Gravesande, Willem Jacob 's
,
Physices elementa mathematica, experimentis confirmata sive introductio ad philosophiam Newtonianam; Tom. 1
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Notes
Handwritten
Figures
Content
Thumbnails
Table of Notes
<
1 - 5
[out of range]
>
[Note]
Page: 44
[Note]
Page: 44
[Note]
Page: 44
[Note]
Page: 44
[Note]
Page: 44
[Note]
Page: 44
[Note]
Page: 44
[Note]
Page: 45
[Note]
Page: 45
[Note]
Page: 45
[Note]
Page: 45
[Note]
Page: 45
[Note]
Page: 45
[Note]
Page: 45
[Note]
Page: 46
[Note]
Page: 46
[Note]
Page: 46
[Note]
Page: 46
[Note]
Page: 47
[Note]
Page: 47
[Note]
Page: 47
[Note]
Page: 47
[Note]
Page: 47
[Note]
Page: 47
[Note]
Page: 47
[Note]
Page: 48
[Note]
Page: 48
[Note]
Page: 48
[Note]
Page: 48
[Note]
Page: 48
<
1 - 5
[out of range]
>
page
|<
<
(65)
of 824
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div434
"
type
="
section
"
level
="
1
"
n
="
146
">
<
p
>
<
s
xml:id
="
echoid-s2758
"
xml:space
="
preserve
">
<
pb
o
="
65
"
file
="
0115
"
n
="
125
"
rhead
="
MATHEMATICA. LIB. I. CAP. XVIII.
"/>
curvam quamcunque BC; </
s
>
<
s
xml:id
="
echoid-s2759
"
xml:space
="
preserve
">celeritate eo acquiſita adſcendet
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0115-01
"
xlink:href
="
note-0115-01a
"
xml:space
="
preserve
">TAB. XI.
<
lb
/>
fig. 1.</
note
>
ad eandem altitudinem aliam partem verſus per cur-
<
lb
/>
vas CD, aut CE, aut C HGF.</
s
>
<
s
xml:id
="
echoid-s2760
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2761
"
xml:space
="
preserve
">Ex demonſtratis in hoc capite , deducimus
<
note
symbol
="
*
"
position
="
right
"
xlink:label
="
note-0115-02
"
xlink:href
="
note-0115-02a
"
xml:space
="
preserve
">71.</
note
>
confirmandi experimentis, quæ de velocitate Corporum
<
lb
/>
cadentium antea ſunt demonſtrata .</
s
>
<
s
xml:id
="
echoid-s2762
"
xml:space
="
preserve
"/>
</
p
>
<
note
symbol
="
*
"
position
="
right
"
xml:space
="
preserve
">2553</
note
>
</
div
>
<
div
xml:id
="
echoid-div437
"
type
="
section
"
level
="
1
"
n
="
147
">
<
head
xml:id
="
echoid-head211
"
xml:space
="
preserve
">
<
emph
style
="
sc
">Machina</
emph
>
,
<
lb
/>
Qua corporum Cadentium velocitates conferuntur.</
head
>
<
p
>
<
s
xml:id
="
echoid-s2763
"
xml:space
="
preserve
">Ex ligno cujus craſſities AB eſt duorum pollicum, & </
s
>
<
s
xml:id
="
echoid-s2764
"
xml:space
="
preserve
">alti-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0115-04
"
xlink:href
="
note-0115-04a
"
xml:space
="
preserve
">276.</
note
>
tudo circiter pollicum novem, formatur machina hæc; </
s
>
<
s
xml:id
="
echoid-s2765
"
xml:space
="
preserve
">ex-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0115-05
"
xlink:href
="
note-0115-05a
"
xml:space
="
preserve
">TAB. XII,
<
lb
/>
fig. 1.</
note
>
cavatur lignum juxta portionem cycloïdis à ſuperiori parte
<
lb
/>
ligni ad F uſque, ubi curva terminatur in ipſius vertice;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s2766
"
xml:space
="
preserve
">continuaturque lignum ab F ad G, juxta tangentem ad cur-
<
lb
/>
vam in vertice F, cujus diſtantia a G eſt unius pedis. </
s
>
<
s
xml:id
="
echoid-s2767
"
xml:space
="
preserve
">Ut
<
lb
/>
lignum hoc exactiſſimè ſit elaboratum habeatque ſuperfi-
<
lb
/>
ciem admodum politam deſideratur. </
s
>
<
s
xml:id
="
echoid-s2768
"
xml:space
="
preserve
">Formationem autem
<
lb
/>
cycloïdis in capite ſequenti explicamus.</
s
>
<
s
xml:id
="
echoid-s2769
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2770
"
xml:space
="
preserve
">Lignum hoc circumdatur regulis ligneis HH, HI, II;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s2771
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s2772
"
xml:space
="
preserve
">ſpatium quod hiſce continetur in duos quaſi canales divi-
<
lb
/>
ditur regulâ LL, cujus altitudo eſt quartæ partis unius pol-
<
lb
/>
licis.</
s
>
<
s
xml:id
="
echoid-s2773
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2774
"
xml:space
="
preserve
">In Canali utroque movetur globus æneus diametri ſemi
<
lb
/>
pollicis, in utroque etiam datur obex O, hi ope cochleæ
<
lb
/>
lateralis ubi deſideraveris firmantur.</
s
>
<
s
xml:id
="
echoid-s2775
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2776
"
xml:space
="
preserve
">Machina tribus ſuſtinetur cochleis æneis, quarum duæ vi-
<
lb
/>
dentur in C, C; </
s
>
<
s
xml:id
="
echoid-s2777
"
xml:space
="
preserve
">harum ope ſuperficies FG in ſitu ponitur
<
lb
/>
horizontali, cujus ſitus indicium dat perpendiculum NM.</
s
>
<
s
xml:id
="
echoid-s2778
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2779
"
xml:space
="
preserve
">Regula LL in ſuperiori parte dividitur, ab F ad G in
<
lb
/>
partes æquales, ab F autem ſurſum inæquales ſunt; </
s
>
<
s
xml:id
="
echoid-s2780
"
xml:space
="
preserve
">ſed de-
<
lb
/>
monſtrant intervalla æqualia inter altitudines.</
s
>
<
s
xml:id
="
echoid-s2781
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2782
"
xml:space
="
preserve
">Hujus Machinæ hæc eſt proprietas, ut globi ab altitudi-
<
lb
/>
nibus, utcunque inæqualibus, dimiſſi, æqualibus tempo-
<
lb
/>
ribus ad F perveniant, quod facile patebit ſi obices O, O,
<
lb
/>
in F firmentur, & </
s
>
<
s
xml:id
="
echoid-s2783
"
xml:space
="
preserve
">globi eodem momento a diverſis altitu-
<
lb
/>
dinibus dimittantur.</
s
>
<
s
xml:id
="
echoid-s2784
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2785
"
xml:space
="
preserve
">Qui hujus proprietatis Geometricam deſiderant </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>