàm alia, ſed
ſemper
ęqualiter ſuper lineam .b.a.d. quieſcat.

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