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
page
|<
<
(19)
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-s8732
"
xml:space
="
preserve
">
<
pb
o
="
19
"
file
="
0197
"
n
="
212
"
rhead
="
"/>
ſionum puncta lineam conſtituent, ſaltem ad lineam conſiſtent, ipſi
<
lb
/>
BC ſimilem. </
s
>
<
s
xml:id
="
echoid-s8733
"
xml:space
="
preserve
">Ductis enim quotlibet lateribus VB, VD, VE, VC,
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s8734
"
xml:space
="
preserve
">ducto plano GKLH ad planum BDEC parallelo, ſint com-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0197-01
"
xlink:href
="
note-0197-01a
"
xml:space
="
preserve
">16. XI.Elem.</
note
>
munes plani VBD cum planis BC, GH ſectiones rectæ BD, CH;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s8735
"
xml:space
="
preserve
">hæ parallelæ erunt. </
s
>
<
s
xml:id
="
echoid-s8736
"
xml:space
="
preserve
">Item communes plani VDE cum iiſdem planis
<
lb
/>
BC, GH Sectiones DE, KL parallelæ erunt. </
s
>
<
s
xml:id
="
echoid-s8737
"
xml:space
="
preserve
">Ergò anguli BDE,
<
lb
/>
GKL ſunt æquales. </
s
>
<
s
xml:id
="
echoid-s8738
"
xml:space
="
preserve
">Item ſe habet recta BD ad GK, ut DE ad
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0197-02
"
xlink:href
="
note-0197-02a
"
xml:space
="
preserve
">10. XI. elen
<
unsure
/>
.</
note
>
KL, quia utraque hæc proportio æqualis eſt illi, quam habet VD
<
lb
/>
ad VK (ſimilia quippe ſunt triangula VDB, VKG, & </
s
>
<
s
xml:id
="
echoid-s8739
"
xml:space
="
preserve
">triangula
<
lb
/>
VDE, VKL) permutandóque BD. </
s
>
<
s
xml:id
="
echoid-s8740
"
xml:space
="
preserve
">DE:</
s
>
<
s
xml:id
="
echoid-s8741
"
xml:space
="
preserve
">: GK. </
s
>
<
s
xml:id
="
echoid-s8742
"
xml:space
="
preserve
">KL. </
s
>
<
s
xml:id
="
echoid-s8743
"
xml:space
="
preserve
">ergò omnes
<
lb
/>
ſubtenſæ in GH proportionales ſunt ſubtenſis omnibus in BC, eas
<
lb
/>
nimirum in utraque linea ordinatim & </
s
>
<
s
xml:id
="
echoid-s8744
"
xml:space
="
preserve
">deinceps accipiendo; </
s
>
<
s
xml:id
="
echoid-s8745
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s8746
"
xml:space
="
preserve
">quæ
<
lb
/>
ſibimet adjacent in una pariter inflectuntur cum iis, quæ ſibi adjacent
<
lb
/>
in altera. </
s
>
<
s
xml:id
="
echoid-s8747
"
xml:space
="
preserve
">Ergò ſecundum ſuperiùs inſinuata lineas BC, GH ſimiles
<
lb
/>
eſſe conſtat.</
s
>
<
s
xml:id
="
echoid-s8748
"
xml:space
="
preserve
">‖ Hinc etiam patet lineas curvas ſimiles BC, GH ean-
<
lb
/>
dem ad ſe proportionem habere, quam Superficierum, in eadem
<
lb
/>
qualibet recta ſita, latera VB, VG. </
s
>
<
s
xml:id
="
echoid-s8749
"
xml:space
="
preserve
">Quum enim ſubtenſarum
<
lb
/>
iiſdem angulis incluſarum (ut BD, GK, vel DE, KL) ſingulæ
<
lb
/>
rationes æquales ſint rationi laterum VB, VG; </
s
>
<
s
xml:id
="
echoid-s8750
"
xml:space
="
preserve
">etiam omnes ante-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0197-03
