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# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 15
# Folio 24r, page id 00068033:0047
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Tangens cogarithmicae
. 168
ubi novae ratiocinationes circa composita eode modo
sit Angulus sint GC et CD sibi aequales et angulos
rectos, et GF ipsi cd aequalis e parallela et ad
easdem partes et ipsius GC vel Cd dimidia
q Inter GF et Cd  sive B. A
sumatur media prop. 2BEA. Et inter Cd et 2B2
et sumatur media 3B3A, et ita porro. Ex D per
omnia puncta A, nempe A, 2A, 3A etc. ducantur
s rectae DAF ipsi CG si opus productae occurrentes
idus continuari
in punctis 17. 2T. 3F. er
intelligatur. donec B incidat in C et curva ducatur
E=F per puncta 1A. 2A. 3A. ete atque intermedia usque
ad D. u et ducatur novissima D T, sive d ea
erit curvae tangens in puncto D. quaeritur ipsa CB
consideranda erit progressio ipsarum BF nam
3C
d
earum ultima est CD. quia ultima B desinit in C
 Est autem 1B, T aequa sit CD ag vel lG sive C, B, sit aequ _
et ultima  in b.
 erit GF seu 1B. A q  L e  1B1 aequ + Et qua Ut autem investi
gemus B.T considerandum e erigantur ex punctis A rectae AE, occurientes
ipsi Cd. patet fore (B.Q 1B, F: 1B. A :: 1Ae BT: BA:: AE: ED
sunt autem
eu cd. B empe 1Ed aequ C A - L.  2E D aequ + - 12. 3E Daequ1 - 2G
seu sunt autem +ED aequ t.  de I. 5Ed oqu   act-
et 1A it aequ 4.
fit ergo BF aequ
seu BTaqu
2AE aequ. l. 3A3E aequ 4A4E aequ x
BF
1
ED
L aede
SE
vel indel fa vel et vel
vel Svel vel r ete R vel 1 vel L vel L vel) et
e
82
sa
Not
12
a
L a1
2. s2
et numeris 1. 2. L.+. 8. 15 ek. appellatis 7.
erit BTaqu 
hatetur BB.
e
8
je
1- = vel 1 - = vel 1 - = vel 1 -  ec
(2
eutseries ipsarum BT cirt: L, 1
si u inffinita
im
e
ds2
e
1 L
27 4 e2 8, H facilis
1- 
Ja
1- 
 appropinqua
1- L per cogates
2
(2
Daequ. ( I2 et )-= (2 aequ . Egofic
Xur
Ergo BTaequ. = 2 (2 sit L aequ. a. fiet BTaqu
1- p212
co
es
E 2E3
∞
Et
et
1= (20s2