Barrow, Isaac
,
Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur
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1 - 10
11 - 20
21 - 30
31 - 40
41 - 50
51 - 60
61 - 70
71 - 80
81 - 90
91 - 100
101 - 110
111 - 120
121 - 130
131 - 140
141 - 150
151 - 160
161 - 170
171 - 180
181 - 190
191 - 200
201 - 210
211 - 220
221 - 230
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<
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119
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0137
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137
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"/>
<
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<
s
xml:id
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xml:space
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">AV. </
s
>
<
s
xml:id
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xml:space
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">TV :</
s
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<
s
xml:id
="
echoid-s7805
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xml:space
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">: CV. </
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<
s
xml:id
="
echoid-s7806
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xml:space
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">CD; </
s
>
<
s
xml:id
="
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"
xml:space
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">& </
s
>
<
s
xml:id
="
echoid-s7808
"
xml:space
="
preserve
">conſequentes ſubduplandò, dividendó-
<
lb
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que AK. </
s
>
<
s
xml:id
="
echoid-s7809
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xml:space
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">KV :</
s
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<
s
xml:id
="
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xml:space
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">: KV. </
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<
s
xml:id
="
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xml:space
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">KD :</
s
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<
s
xml:id
="
echoid-s7812
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xml:space
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">: KV. </
s
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<
s
xml:id
="
echoid-s7813
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xml:space
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">CK. </
s
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<
s
xml:id
="
echoid-s7814
"
xml:space
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">vel AK. </
s
>
<
s
xml:id
="
echoid-s7815
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xml:space
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">KH :</
s
>
<
s
xml:id
="
echoid-s7816
"
xml:space
="
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">: KH. </
s
>
<
s
xml:id
="
echoid-s7817
"
xml:space
="
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">CK;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s7818
"
xml:space
="
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">hoc eſt HN (KX). </
s
>
<
s
xml:id
="
echoid-s7819
"
xml:space
="
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">NG :</
s
>
<
s
xml:id
="
echoid-s7820
"
xml:space
="
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">: KH. </
s
>
<
s
xml:id
="
echoid-s7821
"
xml:space
="
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">CK; </
s
>
<
s
xml:id
="
echoid-s7822
"
xml:space
="
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">quare CK x KX = KH
<
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/>
x NG. </
s
>
<
s
xml:id
="
echoid-s7823
"
xml:space
="
preserve
">eſt autem XZq = CZq - CXq = XGq - CXq =
<
lb
/>
NGq + KHq - 2 NG x KH: </
s
>
<
s
xml:id
="
echoid-s7824
"
xml:space
="
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">- KXq - CKq + 2 CK
<
lb
/>
x KX = NGq + KHq - KXq - CKq. </
s
>
<
s
xml:id
="
echoid-s7825
"
xml:space
="
preserve
">Sumatur K ζ = KX,
<
lb
/>
diſcurſúmque ſimilem adhibendo liquebit fore ξζ = XZ; </
s
>
<
s
xml:id
="
echoid-s7826
"
xml:space
="
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">& </
s
>
<
s
xml:id
="
echoid-s7827
"
xml:space
="
preserve
">ideo
<
lb
/>
Dζ = CZ. </
s
>
<
s
xml:id
="
echoid-s7828
"
xml:space
="
preserve
">unde Cζ - Dζ (DZ - CZ) = Cζ - CZ =
<
lb
/>
ξγ - XG = 2 KH = TV. </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">quare manifeſtum eſt _cnrvas_ TZ,
<
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Vζ eſſe _Hyperbolas,_ quarum axis TV, foci C,D.</
s
>
<
s
xml:id
="
echoid-s7830
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xml:space
="
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"/>
</
p
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<
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<
s
xml:id
="
echoid-s7831
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xml:space
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">IV. </
s
>
<
s
xml:id
="
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xml:space
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">Tertiò demùm, ſit angulus CAE ſemirectus (vel CA =
<
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<
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xlink:label
="
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="
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xml:space
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">Fig. 192.</
note
>
CE) erit tum punctum Z ad parabolam; </
s
>
<
s
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="
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xml:space
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">quæ itidem ita determina-
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tur. </
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<
s
xml:id
="
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xml:space
="
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">Fiat angulus ACP ſemirectus, & </
s
>
<
s
xml:id
="
echoid-s7835
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xml:space
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">ab ipſarum AE, CP in-
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terſectione R ducatur RT ad CE parallela; </
s
>
<
s
xml:id
="
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xml:space
="
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">erit T_Vertex_, atque C
<
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_Focus Parabolæ._ </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">id quod ex bene nota ſectionis hujus proprietate con-
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ſtat; </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">qua ſcilicet eſt TA = TR = TC (ob angulos TAR,
<
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TCR ſemirectos) & </
s
>
<
s
xml:id
="
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"
xml:space
="
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">AX = XG = CZ.</
s
>
<
s
xml:id
="
echoid-s7840
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xml:space
="
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"/>
</
p
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<
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<
s
xml:id
="
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xml:space
="
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">V. </
s
>
<
s
xml:id
="
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xml:space
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">Manifeſtum eſt verò rectam AE ſectiones has ad E contingere.
