Barrow, Isaac
,
Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur
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<
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<
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59
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"/>
+ HK. </
s
>
<
s
xml:id
="
echoid-s3322
"
xml:space
="
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">CN. </
s
>
<
s
xml:id
="
echoid-s3323
"
xml:space
="
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">= AC. </
s
>
<
s
xml:id
="
echoid-s3324
"
xml:space
="
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">KC + AK. </
s
>
<
s
xml:id
="
echoid-s3325
"
xml:space
="
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">AC = AK. </
s
>
<
s
xml:id
="
echoid-s3326
"
xml:space
="
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">KC. </
s
>
<
s
xml:id
="
echoid-s3327
"
xml:space
="
preserve
">verùm eſt
<
lb
/>
NP. </
s
>
<
s
xml:id
="
echoid-s3328
"
xml:space
="
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">CN + AN. </
s
>
<
s
xml:id
="
echoid-s3329
"
xml:space
="
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">CN = NP x AN. </
s
>
<
s
xml:id
="
echoid-s3330
"
xml:space
="
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">CNq. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">ergò erit AK.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s3332
"
xml:space
="
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">KC :</
s
>
<
s
xml:id
="
echoid-s3333
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xml:space
="
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">: NP x AN. </
s
>
<
s
xml:id
="
echoid-s3334
"
xml:space
="
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">CNq. </
s
>
<
s
xml:id
="
echoid-s3335
"
xml:space
="
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">componendóque AC. </
s
>
<
s
xml:id
="
echoid-s3336
"
xml:space
="
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">KC :</
s
>
<
s
xml:id
="
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"
xml:space
="
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">: NP
<
lb
/>
<
note
position
="
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xlink:label
="
note-0077-01
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xlink:href
="
note-0077-01a
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xml:space
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">Fig. 79, 80.</
note
>
x AN + CNq. </
s
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<
s
xml:id
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xml:space
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s
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<
s
xml:id
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"
xml:space
="
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">cum ſit igitur NP x AN = AP x AN
<
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- ANq. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">& </
s
>
<
s
xml:id
="
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"
xml:space
="
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">AP x AN = ACq - CNq; </
s
>
<
s
xml:id
="
echoid-s3342
"
xml:space
="
preserve
">adeóque NP
<
lb
/>
x AN + CNq = ACq - CNq - ANq + CNq; </
s
>
<
s
xml:id
="
echoid-s3343
"
xml:space
="
preserve
">= ACq
<
lb
/>
- ANq. </
s
>
<
s
xml:id
="
echoid-s3344
"
xml:space
="
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">erit AC. </
s
>
<
s
xml:id
="
echoid-s3345
"
xml:space
="
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">KC :</
s
>
<
s
xml:id
="
echoid-s3346
"
xml:space
="
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">: ACq - ANq. </
s
>
<
s
xml:id
="
echoid-s3347
"
xml:space
="
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">CNq : </
s
>
<
s
xml:id
="
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xml:space
="
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">Quod E. </
s
>
<
s
xml:id
="
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xml:space
="
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">D.
