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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 142r, page id 00068196:0281
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9tpil. 167
super
cils
cylinori obtui
sit AB ed superficies cylindr
obliqui  AEBCFd cum
bases circuli AEB DFC. pil
d in planis parallelis positi
Ex  punctis circumferentiae
superioris AEBG demitiantur
perpendiculares in planum
iniferioris nempe AL. EM.
G
C. id est describatur in plano
inferiore circulus superiori paralle
ets renio secodee
aequalis et e regione respondens
ita ut recta a centro unius ad centrum
alterius. sit duobus planis perpen
diculans.
tam
ut metiamur jam superficiem
cylintiicum, considerabium es
compone
qus
eibases sum elementa curdae
circuli, hns latera sunt
recta ut uniqus recta sempe
eadem nempe describens superficier
cylindricam. qualis AD, EF BC, E4
possunt aotem bases et latera
et tomeo area mutari, quia
Nomleio intelligi semper eadem, sed anguli
continuo
mutantur, omboidis autem cujusque area invenitur
si ducatur derpendicularis ex  aliquo angulo
.
perpendiculam
in baseu eigui ex Gdemittatu momina in
rectum 9C Telementum curvae B circuli) productar
ad est in circuli tancentem, vel ex E in recta
F circuli tangentem ad F nempe haec minima perpendi
cularis ponatur esse. FTa patet eam esse eiq
compo quadratum aequari quadratis AEM. EI
2
est autem EM quantitas constans, nempe distantia
planorum, quam vocabimus d. quaeritur recta
MT. anguli PLM aequ. ang. HDF. ergo P+M.
parallela HF. Porro pH. distantia centrorum sit e
et patet pH esse ad HR ut secans arcus, DF est ad radium
socaua sinus complemensi arcus y. erit secans a. Ergo
k Hk: C:: a: a
seu HRaequ. ey. sivc VHAp_ HS
EF requ. a- eZ. Ergo YMaequ. DM - RF aequ. (a- a+ exte
M F aequ. HR aequ. P_.
Et ET aequ. 142 rC et
4