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# Title: Leibniz-Handschriften zur Mathematik LH 35, 2, 1
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11. 29
prop. 30
la similia: AEH et AD C. Ergo Ad = DC = AC= AC
rop. 28.
AE AK KE
seu sinam complementi
AD AK = AE DC. seu secanscomplementi in dlistantiam a basi per centrum transeunte, aquatur, radio in tangentem complemendias
seu cylinder tangentium complemonti (quadrabilis de quo infra) aequatur, momento secantium complementi exuasi
o momentum  quadrabile est. aode prop. +. Et adde pro p. 27 coroll trigonometriae uassigna bituumo qua
ADCHE = AE B.  sinus in secantem complementi, aequatur quadrato radii, seu radius est media proportionalis inten
inter sinum arcus dati, et secantem arcus complementi. Quare ductus circularis in figuram secantium f
 invertus cosequatur prismati, cujus basis quadratum radis altitudo, distantial a vertice quadrantis rgo qui t
d. prop. 41.
DC KE = AKAE. sinus in tangentem complementi aequatur radio in distantiam a basi quadrantis, quare ductus portionis
abscissum trianguli a basi, ergo  ductus iste est quadrabilis.
ia
AD AE = AHDC.  radius in secantem complementi, aequatur secanti in tangentem complementi, atque ideo cylinder secantium
r ludtem decanumcomplomnialo
la similia: AEH et AdC. Ergo =
AE
no compmui aeguatur cntindo
AD HE = AH AE. radius in secantem, aequatur tanenti complementi in tangentem, atque ideo cylinder hyperbolicus ciqua-
ocant
tur ductui inverso tam conchoeidis in portionis conchoeidalis in portionem ang figurae secti  a
DCHE. = AE, B. tangens in tangentem complementi, aequatur quadrato radii atque ideo ductu prisma, cujus babis quadra
adde prop. 4
ejusdem altitadin
tum radii, altitudo, distantia a vertice quadrantis, aequatur ductui inverso portionis condocicalis a vertice
abscissae, in portionem figurae tangentium complementi a basi abscissam
Coroll. atque ideo per prop. 29. sinus in secantem complementi, aequatur tangenti intangentem complemendi
ductusque circularis inversus su figuram secantum complementi, ductui conchocidati in verso infiguram  ts. 13159
BAEX = HE DC. secans complementi in sinum = tangenti in tangentem complementi. habuimius prop. 33. Corollar. quadcabile
Ila similia: HEK et ADC. ergo D - DC - AC
HE EK  HK
DR HK = HE AC. differentia inter secantem et sinum complementi, aequatur in secantem complementi, aequatur tangenti
Cylindeo conchoeidalis aequatur ngductui inverso figurae hysperbolicae in scafiguram
secantium complementi demto momento decantium complementi ex basi quadrantis seu vertice suo. ade prop. 4
DEHK= EK AC. radius in sinum, = tangenti complementi in differentiam secantist sinus complementi. Ate ideo colinder
in radium, atque ideo
portionis circularis aequatur ductui inverso hyperbolae in figuram tangentium complemendi (cylindio secantium
complementi) demto momento tangentium complementi ex vertice suo seu basi quadrantis.
Vla simicia: AdC. et HZ F. est autem 2F. radio. A HF = tangenti arcus dati +hengenti arcus dimidi complementi. et HQ est differentia
inter sinum secautem et tangentem dm. compl. dimid. vel est summa ex differentiis duabus, altera inte secantem
Xt sinum complementi, altera inter sinum complementi et tangentem complementi dimidii. hinc jam:
DC
(vel in secantem
 tangenti complementi in summam tangente et tangente complementi diundii
atque ideo cylinder secantium complementi sub radio, aequatur tangentibus intangentes complementi in tangentes
HE ex iA 
quadrabilibus, per prop. 33. coroll. et 3 prop. 34) additis tangentibus complementi in tangente complemen
ti dimidii. Atqui tangentes complementi in tangentes complementi dimidii, aequantur radio in secantes com–
plementi, demto radio in radios; seu cylindro secantium complementi, demto quadrato radii in distantiam a vertice
ciculi. per prop. 13. Utraque ergo propositio 13. et 37. eodem redit, argumento veritatis calcul. adde proper
Ade GH L HF AC. secans complementi in differentiam secantis et tangentis complementidimidue, aequatur radio in summan
ex fangente et tangente complementi dinudii atque ideo: se cylinder conchoeidalis, addito cylindro conctoeidis
falsa dimidiata ar tangentis complementi dimidiati, aequatur ductui hyperbolico infiguram secantium com-
cylindro conchoeidali mumento secantium complementi, ex basi quadrantis, qua-
drabiti aucto) demto secante complementi in tangentem complementi dimidii. Atqui secans complemen-
 in tangentem complementi dimidii aequatur differentiae inter tangentem complementi, et tangeatem com–
detihus rantemato (qui per prop. 35
plementi dimidii in radium Supra prop. 124. Huc talis aequatioorietur. Esto radius a. tangens c. secans d
secans complementi  angensinudii complementi C. literi superioribus retentis. ergo: gd- ge- act ae.
sed quia pro ad substitmi potest ac +si eB (3 ds quaditum quid ilb. n) et pro ge
et per prop., 12. pro ge substitui potest hacco ah- ae. Aed aequatiotalis. _ 1 43 +a  ae.
ac +ak - a3 + ac = aC + aC. seu aC + 34C - ah = aC. Ergo 3a C- ah = 0. seu 3ac = ah.
seu ac + ae = ac + ac. insigni documento calculi recte positi
ntie seni complementi aegratur quadrato
cibolicam domto ejus ductu  samo
radii. Atque ideo Figura targentium complemeati invese clindio secantium complementia
radi in distantiam a vertice circuli seu sasittam, aequatur quadrato radi in sagittam, rursus omnia eodem
tangentium semisupplementi, seu demto cylindro tam
redeunt crtissimo argumento veritatis.
prop. 32.
prop. 33
prop. 34
prop. 35.
prop. 36.
prop. 37
prop. 38.
prop. 29
verte