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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 113r, page id 00068196:0223
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silesectio
si ad eandem sectionis lonicae  MCDN diametrum
in aequalio
BL ordinatim applicatarum duarumCd, MN extrema ad
easdem diametri partes posita jungantur, rectae jungentes cM, dN
concurrent in eodem dumetri puncto G. Nam bisecantur cd et
N MN in B et L ergo C A ad Bd, ut M L ad LN, et CB ad M L
ut _ dB ad NL ponatur jam MC diametro concurrere in
G, et Nd in (G) _ Est autem. GB ad GL, ut CB ad ML, ergo
ut D. B ad NL, ergo ut (9) B ad GL  ereo (G)B et GB sunt aquales
et adeo coincident G et (G)
Si duae rectae fF et si crcum ationis conicae tangant re
b, sa sectionis eonicae arcum CHdetangaat in extremis rectae CF, dF,
rector, concurrent in
sectionis conicae artum ad ext in extremis tangentes rectae
concurrunt in diametro subtensam arcus bifariam secante 
patet ex praecedenti, nam in casu contactus coincidunt cd et MN, et tangentes
eF et dF concurrent in puncto F diametri HB.
iisdem positis sit H punctum quo diameter arcui occurrit, jungantur
CH et dH. item KC, Xd ex centro K.
producatur AHHK ad KV aequalem ipsi HK est YBH = CB qu.
VB + kB, HB = CBqu. VK+KDKL, LH= MLqu. C Errgo eut
GB qu: GL qu= CB qu: ML qu= VB + KB, HB: VK+K L LH
VB = VHQ AB fit GBqu: GL qu = V H HB L HBqu : W H. LH - LH qu
harm. inter phime. Constat ex natura sectionis conicae centro praeditae esse KB, KH, KF
in continua proportione a Geometrica, itaue erunt et polysgona inscriptum
Primum, inscriptum secundum, et circumscriptum primum, nempe Xd CAd, XCC)
quar qua to continue proportionalia, nam reolountur in primum
quidem in triangulum KCD, sequentiam Trapezia, ut KCHd, RFd. sed haec triangali
pt Trapegia, euorum dimidia sunt triangula ACB, K CH, RCF, quae cum sint ejusdem
altitudinis, erunt ut bases KB, K
H, KHKF. D
Polygonum KCPH = polyus. K HZd vid Greu a S. vinc.
TKCH, KCRH, Asunt progr. geom.
KDH, HDPH, KD ZH sunt prioribus aequalia respective vid. Gregs. an
_ Ergo summae priorum ret posteriorum sunt
KCHd KCRHSD, KCPHed sunt etiam progressionis com.
et ita semper duplicari possunt numeri late lum, aut dimichari
mavente eadem proportione
Superest ut perimetur quoque considerentur qui in circula
t ectora
quidem procedunt ut polygona; sed non in sectore Elliptico
ujus tr perbolico. Haec eergo inquisitio superest
a
sit 4. latus rectum a AB, RX CB, y VBH - CBqu seu
 9+X, 2qu. q x   4+X, q.x = 49 - xx ex prop. r. (ouico
est 2 ax - a XX = gy seu 29 - x ; y = y : a X. sit X = 9- Z fret
(aq 2aZ 99(+ 2a 92( a Z3 = yy seu a9 - 4 27- yy
L
1Z = ydus dy- dZ =  EZ: y. fiat BP = 2Z et BF = yy: L
= 9q. Z = Z seu dy. dzue quque +Zet KF = 49: Z. Ergo est
XH med. prop. inter RB et KF. jum datis Habemus em  KF, ex KH
constons 1 c B abscissa. habemus et CB= D Bordinatam. jam o s ut calculo ine
niamus , EF, ut et ex, altera parte: quia in triangulo datis duobus. la C(F, datis 2 laterco
Et m-n, l- m +n,
et mitn, et men, i tt 16 = qu adr area et quae set data p.
C med.Geom inter A et B
ipsipum A et B
D med. Ixariu. ac B et C
sed in circulo
perimeter ipsius eest
medGeom inter per
metuos polygonorum
Perim. ipsius d est men