Borelli, Giovanni Alfonso
,
De motionibus naturalibus a gravitate pendentibus
,
1670
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A
,
B
,
C
,
D
,
E
, &
F
,
H
,
I
,
K
,
L
,
quæ
centra
grauitatum̨
partium
aquæ
eſſe
intelligantur
vt
prius
, &
ductis
ad
horizontalem
perpendicularibus
AG, BV, CN,
DO
,
FM, H3, &
c
.
pariterque
coniunctis
rectis
DK,
CI
,
BH.
quia
anguli
ad
L
,
E
æquales
ſunt
in
iſoſcele, &
ſunt
quoque
anguli
recti
O
&
T
, & hypothenuſæ
DE
,
KL
ſunt
inter
ſe
æquales
,
ergo
in
ſimilibus
triangulis
DOE, & KTL
latera
DO
, KT
æqualia
erunt
&
recta
OE
æqualis
erit
TL, &
addita
communi
TE
erit
LE
æqualis
OT
quæ
non
minus
quàm
DK biſſecta
erit
in
puncto
Z
,
propter
æquidiſtantiam &
æqualitatem
la-
terum
DO
, & TK.
ſimiliter
reliquæ
rectæ
lineæ
NY
&
CI
æquales
erunt
prioribus
, & biſſectæ
in
puncto
P
,
idemque
de
reliquis
dicendum
eſt
.
&
quia
canales
,
&
moles
aqueæ
in
eis
contentæ
AB
, & FH,
æquales
ſunt
,
ergo
BFH
æqualis
eſt
AF;
fiat
iam
HB
ad
BQ,
vt
BFH
ad
FH,
vel
potius
vt
FA
ad
AB
:
quare
ſemiſ-
ſes
antecedentium
ad
eaſdem
conſequentes
in
eadem
ratione
erunt
,
nempè
vt
EA
ad
AB
,
ita
erit
XB
ad
B
Q
, &
per
conuerſionem
rationis
EA
ad
EB
ſeu
AG
ad
BV,
vel
GE
ad
EV, &
tandem
vt
duplum
GM
ad
duplum
MN
erit
vt
BX
ad
XQ,
ſeu
vt
VX
ad
XN,
vel
vt
BV
ad
QN.
igitur
erunt
tres
continuæ
propor-
tionales
AG, BV, & QN
in
eadem
ratione
quam
ha-
bet
MG
ad
MN,
quare
vt
quadratum
MG
ad
quadra-
tum
MN,
ita
erit
longitudine
AG
ad
QN ideoquę
duo
puncta
A
&
Q
in
parabola
erunt
.
Cap. 2. dę
momentis
grauium
in
fluido
inna-
tantium
Conſtat
ergo
quòd
ſi
brachia
ſiphonis
perpendicu-
laria
fuerint
ad
horizontem
,
ſiuè
ambo
fuerint
eiuſ-
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