<
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</
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<
s
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xml:space
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">_Coroll_. </
s
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<
s
xml:id
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xml:space
="
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s
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<
s
xml:id
="
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xml:space
="
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">KC :</
s
>
<
s
xml:id
="
echoid-s3353
"
xml:space
="
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">: AN x NP. </
s
>
<
s
xml:id
="
echoid-s3354
"
xml:space
="
preserve
">CNq.</
s
>
<
s
xml:id
="
echoid-s3355
"
xml:space
="
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"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s3356
"
xml:space
="
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">VI. </
s
>
<
s
xml:id
="
echoid-s3357
"
xml:space
="
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">Etiam hoc _Theorema_ ſubdemus: </
s
>
<
s
xml:id
="
echoid-s3358
"
xml:space
="
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">Si fiat 2 CA. </
s
>
<
s
xml:id
="
echoid-s3359
"
xml:space
="
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">CN :</
s
>
<
s
xml:id
="
echoid-s3360
"
xml:space
="
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">:
<
lb
/>
CN. </
s
>
<
s
xml:id
="
echoid-s3361
"
xml:space
="
preserve
">E. </
s
>
<
s
xml:id
="
echoid-s3362
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s3363
"
xml:space
="
preserve
">2 CK. </
s
>
<
s
xml:id
="
echoid-s3364
"
xml:space
="
preserve
">CN :</
s
>
<
s
xml:id
="
echoid-s3365
"
xml:space
="
preserve
">: CN. </
s
>
<
s
xml:id
="
echoid-s3366
"
xml:space
="
preserve
">F; </
s
>
<
s
xml:id
="
echoid-s3367
"
xml:space
="
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">& </
s
>
<
s
xml:id
="
echoid-s3368
"
xml:space
="
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">ſumatur CQ = E + F;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s3369
"
xml:space
="
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">erit ducta NQ ad CA perpendicularis. </
s
>
<
s
xml:id
="
echoid-s3370
"
xml:space
="
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">vel reciprocè; </
s
>
<
s
xml:id
="
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"
xml:space
="
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">poſito quòd
<
lb
/>
ſit NQ ad CA perpendicularis; </
s
>
<
s
xml:id
="
echoid-s3372
"
xml:space
="
preserve
">erit CQ = E + F. </
s
>
<
s
xml:id
="
echoid-s3373
"
xml:space
="
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">‖ Nam (ut
<
lb
/>
hoc poſterius oſtendamus) quoniam eſt 2 CA. </
s
>
<
s
xml:id
="
echoid-s3374
"
xml:space
="
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">CN :</
s
>
<
s
xml:id
="
echoid-s3375
"
xml:space
="
preserve
">: CN. </
s
>
<
s
xml:id
="
echoid-s3376
"
xml:space
="
preserve
">E. </
s
>
<
s
xml:id
="
echoid-s3377
"
xml:space
="
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">
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s3378
"
xml:space
="
preserve
">CN. </
s
>
<
s
xml:id
="
echoid-s3379
"
xml:space
="
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">2 CK :</
s
>
<
s
xml:id
="
echoid-s3380
"
xml:space
="
preserve
">: F. </
s
>
<
s
xml:id
="
echoid-s3381
"
xml:space
="
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">CN. </
s
>
<
s
xml:id
="
echoid-s3382
"
xml:space
="
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">erit ex æquo perturbatè 2 CA. </
s
>
<
s
xml:id
="
echoid-s3383
"
xml:space
="
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">2 CK
<
lb
/>
:</
s
>
<
s
xml:id
="
echoid-s3384
"
xml:space
="
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">: F. </
s
>
<
s
xml:id
="
echoid-s3385
"
xml:space
="
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">E. </
s
>
<
s
xml:id
="
echoid-s3386
"
xml:space
="
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">vel CA. </
