Fabri, Honoré
,
Tractatus physicus de motu locali
,
1646
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Figures
Thumbnails
List of thumbnails
<
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
231 - 240
241 - 250
251 - 260
261 - 270
271 - 280
281 - 290
291 - 300
301 - 310
311 - 320
321 - 330
331 - 340
341 - 350
351 - 360
361 - 370
371 - 380
381 - 390
391 - 400
401 - 410
411 - 420
421 - 430
431 - 440
441 - 450
451 - 460
461 - 470
471 - 480
481 - 490
491 - 491
>
281
282
283
284
285
286
287
288
289
290
<
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
231 - 240
241 - 250
251 - 260
261 - 270
271 - 280
281 - 290
291 - 300
301 - 310
311 - 320
321 - 330
331 - 340
341 - 350
351 - 360
361 - 370
371 - 380
381 - 390
391 - 400
401 - 410
411 - 420
421 - 430
431 - 440
441 - 450
451 - 460
461 - 470
471 - 480
481 - 490
491 - 491
>
page
|<
<
of 491
>
>|
<
archimedes
>
<
text
>
<
body
>
<
chap
id
="
N1EE3A
">
<
p
id
="
N20439
"
type
="
main
">
<
s
id
="
N204BF
">
<
pb
pagenum
="
256
"
xlink:href
="
026/01/290.jpg
"/>
ad ſinum totum EB, & per DB vt DS ad DB: idem dico de aliis. </
s
>
</
p
>
<
p
id
="
N204CC
"
type
="
main
">
<
s
id
="
N204CE
">Hinc colligo primò, omnes determinationes nouas in hypotheſi glo
<
lb
/>
borum æqualium eſſe ſubduplas in eiſdem angulis priorum determina
<
lb
/>
tionum in hypotheſi corporis reflectentis immobilis. </
s
>
</
p
>
<
p
id
="
N204D5
"
type
="
main
">
<
s
id
="
N204D7
">Colligo ſecundò, omnes reflexiones fieri neceſſariò per eandem li
<
lb
/>
neam, quæ ſcilicet eſt Tangens puncti contactus globi reflectentis, quod
<
lb
/>
valdè mirificum eſt, & facilè obſeruabunt, qui Tudicula minore ludunt. </
s
>
<
s
id
="
N204DE
">
<
lb
/>
Colligo ſexto, cum angulus incidentiæ eſt 60. lineam reflexam eſſe ſub
<
lb
/>
duplam directæ quæ vlteriùs produceretur; infrà verò ſexto eſſe maio
<
lb
/>
rem, ſuprà verò eſſe minorem, eſt autem longitudo lineæ ſinus comple
<
lb
/>
menti anguli incidentiæ. </
s
>
<
s
id
="
N204E9
">v.g. ſi linea incidentiæ ſit EB eſt EG, ſi DB
<
lb
/>
eſt DH, ſi VB eſt VX. </
s
>
</
p
>
<
p
id
="
N204F0
"
type
="
main
">
<
s
id
="
N204F2
">
<
emph
type
="
center
"/>
<
emph
type
="
italics
"/>
Theorema
<
emph.end
type
="
italics
"/>
64.
