Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Notes
Handwritten
Figures
Content
Thumbnails
Table of Notes
<
1 - 2
[out of range]
>
[Note]
Page: 124
[Note]
Page: 125
[Note]
Page: 126
[Note]
Page: 126
[Note]
Page: 127
[Note]
Page: 127
[Note]
Page: 128
[Note]
Page: 128
[Note]
Page: 140
[Note]
Page: 142
[Note]
Page: 143
[Note]
Page: 144
[Note]
Page: 144
[Note]
Page: 145
[Note]
Page: 147
[Note]
Page: 148
[Note]
Page: 152
[Note]
Page: 152
[Note]
Page: 156
[Note]
Page: 156
[Note]
Page: 161
[Note]
Page: 161
[Note]
Page: 161
[Note]
Page: 162
[Note]
Page: 162
[Note]
Page: 162
[Note]
Page: 163
[Note]
Page: 163
[Note]
Page: 164
[Note]
Page: 164
<
1 - 2
[out of range]
>
page
|<
<
(417)
of 568
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div149
"
type
="
section
"
level
="
1
"
n
="
66
">
<
pb
o
="
417
"
file
="
0135
"
n
="
144
"
rhead
="
ET HYPERBOLÆ QUADRATURA.
"/>
</
div
>
<
div
xml:id
="
echoid-div150
"
type
="
section
"
level
="
1
"
n
="
67
">
<
head
xml:id
="
echoid-head100
"
xml:space
="
preserve
">PROP. III. THEOREMA.</
head
>
<
head
xml:id
="
echoid-head101
"
style
="
it
"
xml:space
="
preserve
">Dico triangulum B A P, & trapezium A B I P ſimul,
<
lb
/>
eſſe ad trapezium A B I P, ut duplum trapezii A B I P ad polygonum A B D L P.</
head
>
<
note
position
="
right
"
xml:space
="
preserve
">TAB. XLIII.
<
lb
/>
Fig. 1. 2. 3.</
note
>
<
p
>
<
s
xml:id
="
echoid-s2831
"
xml:space
="
preserve
">In antecedente demonſtratum eſt trapezia A B F P, A B I P
<
lb
/>
ſimul, eſſe ad duplum trapezii A B I P, ſicut trapezium
<
lb
/>
A B F P ad polygonum A B D L P: </
s
>
<
s
xml:id
="
echoid-s2832
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s2833
"
xml:space
="
preserve
">permutando tra-
<
lb
/>
pezia A B F P, A B I P ſimul, ſunt ad trapezium A B F P,
<
lb
/>
ut duplum trapezii A B I P ad polygonum A B D L P. </
s
>
<
s
xml:id
="
echoid-s2834
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s2835
"
xml:space
="
preserve
">
<
lb
/>
quoniam trapezium A B F P, trapezium A B I P & </
s
>
<
s
xml:id
="
echoid-s2836
"
xml:space
="
preserve
">trian-
<
lb
/>
gulum A B P, ſunt continuè proportionalia; </
s
>
<
s
xml:id
="
echoid-s2837
"
xml:space
="
preserve
">erit trape-
<
lb
/>
zium A B I P ad trapezium A B F P, ut triangulum A B P
<
lb
/>
ad trapezium A B I P; </
s
>
<
s
xml:id
="
echoid-s2838
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s2839
"
xml:space
="
preserve
">componendo, ut trapezia A B I P,
<
lb
/>
A B F P ſimul, ad trapezium A B F P, ita triangulum
<
lb
/>
A B P & </
s
>
<
s
xml:id
="
echoid-s2840
"
xml:space
="
preserve
">trapezium A B I P ſimul, ad trapezium A B I P:
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s2841
"
xml:space
="
preserve
">erat autem, ut trapezia A B I P, A B F P, ſimul, ad tra-
<
lb
/>
pezium A B F P, ita duplum trapezii A B I P ad polygo-
<
lb
/>
num A B D L P; </
s
>
<
s
xml:id
="
echoid-s2842
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s2843
"
xml:space
="
preserve
">igitur ut triangulum A B P & </
s
>
<
s
xml:id
="
echoid-s2844
"
xml:space
="
preserve
">trape-
<
lb
/>
zium A B I P ſimul, ad trapezium A B I P, ita duplum
<
lb
/>
trapezii A B I P ad polygonum A B D L P, quod demon-
<
lb
/>
ſtrare oportuit.</
s
>
<
s
xml:id
="
echoid-s2845
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2846
"
xml:space
="
preserve
">Producantur (ſi opus ſit) rectæ A D, A L, ſegmentum
<
lb
/>
ſecantes in punctis E & </
s
>
<
s
xml:id
="
echoid-s2847
"
xml:space
="
preserve
">O, & </
s
>
<
s
xml:id
="
echoid-s2848
"
xml:space
="
preserve
">rectas B I, I P, in H & </
s
>
<
s
xml:id
="
echoid-s2849
"
xml:space
="
preserve
">M:
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s2850
"
xml:space
="
preserve
">deinde jungantur rectæ B E, E I, I O, O P, ut complea-
<
lb
/>
tur polygonum A B E I O P.</
s
>
<
s
xml:id
="
echoid-s2851
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div151
"
type
="
section
"
level
="
1
"
n
="
68
">
<
head
xml:id
="
echoid-head102
"
xml:space
="
preserve
">PROP. IV. THEOREMA.</
head
>
<
head
xml:id
="
echoid-head103
"
style
="
it
"
xml:space
="
preserve
">Dico polygonum A B E I O P eſſe medium pro-
<
lb
/>
portionale inter polygonum A B D L & trapezium A B I P.</
head
>
<
note
position
="
right
"
xml:space
="
preserve
">TAB. XLIII.
<
lb
/>
Fig. 1. 2. 3.</
note
>
<
p
>
<
s
xml:id
="
echoid-s2852
"
xml:space
="
preserve
">Ex hujus prima manifeſtum eſt trapezium A I L P, tra-
<
lb
/>
pezium A I O P & </
s
>
<
s
xml:id
="
echoid-s2853
"
xml:space
="
preserve
">triangulum A I P eſſe </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>