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Liber
PROBLEMA 11.
Data IJUalllitatc itineru & r11mbo , invenirc
· mmimim ad quem ,',fa" differentiam
lo11gi111'-inü & latit,
j
A e
Geometrice.
1 • Ur limas rotus
1 • ad linmn complememi ABC,
; , ira quamiras itineris AB . . . .
4 . ad differemiam latir. in m1lltanbus aut mm.
Arirbmerice.
1. Logarith. linus totius
"Logarirh. limts complem. AB
3. Logarirh. itineris AB . . . . . . .
4. Logarith. differemia: laumdmts m m1llian–
bus , & minutis , divifa per 60 dar gradus.
Pr1 longitudine.
GeometricO.
1. Ur linus rocus
2 • ad rágenrem anguli ABC,
3. ita BC di.fferenria latitudi-
nis in milliaribus
Ari1bme1ici:.
J. Log íinns ro.
2. Log. tang.
; •Logarith.
..¡. ad A C milliaria E!l & 4. Logar.
Oüe!l.
Q_iae reduél:a dam diffent'.am long.i~u~inis. ~a­
ta autcm mraque diffcrenua , factlc .mventtur
locus.
PROBLEMA III.
Vi!la qua1ltitd1e íiineris , & larirudine utriufq11e
termini, invenire r11mb11m & differentiarn
longiwdinis.
Vide figuram przccdcntcn1.
Geomeerice. Arirb.
1. Ur quamiras irineris 1. Log.
1. ad differenriam latirudinis, 2. Log.
~. ira linus rorus , . , ; . Log.
+ ad íinú c.óplementi anguli loxod. 4•Log.
.Pro longittedint.
Geometric<. Arirbmetic<.
J. Ur Ítnus rorus 1,U1 Log. lin,
2. ad tangenrem angu!i lo- 1. ad Log. tang.
xodr. ABC,
;.ira BC .in 3.iraLog.
· milliarib.
4. ad AC milliaria Ell & 4. ad.Log.
Oüeíl:.
H:i:c milliaria reduéb dant differenriam lon–
ilitudinis.
IV. 247
PROBLEMA l v.
Dato ""?"bo & latitudine 111ri11fque termini ;11~
vemre qtttmtitatem itineri<5, & differentiam
IOT1gi11<dini.s,
Geomttrice.
1, Uc finus totus
·1. ad fecanrem anguli
· AllC,
3. ita B C diffcrentia
latirudinum
4. ad A B quanritacem
irineris.
Arithmttici:.
I . Logarichmuscomplc~
mcnri anguli ABC
1. ad linum roturo,
3. ira log. BC
4, ad log. A B.
Pro longitredine 11t in prttcedenti,
PRQ BL EMA V.
Dttta differemia longimdinú, dij/antia & latitudi–
n"t unisu teru1ini, invenire differentfom lmi–
tudinu & mmb11m.
Vide figuram pra:ccdcntcrn,
Prim?i reducenda er\: \ongirudinis diffcrch:iá
in milliaria Eíl:, & Oüe!l,cavendo an darn diíl:~n­
tia, Ítr ha:c qua: in przdiélo paralle\o refpondet
huic longimdinis diffcrenriz , {j enim hoc ita fo •
haberer navigatum effcr per E!l am Oüeíl:.
Geom. Arirb.
1. Ur leer AB 1. Logar1
2. ad mi\lia Eíl: & Oüeft AC, 1. Log.
3• ira Ítnus rotus 3. Log.
4. ad finum anguli lox<ldro- 4. Logar,
miciABC.
Pro dijferentia latit11.
Geom.
T. Ur linus rorus
Arirh.
1. L_og. finus t<l•
tlUS.
1. Log. rangemls•.
1. ad rangenté complem.
anguli ABC,
; . ira milliaria Ell Oüeft
AC
3. Log mill, Eíf
'Oüeíl:.
..¡.Log. differenti:i;
latir. 4 . ad A B diffcreminm la–
timdinis in milliaribus.
P R O BL E M A V l.
Datb rumbo differenria longitudinu, e?' /111i't11.~
dine uní.u terinini, immtire differen11am la~i:.
mdinú,lf¡ q11a111itarem i1i1uri1.
Dijferentia longit11 ad milh1rria primo re0
ducenda Geometric'e.
1. Ur linus totus
2. ad finum complem.anguli loxodr.
;. ita milliaria Eíl: & Oücíl: AC
1. Log.
1. Log.
3 . Log•
4. Log.
4. ad BC diffcrentiam laritudinis.
Pro diflantia.
Geome.
t. Ut Ítnus roms
1. ad (ecamem anguli
IÓxodr.
; • ira differentia lari–
rndinis BC
1 . ad AB dilhntiarn.
A rirh.
Oc Jogarid101. linL1S
1
' coniplcrnent! ABC.
1 , ad Logarithmum fi;
nus cotius.
3 . ita Logar. BC.
.¡. ad Log. A B.
PRO PO