<
emph.end
type
="
center
"/>
</
s
>
</
p
>
<
p
id
="
N204FE
"
type
="
main
">
<
s
id
="
N20500
">
<
emph
type
="
italics
"/>
Si globus minor in maiorem impingatur, qui ab eo tamen moueatur per li
<
lb
/>
neam connectentem centra vtriuſque impactus, reflectitur
<
emph.end
type
="
italics
"/>
; </
s
>
<
s
id
="
N2050B
">ratio eſt, quia ma
<
lb
/>
ior globus eſt maius impedimentum, vt iam diximus Th. 131.lib.1.id
<
lb
/>
eſt, vt clariùs hic explicetur, quæ ibidem tantùm obiter indicauimus,
<
lb
/>
noua determinatio maior eſt priore, quia ceſsio eſt minor impulſione; ſit
<
lb
/>
autem. </
s
>
<
s
id
="
N20517
">v.g. globus reflectens duplus impacto; </
s
>
<
s
id
="
N2051D
">igitur motus eſt ſubduplus,
<
lb
/>
quia ſcilicet impetus diſtribuitur pluribus partibus ſubjecti; </
s
>
<
s
id
="
N20523
">igitur ſin
<
lb
/>
gulæ minùs habent; </
s
>
<
s
id
="
N20529
">igitur impetus eſt remiſsior; </
s
>
<
s
id
="
N2052D
">igitur motus tardior; </
s
>
<
s
id
="
N20531
">
<
lb
/>
igitur ceſsio minor ſubduplo; </
s
>
<
s
id
="
N20536
">igitur determinatio noua eſt maior æqua
<
lb
/>
li 1/2 hinc debet neceſſariò reflecti, quia quotieſcunque ad lineas op
<
lb
/>
poſitas ex diametro determinatur impetus, maior determinatio præua
<
lb
/>
let pro rata per Th.134.lib.1. nam perinde ſe habet, atque ſi eſſet duplex
<
lb
/>
impetus; </
s
>
<
s
id
="
N20542
">quanta porrò eſſe debeat linea reflexa, determinari poteſt; </
s
>
<
s
id
="
N20546
">ſi
<
lb
/>
enim determinatio noua eſſet ſolilaria mobile cum eo impetu, quem ha
<
lb
/>
bet
<
expan
abbr
="
cõficeret
">conficeret</
expan
>
v.g. BA vel BF; </
s
>
<
s
id
="
N20554
">diuidatur BF in duas partes æquales in
<
foreign
lang
="
grc
">υ</
foreign
>
,
<
lb
/>
determinatio noua eſt ad priorem vt 3. ad 2. aſſumatur F
<
foreign
lang
="
grc
">β</
foreign
>
æqualis B
<
foreign
lang
="
grc
">υ</
foreign
>
; </
s
>
<
s
id
="
N20566
">
<
lb
/>
igitur propter determinationem priorem oppoſitam ſcilicet BA detra
<
lb
/>
hi debent duæ partes toti B
<
foreign
lang
="
grc
">β</
foreign
>
ſcilicet
<
foreign
lang
="
grc
">βυ</
foreign
>
æqualis BA; </
s
>
<
s
id
="
N20575
">igitur linea re
<
lb
/>
flexa erit B
<
foreign
lang
="
grc
">υ</
foreign
>
dupla totius BF; </
s
>
<
s
id
="
N2057F
">ſit etiam globus reflectens, qui mouetur
<
lb
/>
ab impacto, quadruplus, determinatio noua erit ad priorem vt 7. ad 4.
<
lb
/>
fit B
<
foreign
lang
="
grc
">δ</
foreign
>
ad BA vt 7. ad 4. ex B
<
foreign
lang
="
grc
">δ</
foreign
>
detrahatur DH æqualis BA, ſupereſt
<
lb
/>
HB id eſt 3/4 totius BF; non poteſt autem eſſe maior determinatio no
<
lb
/>
ua priore quàm in ratione dupla, vt diximus ſuprà. </
s
>
<
s
id
="
N20593
">Ratio eſt, quia eò mi
<
lb
/>
nor eſt determinatio noua, quò maior eſt motus impreſſus globo maiori
<
lb
/>
reflectenti; </
s
>
<
s
id
="
N2059B
">igitur tantum detrahitur duplæ, quantum additur motus; </
s
>
<
s
id
="
N2059F
">ſi
<
lb
/>
motus eſt æqualis, detrahitur duplæ æqualis priori; </
s
>
<
s
id
="
N205A5
">igitur ſupereſt æqua
<
lb
/>
lis; </
s
>
<
s
id
="
N205AB
">ſi motus eſt ſubduplus, detrahitur duplæ ſubdupla prioris; </
s
>
<
s
id
="
N205AF
">igitur ſu
<
lb
/>
pereſt 1/2 ſi ſubquadruplus detrahitur duplæ ſubquadrupla prioris, igitur
<
lb
/>
ſupereſt 1 3/4 ſi ſit duplus motus, determinatio noua eſt ſubdupla; </
s
>
<
s
id
="
N205B7
">igitur
<
lb
/>
priori detrahitur 1/2 de quo infrà; </
s
>
<
s
id
="
N205BD
">quod autem ſpectat ad longitudi
<
lb
/>
nes linearum non eſt difficultas; quippe determinatio minor detrahi
<
lb
/>
deber maiori. </
s
>
</
p
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>