Page 421 - Benedictus Stay: Philosophiae recentioris versibus traditae, libri X, tomus II
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Verum ubi cilipcicicisfic exigua, habeo methodum aihue multo cos'
trafliorem , qu* immediate deducat ad foimulas fimplicespro omnibus qua-
tuor iis pn.blematis, quam lirius in» ntam poiuli in ipfo fine ejus operti:
innititur autem huiclemmiti pertinenti ad fedioues conicas:
ubi ellipticitat
fit exigua
,
d fe re n tia dim idii lateris relti axis utriuyltbet a fem iaxe a l
tero
,
ad differentiam ejujdem a normali term inata ad eundem priorem
axem e/l proxime m ratione duplicata radit ad tofinum la titu d in is.
U
lemma admodum expeditam habet demonUrationem , quamexliibui ibide.»
num. j )4 . Qiian-ubrcm fi dimidium lacus rc2uni ax.s
lib
dicatur i , i jus dif
ferentiai W dicatur* , colinus Ijiitmli.iis / ad laJiuTi i (it, ut p r i i ^ C ,
colinus
i
fit
c
, failis i . CC : :
x
. Ci.x' , ciic normalis /F —~ i .
CCx
»
4
inde
j •
C
i i
Fi
i
■
CCx
•
/ H
S—*
C
—
CSx j
cum autem radius circuli
ofculitoris fit quartus continue propw tionalis poli dimidium lacus refturn ,
U
normilcm num.
j
34
.
eric ejusdifferentia a latere re£lo proxime tripli dif
ferenti* normalis ab eodein , nimirum
j C C x
,
adeoque erit ij radius ofculi
i — ;
CCx .
S t9
Habemus igitur pro radio paralleli,
5
; radio ofculi in / binos valo-
res C — Cl x i
&
i
“
}CCx
j
Si
eodem padto
,
pro iifdcm in
i
valores erunt
e
—•
clx
, & i - *
\tcx
.
Hi raloies funt ut gradus , adeoque datis vel bini»
gradibus
G
, &
g
paralleli, vel binis meridiani, vel gradu paralleli, S:
meridiani in eodem loco, rei gradu paralleli In uno, & meridiani in alio,
h a b e t u r
femper proportio , qua’ valurem exhibeat admodum (implicem
X
j
i;
a u c e m
valor
efl ipfa cllipticitas ; cum enim (ic
CB
ad
C A
, uc
CA
ad di
midium lacus reftum , erit priorum d ffirentia divifa per primum , fivc- J »
squalis pollcriorum differenti* divif* per cercium , nimirum cllipcicicaci•
340 Pro binisgradibus meridiani datis, 1 — ;
CCx .
1 —
:
: G
.g ;
indc£ — jCC»x = G —
iccGx
, i x r j X
TT
t
H
t i
'
341 Pro binis gradibus parallelorum datis C — c
\x
.
c
—-
c
?X : i G .
g
£
(O- d
inde
Cg
—
C*gx —~ c G
—
c
J u x ,
& X
—
9
341 Pro gradu meridiani > & paralleli .1» t o n m l o c o * ut in
I
, datij »
pofito primo
G
, & fecundo
g
fic 1 — i CCx . C — <
1
* :: G
,g
> fivc
g
—
jCCgx
—
CG
O G x
, & * =
=
F T
c o
!
u
)'
j 4 ) Pro gradu meridiani G' in
J
, & pa.illcli
g in i
dari» i — ?CCx .
c —
c ix : : G . g
, live
g —■ )CC gx
=
cG
—
x = — ) CQ *
; 44 Ego quidem vix crediderim polle fimpliciore , Ji magi» uniloimi me*
thodo folvi h*c quatuor problenma, qu* omnes hoc in genere combinacione*
compleftuntur , & prima quidem formula ob
G
proxime squalem
g
, & CC
■— 1 •—- \.f ,
c c ^ Z
1 —
ss
, adeoque
c c
— •
C C s S
—
Ss
abit in illam
JL X
Y slf ' u }
l)u,‘um num.3 3
6.
Earundcin auccm formularum opefacile ad-
niodum, & magnitudo invenitur ellipfeos . Si enim dimidium latus reilum
fuirtet appellatum i pro i , haberetur pro radio ofculi X. —'
} CC x
, & pr»
radioparalleli C t — jCCK > ac valor
x
in lingulis e quatuor formulis obve-
C c
1
nircc
AT)
L T R R
1
TM Q U I N T U M
4o?