<
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/>
</
s
>
<
s
xml:id
="
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"
xml:space
="
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">quia nempe perpetuò major eſt CZ (vel XG) ordinatâ XZ; </
s
>
<
s
xml:id
="
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"
xml:space
="
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">adeó-
<
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/>
que puncta G extra cuŕvas unaquæque jacent hoc eſt tota AG extra
<
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illas cadit.</
s
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<
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</
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<
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<
s
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xml:space
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">VI. </
s
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<
s
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xml:space
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">Hiſce præſtratis: </
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>
<
s
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xml:space
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">_Eſto Circulare ſpeculum_ MBND, cen-
<
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<
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position
="
right
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xlink:label
="
note-0137-02
"
xlink:href
="
note-0137-02a
"
xml:space
="
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">Fig. 193.</
note
>
trum habens C; </
s
>
<
s
xml:id
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echoid-s7849
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xml:space
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">cui exponatur recta quæpiam F α G; </
s
>
<
s
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="
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">& </
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<
s
xml:id
="
echoid-s7851
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xml:space
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">huic per-
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pendicularis ſit recta C α; </
s
>
<
s
xml:id
="
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xml:space
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">quam ad parte@ averſas ſumpta CA, ad-
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æquet. </
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<
s
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xml:space
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">Sit etiam CE ad CA perpendicularis, ac æqualis qua-
<
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dranti diametri BD; </
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<
s
xml:id
="
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"
xml:space
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">connexáque recta AE producatur utcunque.
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</
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<
s
xml:id
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xml:space
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">ſumpto jam in recta F α G puncto quolibet F, connectatur FC, & </
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<
s
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<
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radiationis ab F in ipſa FC limes, ſeu _focus_, ſit Z; </
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<
s
xml:id
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xml:space
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">ac per Z du-
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catur ZX ad AC perpendicularis, ipſi AE occurrens in H; </
s
>
<
s
xml:id
="
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xml:space
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">dico
<
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fore XH parem ipſi CZ.</
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<
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</
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<
s
xml:id
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xml:space
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">Nam (è jam antè monſtratis) eſt FC. </
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<
s
xml:id
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<
s
xml:id
="
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xml:space
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<
s
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xml:space
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:</
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<
s
xml:id
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echoid-s7864
"
xml:space
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">: FC - CB. </
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<
s
xml:id
="
echoid-s7865
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xml:space
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">CB - CZ. </
s
>
<
s
xml:id
="
echoid-s7866
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xml:space
="
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">hinc erit α C. </
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<
s
xml:id
="
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xml:space
="
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">CX (AC. </
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<
s
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="
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">CX) :</
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<
s
xml:id
="
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xml:space
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<
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FC - CB. </
s
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<
s
xml:id
="
echoid-s7870
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xml:space
="
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">CB - CZ. </
s
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<
s
xml:id
="
echoid-s7871
"
xml:space
="
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">quare (ducendo in ſe extrema, ac media)
<
lb
/>
erit AC x CB - AC x CZ = CX x FC - CX x CB. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">hoc
<
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eſt (ipſi CX x FC ſubſtituendo AC x CZ, propter α C. </
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>
<
s
xml:id
="
echoid-s7873
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xml:space
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">CX :</
s
>
<
s
xml:id
="
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xml:space
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">:
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FC. </
s
>
<
s
xml:id
="
echoid-s7875
"
xml:space
="
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">CZ) erit AC x CB - AC x CZ = AC x CZ - CX x
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CB. </
s
>
<
s
xml:id
="
echoid-s7876
"
xml:space
="
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">tranſponendóque AC x CB + CX x CB = 2 AC x CZ.</
s
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