Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Notes
Handwritten
Figures
Content
Thumbnails
Table of handwritten notes
<
1 - 14
[out of range]
>
<
1 - 14
[out of range]
>
page
|<
<
(136)
of 347
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div443
"
type
="
section
"
level
="
1
"
n
="
185
">
<
p
>
<
s
xml:id
="
echoid-s4571
"
xml:space
="
preserve
">
<
pb
o
="
136
"
file
="
0160
"
n
="
160
"
rhead
="
"/>
ſed quadratum MA minus eſt quadrato HM, ergo quadratum A I
<
note
symbol
="
a
"
position
="
left
"
xlink:label
="
note-0160-01
"
xlink:href
="
note-0160-01a
"
xml:space
="
preserve
">87. h.</
note
>
erit quadrato HI, ſiue perpendicularis intercepta A I, maior intercepto mi-
<
lb
/>
noris axis ſegmento IH. </
s
>
<
s
xml:id
="
echoid-s4572
"
xml:space
="
preserve
">Quod tandem demonſtrare oportebat.</
s
>
<
s
xml:id
="
echoid-s4573
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4574
"
xml:space
="
preserve
">ALITER abſque ope propoſitionis 87. </
s
>
<
s
xml:id
="
echoid-s4575
"
xml:space
="
preserve
">premiſso
<
lb
/>
tantum ſequenti lemmate pro Ellipſi.</
s
>
<
s
xml:id
="
echoid-s4576
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div448
"
type
="
section
"
level
="
1
"
n
="
186
">
<
head
xml:id
="
echoid-head191
"
xml:space
="
preserve
">LEMMA XIII. PROP. XIC.</
head
>
<
p
>
<
s
xml:id
="
echoid-s4577
"
xml:space
="
preserve
">Si ſuerit, in vtraque figura, rectangulum ſub extremis AB, BD
<
lb
/>
æquale quadrato mediæ BC, dico, in prima ſigura, ſi à tertia BD
<
lb
/>
dematur aliqua pars BE, rectangulum ſub AE, ED, minus eſſe
<
lb
/>
quadrato mediæ EC.</
s
>
<
s
xml:id
="
echoid-s4578
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4579
"
xml:space
="
preserve
">Cum ſit enim, vt totum AB ad totum BC, ita ablatum BC ad ablatũ BD,
<
lb
/>
erit reliquum AC ad reliquum CD, vt totum AB ad totum BC.</
s
>
<
s
xml:id
="
echoid-s4580
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4581
"
xml:space
="
preserve
">Et cum ſit CE minor C B, habebit
<
lb
/>
<
figure
xlink:label
="
fig-0160-01
"
xlink:href
="
fig-0160-01a
"
number
="
126
">
<
image
file
="
0160-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0160-01
"/>
</
figure
>
AC ad CE maiorem rationem quàm
<
lb
/>
AC ad CB, & </
s
>
<
s
xml:id
="
echoid-s4582
"
xml:space
="
preserve
">componendo AE ad
<
lb
/>
EC maiorem quàm AB ad BC, vel
<
lb
/>
quàm AC ad CD. </
s
>
<
s
xml:id
="
echoid-s4583
"
xml:space
="
preserve
">Siergo totum AE
<
lb
/>
ad totum EC maioré habet rationem
<
lb
/>
quàm ablatum AC ad ablatum CD,
<
lb
/>
habebit reliquum CE ad reliquũ ED
<
lb
/>
maiorem rationem, quàm totum AE
<
lb
/>
<
note
symbol
="
b
"
position
="
left
"
xlink:label
="
note-0160-02
"
xlink:href
="
note-0160-02a
"
xml:space
="
preserve
">16. 7.
<
lb
/>
Pappi.</
note
>
ad totum EC, vel AE ad EC minorem
<
lb
/>
habebit rationem quàm CE ad ED;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s4584
"
xml:space
="
preserve
">ergo rectangulum ſub extremis A E,
<
lb
/>
ED minus erit quadrato mediæ EC.</
s
>
<
s
xml:id
="
echoid-s4585
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4586
"
xml:space
="
preserve
">SI verò, ijſdem poſitis, in ſecunda ſigura, tertiæ proportionali BD recta
<
lb
/>
quædam BE adijciatur; </
s
>
<
s
xml:id
="
echoid-s4587
"
xml:space
="
preserve
">dico rectangulum ſub AE, ED maius eſſe qua-
<
lb
/>
drato EC; </
s
>
<
s
xml:id
="
echoid-s4588
"
xml:space
="
preserve
">quod licet in 9. </
s
>
<
s
xml:id
="
echoid-s4589
"
xml:space
="
preserve
">prop. </
s
>
<
s
xml:id
="
echoid-s4590
"
xml:space
="
preserve
">huius iam ſit oſtenſum, hic idem aliter nulla
<
lb
/>
facta conſtructione demonſtrabimus.</
s
>
<
s
xml:id
="
echoid-s4591
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4592
"
xml:space
="
preserve
">Quoniam enim CE maior eſt CB, habebit AC ad CE minorem rationem
<
lb
/>
quàm AC ad CB, & </
s
>
<
s
xml:id
="
echoid-s4593
"
xml:space
="
preserve
">componendo, tota AE ad totam EC, minorem quàm
<
lb
/>
<
note
symbol
="
c
"
position
="
left
"
xlink:label
="
note-0160-03
"
xlink:href
="
note-0160-03a
"
xml:space
="
preserve
">ibidem.</
note
>
ablata AB ad ablatam BC, vel quàm AC ad CD, ergo reliqua CE ad re-
<
lb
/>
liquam ED, minorem quoque habebit rationem quàm tota AE ad EC,
<
lb
/>
hoc eſt AE ad EC maiorem quàm EC ad ED, ergo rectangulum ſub AE,
<
lb
/>
ED maius quadrato mediæ EC. </
s
>
<
s
xml:id
="
echoid-s4594
"
xml:space
="
preserve
">Quod, &</
s
>
<
s
xml:id
="
echoid-s4595
"
xml:space
="
preserve
">c.</
s
>
<
s
xml:id
="
echoid-s4596
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4597
"
xml:space
="
preserve
">IAM, vt ad expeditiorem demonſtrationem præcedentis propoſitionis ac-
<
lb
/>
cedamus, ſuper eiſdem delineationibus, repetitis ijs omnibus, quæ ibi
<
lb
/>
(vſque ad ea verba excluſiuè _Ducta enim ex B recta BG, &</
s
>
<
s
xml:id
="
echoid-s4598
"
xml:space
="
preserve
">c.)</
s
>
<
s
xml:id
="
echoid-s4599
"
xml:space
="
preserve
">_ exponuntur, ac
<
lb
/>
demonſtrantur, ſic vlteriùs proſequemur. </
s
>
<
s
xml:id
="
echoid-s4600
"
xml:space
="
preserve
">Cum enim in ſingulis figuris triã-
<
lb
/>
gula DAE, LAI ſint rectangula ad A, ex quo baſibus ductæ ſunt perpendi-
<
lb
/>
culares AF, AR; </
s
>
<
s
xml:id
="
echoid-s4601
"
xml:space
="
preserve
">erit in triangulo DAE rectangulum EDF æquale </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>