Barrow, Isaac
,
Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Notes
Handwritten
Figures
Content
Thumbnails
Table of Notes
<
1 - 7
[out of range]
>
[Note]
Page: 135
[Note]
Page: 136
[Note]
Page: 137
[Note]
Page: 137
[Note]
Page: 138
[Note]
Page: 138
[Note]
Page: 139
[Note]
Page: 140
[Note]
Page: 141
[Note]
Page: 141
[Note]
Page: 142
[Note]
Page: 143
[Note]
Page: 194
[Note]
Page: 197
[Note]
Page: 197
[Note]
Page: 199
[Note]
Page: 203
[Note]
Page: 204
[Note]
Page: 205
[Note]
Page: 207
[Note]
Page: 207
[Note]
Page: 207
[Note]
Page: 208
[Note]
Page: 208
[Note]
Page: 208
[Note]
Page: 209
[Note]
Page: 210
[Note]
Page: 211
[Note]
Page: 211
[Note]
Page: 212
<
1 - 7
[out of range]
>
page
|<
<
(20)
of 393
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div218
"
type
="
section
"
level
="
1
"
n
="
29
">
<
p
>
<
s
xml:id
="
echoid-s8770
"
xml:space
="
preserve
">
<
pb
o
="
20
"
file
="
0198
"
n
="
213
"
rhead
="
"/>
dividatur BC in partes æquales, & </
s
>
<
s
xml:id
="
echoid-s8771
"
xml:space
="
preserve
">connectantur latera VD, VE
<
lb
/>
non erunt Superficies BVD, DVE, EVC æquales inter ſe, ſed
<
lb
/>
inſerutabili plerumque ratione; </
s
>
<
s
xml:id
="
echoid-s8772
"
xml:space
="
preserve
">juxta varias angulorum incluſorum,
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s8773
"
xml:space
="
preserve
">laterum inæqualium differentias, inæquales; </
s
>
<
s
xml:id
="
echoid-s8774
"
xml:space
="
preserve
">id quod hactenus
<
lb
/>
ill
<
unsure
/>
o
<
unsure
/>
s divexavit & </
s
>
<
s
xml:id
="
echoid-s8775
"
xml:space
="
preserve
">torſit, _qui dimetiendæ coni ſcaleni ſuperficiei incu-_
<
lb
/>
buerunt.</
s
>
<
s
xml:id
="
echoid-s8776
"
xml:space
="
preserve
">‖ Ex his conſectatur quòd poſſit hujuſmodi circumlatio
<
lb
/>
facta quadantenus concipi motu quoque tali lineæ rectæ genetricis,
<
lb
/>
ità ut ejus ſingula quæque puncta parallelωs lata ſimiles directrici lineæ
<
lb
/>
lineas deſcribant, modo tamen concipiatur linea genetrix ubique pro-
<
lb
/>
portionaliter aut contrahi, vel dilatari ſecundum omnes ſui partes.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s8777
"
xml:space
="
preserve
">Quomodo nempe ſi recta VB ita ſenſim diduci concipiatur, ut pun-
<
lb
/>
ctum B totam lineam BC perambulet, etiam punctum G parallelo-
<
lb
/>
ad BC motu delata, lineam GH ipſi BC ſimilem deſcribet. </
s
>
<
s
xml:id
="
echoid-s8778
"
xml:space
="
preserve
">Qui-
<
lb
/>
nimò ſi conſimili pacto curva BC, directo quoad lineam rectam BV
<
lb
/>
motu ſitúque ſemper ad ſeipſam parallelo concipiatur promoveri, ſic
<
lb
/>
ut ejus ſingula quæque puncta lineas rectas deſcribant, ſecum omnes
<
lb
/>
in punctum V concurrentes; </
s
>
<
s
xml:id
="
echoid-s8779
"
xml:space
="
preserve
">hoc eſt ità ut ipſa per totum ſuum pro-
<
lb
/>