s
>
<
s
xml:id
="
echoid-s3387
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xml:space
="
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">CK :</
s
>
<
s
xml:id
="
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xml:space
="
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">: F. </
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>
<
s
xml:id
="
echoid-s3389
"
xml:space
="
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">E. </
s
>
<
s
xml:id
="
echoid-s3390
"
xml:space
="
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">componendóque CA + CK. </
s
>
<
s
xml:id
="
echoid-s3391
"
xml:space
="
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">CK
<
lb
/>
:</
s
>
<
s
xml:id
="
echoid-s3392
"
xml:space
="
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">: F + E. </
s
>
<
s
xml:id
="
echoid-s3393
"
xml:space
="
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">E. </
s
>
<
s
xml:id
="
echoid-s3394
"
xml:space
="
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">Porrò quoniam eſt ANq = ACq + CNq - 2 AC
<
lb
/>
x CQ; </
s
>
<
s
xml:id
="
echoid-s3395
"
xml:space
="
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">erit 2 AC x CQ - CNq = ACq - ANq. </
s
>
<
s
xml:id
="
echoid-s3396
"
xml:space
="
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">itaque
<
lb
/>
(juxta præcedentem) erit 2 AC x CQ - CNq. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">CNQ :</
s
>
<
s
xml:id
="
echoid-s3398
"
xml:space
="
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">: AC. </
s
>
<
s
xml:id
="
echoid-s3399
"
xml:space
="
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">
<
lb
/>
CK. </
s
>
<
s
xml:id
="
echoid-s3400
"
xml:space
="
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">hoc eſt ( ob CNq = 2 AC x E) 2 AC x CQ - 2 AC
<
lb
/>
x E. </
s
>
<
s
xml:id
="
echoid-s3401
"
xml:space
="
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">2 AC x E :</
s
>
<
s
xml:id
="
echoid-s3402
"
xml:space
="
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">: AC. </
s
>
<
s
xml:id
="
echoid-s3403
"
xml:space
="
preserve
">CK. </
s
>
<
s
xml:id
="
echoid-s3404
"
xml:space
="
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">hoc eſt CQ - E. </
s
>
<
s
xml:id
="
echoid-s3405
"
xml:space
="
preserve
">E :</
s
>
<
s
xml:id
="
echoid-s3406
"
xml:space
="
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">: AC. </
s
>
<
s
xml:id
="
echoid-s3407
"
xml:space
="
preserve
">CK. </
s
>
<
s
xml:id
="
echoid-s3408
"
xml:space
="
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">
<
lb
/>
vel componendo CQ. </
s
>
<
s
xml:id
="
echoid-s3409
"
xml:space
="
preserve
">E :</
s
>
<
s
xml:id
="
echoid-s3410
"
xml:space
="
preserve
">: AC + CK. </
s
>
<
s
xml:id
="
echoid-s3411
"
xml:space
="
preserve
">CK. </
s
>
<
s
xml:id
="
echoid-s3412
"
xml:space
="
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">erat autem AC
<
lb
/>
+ CK. </
s
>
<
s
xml:id
="
echoid-s3413
"
xml:space
="
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">CK :</
s
>
<
s
xml:id
="
echoid-s3414
"
xml:space
="
preserve
">: F + E. </
s
>
<
s
xml:id
="
echoid-s3415
"
xml:space
="
preserve
">E. </
s
>
<
s
xml:id
="
echoid-s3416
"
xml:space
="
preserve
">ergò CQ = F + E: </
s
>
<
s
xml:id
="
echoid-s3417
"
xml:space
="
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">Quod E. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">D.</
s
>
<
s
xml:id
="
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"
xml:space
="
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"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s3420
"
xml:space
="
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">VII. </
s
>
<
s
xml:id
="
echoid-s3421
"
xml:space
="
preserve
">Ex iſtis porrò deducetur, ſi dividatur Semidiameter BC in
<
lb
/>
Z, ut ſit AC. </
s
>
<
s
xml:id
="
echoid-s3422
"
xml:space
="
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">AB :</
s
>
<
s
xml:id
="
echoid-s3423
"
xml:space
="
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">: CZ. </
s
>
<
s
xml:id
="
echoid-s3424
"
xml:space
="
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">BZ; </