"
xlink:href
="
note-0197-03a
"
xml:space
="
preserve
">12. V. Elem.</
note
>
cedentes conjunctæ (hoc eſt tota BC) ad omnes conſequentes con-
<
lb
/>
junctas (hoc eſt totam GH) ſe habebunt ut VB ad VG. </
s
>
<
s
xml:id
="
echoid-s8751
"
xml:space
="
preserve
">Hinc etiam
<
lb
/>
tali motu productarum ſuperficierum emergit hæc proprietas; </
s
>
<
s
xml:id
="
echoid-s8752
"
xml:space
="
preserve
">quòd
<
lb
/>
interceptæ ſcilicet à parallelis ad BC planis, à vertice deſumptæ,
<
lb
/>
quibuſcunque lateribus iiſdem incluſæ partes ipſarum ſint inter ſe ſi-
<
lb
/>
miles; </
s
>
<
s
xml:id
="
echoid-s8753
"
xml:space
="
preserve
">ut puta Superficies BVC, GVH; </
s
>
<
s
xml:id
="
echoid-s8754
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s8755
"
xml:space
="
preserve
">BVD, GVK.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s8756
"
xml:space
="
preserve
">(Quod ex generali ſimilitudinis doctrina poſthac explicanda luculen-
<
lb
/>
tiùs apparere poterit; </
s
>
<
s
xml:id
="
echoid-s8757
"
xml:space
="
preserve
">interim ex ſimilitudine linearum curvarum, & </
s
>
<
s
xml:id
="
echoid-s8758
"
xml:space
="
preserve
">
<
lb
/>
earum cum Superficiei lateribus analogia, penitúſque conſimili Superſi-
<
lb
/>
cierum generatione ſatìs eluceſcit; </
s
>
<
s
xml:id
="
echoid-s8759
"
xml:space
="
preserve
">ſaltem ex triangulorum VBD,
<
lb
/>
VGK; </
s
>
<
s
xml:id
="
echoid-s8760
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s8761
"
xml:space
="
preserve
">VDE, VKL, & </
s
>
<
s
xml:id
="
echoid-s8762
"
xml:space
="
preserve
">talium omnium ſimilitudine ſatìs con-
<
lb
/>
ſtat; </
s
>
<
s
xml:id
="
echoid-s8763
"
xml:space
="
preserve
">ſiquidem ex talibus infinitis triangulis utraque Superficies com-
<
lb
/>
poſita cenſeatur.) </
s
>
<
s
xml:id
="
echoid-s8764
"
xml:space
="
preserve
">Unde ſimilium Superficierum proprietates iis con-
<
lb
/>
venient. </
s
>
<
s
xml:id
="
echoid-s8765
"
xml:space
="
preserve
">Verùm quòd interceptas attinet à diverſis lateribus Super-
<
lb
/>
ficies, eas inter ſe comparando, notandum eſt quòd baſibus ſuis, ſeu
<
lb
/>
directricis lineæ reſpectivis partibus non ſemper proportionales ſunt; </
s
>
<
s
xml:id
="
echoid-s8766
"
xml:space
="
preserve
">
<
lb
/>
at ſaltem hoc tum evenit, cùm omnia dictæ Superficiei latera ſunt
<
lb
/>
æqualia inter ſe, adeóque cùm linea directrix eſt peripheria circuli; </
s
>
<
s
xml:id
="
echoid-s8767
"
xml:space
="
preserve
">
<
lb
/>
quo caſu producta Superficies erit conica Superficies ſtrictè dicta,
<
lb
/>
rectúmque quidem ad conum pertinens. </
s
>
<
s
xml:id
="
echoid-s8768
"
xml:space
="
preserve
">Quod ſi directrix BC ſup-
<
lb
/>
ponatur e. </
s
>
<
s
xml:id
="
echoid-s8769
"
xml:space
="
preserve
">g. </
s
>
<
s
xml:id
="
echoid-s8770
"
xml:space
="
preserve
">peripheria circularis, lateráque ſibimer inæqualia, </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>