greſſum juxta ſuas omnes partes analogicè contrahatur, ad verticem
<
lb
/>
uſque V; </
s
>
<
s
xml:id
="
echoid-s8780
"
xml:space
="
preserve
">producentur ex hujuſmodi motibus Superficies conicæ pror-
<
lb
/>
ſus eædem cum jam proximè tractatis. </
s
>
<
s
xml:id
="
echoid-s8781
"
xml:space
="
preserve
">Verùm hujuſmodi motus ima-
<
lb
/>
ginarii ſunt, & </
s
>
<
s
xml:id
="
echoid-s8782
"
xml:space
="
preserve
">quales rerum natura reſpuit. </
s
>
<
s
xml:id
="
echoid-s8783
"
xml:space
="
preserve
">Explicandæ tamen
<
lb
/>
hujuſmodi Superficierum naturæ deſervire poſſunt, & </
s
>
<
s
xml:id
="
echoid-s8784
"
xml:space
="
preserve
">ſupponi ſaltem
<
lb
/>
ut per _divinam potentiam effectibiles._</
s
>
<
s
xml:id
="
echoid-s8785
"
xml:space
="
preserve
">‖ Ad hæc, ſi _linea directrix_
<
lb
/>
in motu proximè memorato ſupponatur undique clauſa, ſic ut figuram
<
lb
/>
quamvis comprehendat, Superficies curva progenita cum hac figura,
<
lb
/>
ceu baſe, corpus ſolidum includet pyramidale, vel conicum (ſtrictè
<
lb
/>
vel laxè pro dictæ figuræ natura ſumptum) cujus generalia ſympto-
<
lb
/>
mata ſatìs è dictis eluceſcunt. </
s
>
<
s
xml:id
="
echoid-s8786
"
xml:space
="
preserve
">Nempe quòd à parallelis ad hujuſce
<
lb
/>
ſolidi baſin planis abſcindentur ſimiles ad verticem Superficies, ſimiléſ-
<
lb
/>
que baſes intercipientur, & </
s
>
<
s
xml:id
="
echoid-s8787
"
xml:space
="
preserve
">ſimilia corpora Solida progignentur. </
s
>
<
s
xml:id
="
echoid-s8788
"
xml:space
="
preserve
">
<
lb
/>
Verbo dicam, quæ de _Conis_ generatim _E@clides, Apollonius,_ aliique
<
lb
/>
tradiderunt, ea conicis ho@ modo factis, ſervatâ debitâ analogia,
<
lb
/>
convenient, & </
s
>
<
s
xml:id
="
echoid-s8789
"
xml:space
="
preserve
">ſimili ferme modo demonſtrabuntur convenire.</
s
>
<
s
xml:id
="
echoid-s8790
"
xml:space
="
preserve
">‖ Ve-
<
lb
/>
rùm uſitatiſſimus apud Mathematicos corpora progignendi modus eſt
<
lb
/>
is qui peculiari nomine _Rotatio_ dicitur, & </
s
>
<
s
xml:id
="
echoid-s8791
"
xml:space
="
preserve
">fit ſuppoſito lineam quam-
<
lb
/>
vis, aut quamlibet Superſiciem planam cirea rectam lineam fixam,
<
lb
/>
tanquam axem, revolvi. </
s
>
<
s
xml:id
="
echoid-s8792
"
xml:space
="
preserve
">Quomodo ex motu Semiperipheriæ circu-
<
lb
/>
laris circa diametrum producitur _Sphærica Superſicies,_ ex motu Se-
<
lb
/>
micirculi ipſius circa eundem _Sphæra_ detornatur; </
s
>
<
s
xml:id
="
echoid-s8793
"
xml:space
="
preserve
">ex motu lineæ rectæ
<
lb
/>
circa lineam ipſi parallelam _Superſicies Cylindrica;_ </
s
>
<
s
xml:id
="
echoid-s8794
"
xml:space
="
preserve
">ex motu parallelo-
<
lb
/>
grammi rectanguli circa latus unum ipſé _Cylindrus rectus;_ </
s
>
<
s
xml:id
="
echoid-s8795
"
xml:space
="
preserve
">ex motu </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>