s
>
<
s
xml:id
="
echoid-s3425
"
xml:space
="
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">punctum Z limes erit citra quem
<
lb
/>
(reſpectu centri C) nullus hujuſmodi reflexus axem decuſſabit. </
s
>
<
s
xml:id
="
echoid-s3426
"
xml:space
="
preserve
">Cu-
<
lb
/>
juſvis, inquam, radii AN eſto reflexus GN; </
s
>
<
s
xml:id
="
echoid-s3427
"
xml:space
="
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">axi occurrens in K.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s3428
"
xml:space
="
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">dico fore CK &</
s
>
<
s
xml:id
="
echoid-s3429
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xml:space
="
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">gt; </
s
>
<
s
xml:id
="
echoid-s3430
"
xml:space
="
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">CZ. </
s
>
<
s
xml:id
="
echoid-s3431
"
xml:space
="
preserve
">Nam ob hypotheſin (permutandóque) eſt AC. </
s
>
<
s
xml:id
="
echoid-s3432
"
xml:space
="
preserve
">
<
lb
/>
CZ :</
s
>
<
s
xml:id
="
echoid-s3433
"
xml:space
="
preserve
">: AB. </
s
>
<
s
xml:id
="
echoid-s3434
"
xml:space
="
preserve
">BZ. </
s
>
<
s
xml:id
="
echoid-s3435
"
xml:space
="
preserve
">igitur (antecedentes, & </
s
>
<
s
xml:id
="
echoid-s3436
"
xml:space
="
preserve
">conſequentes copulan-
<
lb
/>
do) AC. </
s
>
<
s
xml:id
="
echoid-s3437
"
xml:space
="
preserve
">CZ :</
s
>
<
s
xml:id
="
echoid-s3438
"
xml:space
="
preserve
">: AC + AB. </
s
>
<
s
xml:id
="
echoid-s3439
"
xml:space
="
preserve
">CB. </
s
>
<
s
xml:id
="
echoid-s3440
"
xml:space
="
preserve
">quare ( poſterioris hujuſce
<
lb
/>
rationis utrumque terminum in æquales AC - AB, & </
s
>
<
s
xml:id
="
echoid-s3441
"
xml:space
="
preserve
">BC ducen-
<
lb
/>
do) erit AC. </
s
>
<
s
xml:id
="
echoid-s3442
"
xml:space
="
preserve
">CZ :</
s
>
<
s
xml:id
="
echoid-s3443
"
xml:space
="
preserve
">: ACq - ABq. </
s
>
<
s
xml:id
="
echoid-s3444
"
xml:space
="
preserve
">CBq. </
s
>
<
s
xml:id
="
echoid-s3445
"
xml:space
="
preserve
">eſt autem ACq
<
lb
/>
- ABq &</
s
>
<
s
xml:id
="
echoid-s3446
"
xml:space
="
preserve
">gt; </
s
>
<
s
xml:id
="
echoid-s3447
"
xml:space
="
preserve
">ACq - ANq; </
s
>
<
s
xml:id
="
echoid-s3448
"
xml:space
="
preserve
">adeóque ACq - ABq CBq. </
s
>
<
s
xml:id
="
echoid-s3449
"
xml:space
="
preserve
">
<
lb
/>
&</
s
>
<
s
xml:id
="
echoid-s3450
"
xml:space
="
preserve
">gt; </
s
>
<
s
xml:id
="
echoid-s3451
"
xml:space
="
preserve
">ACq - ANq. </
s
>
<
s
xml:id
="
echoid-s3452
"
xml:space
="
preserve
">CBq :</
s
>
<
s
xml:id
="
echoid-s3453
"
xml:space
="
preserve
">: AC. </
s
>
<
s
xml:id
="
echoid-s3454
"
xml:space
="
preserve
">CK (è mox oſtenſis hoc) qua-
<
lb
/>
propter erit AC. </
s
>
<
s
xml:id
="
echoid-s3455
"
xml:space
="
preserve
">CZ &</
s
>
<
s
xml:id
="
echoid-s3456
"
xml:space
="
preserve
">gt; </
s
>
<
s
xml:id
="
echoid-s3457
"
xml:space
="
preserve
">AC. </
s
>
<
s
xml:id
="
echoid-s3458
"
xml:space
="
preserve
">CK. </
s
>
<
s
xml:id
="
echoid-s3459
"
xml:space
="
preserve
">indéque CK &</
s
>
<
s
xml:id
="
echoid-s3460
"
xml:space
="
preserve
">gt; </
s
>
<
s
xml:id
="
echoid-s3461
"
xml:space
="
preserve
">CZ: </
s
>
<
s
xml:id
="
echoid-s3462
"
xml:space
="
preserve
">
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0077-02
"
xlink:href
="
note-0077-02a
"
xml:space
="
preserve
">Fig. 81, 82.</
note
>
Q. </
s
>
<
s
xml:id
="
echoid-s3463
"
xml:space
="
preserve
">E. </
s
>
<
s
xml:id
="
echoid-s3464
"
xml:space
="
preserve
">D.</
s
>
<
s
xml:id
="
echoid-s3465
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s3466
"
xml:space
="
preserve
">VIII. </
s
>
<
s
xml:id
="
echoid-s3467
"
xml:space
="
preserve
">Aliter hoc idem; </
s
>
<
s
xml:id
="
echoid-s3468
"
xml:space
="
preserve
">ut quibuſdam fortaſſe videbitur, minùs
<
lb
/>
involutè: </
s
>
<
s
xml:id
="
echoid-s3469
"
xml:space
="
preserve
">per N ducatur VT circulum contingens. </
s
>
<
s
xml:id
="
echoid-s3470
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s3471
"
xml:space
="
preserve
">quoniam </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>