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# Title: Leibniz-Handschriften zur Mathematik LH 35, 2, 1
# Folio 323r, page id 00067993:0647
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quad ratura coneidis culus basis est circulus en diametri infiniaae, sen erjusmons ossugrota in uboru falsur
praecedenti plagnta multa dixi ad Gyilometria pertinentio, decti dedi quadraturam ductus
liculorum asmpo
cujusdam Cyclosa rabolici alioque id genus Ea tentabois persequi si merenti. Simma Deorum Hyperbolu rectantu
ductus spubi Hyperbolici rectus in se ipsum adento cylindro spatios hypervolgi asyriptoti in radium aequatu langenti
in seisum, dento tangente arcus dnidii porro Tangens est media proportionalis intersinum et differentiam simus a
secante, simi ergo posito b. (ut radio a) pono ac basui AC. in partes sectam aequalet. ergo datur AK. velub
differentia puius versi a radio, vel. d numerus unitatu  esto b. ejus p. .  a quad radii a. fiet B9a2 
sinus IN. posito sinu facile habet longens quia ut  b ad a, itao sinus ad tangentem Tangens
d Rgar=d. Ergo
s
C. sed cum AB. aeguidividitu
ordinatae ad Asymptolam hyperbolae prodeunt. Et necesse est sunus aequaliter crescere non
sius versos, vel corum  coplementa. Ergo aliter imhuandem
a - b b - a - b aq. langens. (19 at a
l
inde A a  L a  aV. Egod aet (4 = a - ab. Ergo 2ab = b - a t. Ego Z)
Nunc quaeramus tangente arcus dimidii, hoc modo. Datur AN - a- b nq ergo et NC = a ba - Aq a b
datur AN = a = b 5 R9. ergo e MC = a = R9 a b ergo et ic.
aliter: ut AD. ad DE. ita AC. ad 1)F. vel FC ergs 1F = DE. Ergo H = DEAC
pergo a - q
B a a a ab a - a b - a 20c N
intangulo DiG. datur di - a a  et DG=  Rg a b = b Porro dubitu, et EG
EG = Di. Ergo EG - i AC aL a a a, a- a 4 a ab, a. b. fals
eo AC na AD
Ad. 
eut b
Ero sic emendanda res est. sinus debet sumi KE. =b se cant AD. eut 1a Tansens at, a Rg
Ang sinus KEA = fi An) DAC quia ang. EAC. est angulo KAE suypo ad rectu, et X EA eigem XAE C
sit in eodem ilo rectangulo. Ergo vta Esse A et AdC. similia. Ergo AdA
Unde apparet se cantes ipsi AC a
porro datur recta EG = b a - b.
pplicetos rmperbolim dare.
a a -b =-
datur et DG nempe dG 5G
Est = est
DEDG- DCEG.
Rg a 1, a- b - a + b 2ab a2
una AC
porro cum Ila DEF et AEN sint simulia, cum sint rectangula, et praeterea angulis habeantae quale
CAC. et CDFEFd. Ergo et = DE ergo EF = DEC AN r. Esx autem es  Aq a = b t Ergo
EF = FC tangens auu dimili = a- a,  b Rq a  b = a - ab
EErgo ia tangs. dimid. = Tangs. dupl. a- Atanus. auc. dimid.
d a- b
Hoc Theorema comperare
2ae tans dimidii Tang. dupli
a B Tang. aus dinidi
s autem primo tangentem ud a nobis determinatus est, a a, Aq. ducemus in se ipsum, fiet a a
St hoc spatium quodvari pt.  restant summa rectangulorum, tangentus in tangentes arcuum dimidiorum.
summahom hpberi,
as
a+ ab- 2ab- a- a + aeb- 2ab
aeb - b+
An ergo brevius hoc modo quia tangens itiam alibr euuntiari potest: Tanus
Erit mdlliplicatio hoc modo concipienda: Ag a b. a
fieret a a b seu a - a. l
a. ab
Rga- b.
Sint ngab
a + aeb  a, Rq.
a- b
a. Ergoteus.
spelium hyperbolicum in radium ductum. nam a facdarent spatium huperbolicum
Habemus ergo aequationem hanc: sum. d plicati  ferbolaecd Asmpt.
L. Cylind. Spat. Hyperb.
aequationem signum ingens veritalis; etsi nihil novi delera
e Expelliano Theorenale ducabo a sah in R4a b a in
fil. B4a
egab
Cst .242
 ab
ega   s- N + aet ab2a6
eror forte aliqui sed res permulle
ti entiter
- X = 
e a- ab
i
+ar
aes  et 
196. 6, 2a
a- ab
Bgab
tue ex actissimo
a+ a6