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# Title: Leibniz-Handschriften zur Mathematik LH 35, 15, 6
# Folio 33v, page id 00068208:0066
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aec: aa et aequal e
seu aB: gaa ee aequal AN get MY
a et ad: aa - ec. de aurater
et  a. aa ec aequ 4aa: are + Gaa: a-C. Describatur jam Hyperbola
gate+
are
e
in unum additi
summo et diffen
lop e rogpiu
 cujus centranS. vertex A asyemptotos sC
potentia S, cujus latus se vel C. In hac asusm
ptoto Cumantur CM et CT aequales sinni e lalitudinis
sinui, CM. eritque sma vel e. et erit sT a - e
et s erit a+X. et ordinata YF erit Y6 TS erit aa: a e
et ordinata eit MB erit aa: a+ e. et ae quadrilineum
 Hyperboticum, aequalsur C  Ad erit et quadrilineum Hyper
bolicuntotio S TC Ad _ erit aa (de: a- e. et quadriliaeum Hyperbolicum
BMC_B erit aasde: ate: Ergo compsitiia ex utroque quadriliner
domigum
Hypertio sic d CBd gol 02fde: an ec, cujus dimidium
adime fa seu ae, habebis seu rectanu
qream
habebis a) ee de:na ee aequalem dimedio, quadrilineo ddYMBd
demto rectangulo AM, at erodem A rea AR Y A, est etiam aequalis
Areae ACMVA, demto rectangalo AM, ergo dimidium rectitneum
quadlineum dincdicim aequabitur Ergo compositi ex
utroque quadrilinei Hyperbolicae ostendimus autem peantem
et compositum exutroque quadrilineum Hyperbolicum d TMBd erit
summae
prulo aute ostendime
aequari areae ACM, V4 ergo dimidium quatrlineum dTM(3d
seu dimidius logarirhmus, differentiae inter radium et sinum, demto
hyperbolicus summae
differentiae inte
dimidio loganthmo hyperbolico summae ex radimu, et sinu aequa
summa secantium ad arcum.
quoniam numeri cx mingres quam se habent cogacithinis negativos
abitur areae AC MVA
ter
Ergo longitudines Coxodromiae A2G, A34 loxodr variationes
longitudinum ejusdem loxodromia AC ab aquatore iilipoentis sumtae,
sunt inter se, ut summae ex duohus quac in qualibet latitudine dant
logarithmus differentiae et lonarithmus mnimae si radii et sinus latitudinis
at adimidius logarithimus es a-e derpa cum dimidio logarithmo
atisinus
aa
seu logarithmo
se
secatiae  seu logarichmo rtitionis seupure et differe
e
sendimidio d
ettrema
BAd. A
qa ac: da-ec
due
dimidio cogalithuro dam
x
e
esse sinum.
Lins
te
mas logarit moratio
a ese lagarit Emo sinus
radis et simnis
Ergo area ACMVA seu summa
dectae rationis
secantium ad arcum aequatur logarit Emo Hhyperbo lico sinus complementieus
+3H
conprementi posito
Ergo Ut ergo ad Loxodromiam per tot ambages redeamus; inLoxodromit
LL Longitudines A2n A, q sumtae ind variationes longitudinum A2g. A3a
rationis ulter
ex quo Laxod romin digressa est ab aequatore) sunt ad logariphmus sonuum
impleenti lasitudinem A2 h, A vel AZh i X atia lonus, tudiuno 1434 est
l E
5
ini
sumtae
 ut distrnctintm suus
summa et visferes
 spharcid et sinus latita dimie in uncgona
nisomat axtiemaed
10g
inter ondspumca
anumanet diferulu