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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folio 125v, page id 00068195:0250
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chordae in qualibet assignabili minores
in semicgplicide afbic. decrescunt arcuval tangentes eycloeidem componentes, ab a-
tra in Semicuclocide aequali et simili ahdle. crescunt ab a versus e.
ua
Hinc mexina dhordarum dimidiula, seu maxima semchorda, ducitur in m mininam seuprim
chordam. sccunda in in penultima in pirim in et sequentem, seu pumam et secundam antepenut
tima in primam secundam et tertiam, penantepenultima in prmam secundam tertiam
quadam. de productum dumdratum, dabit figuiam evolutionis.
2
1
1+ 2
1.92 + 3
4243+4
a +b = c+ d
a-b = c+ d - 2b,
cadc-d = 4) b-
a Ctd- 2b ∞ a +b - 2d
imo stra:
Mimima seu prima senichorda ducitur in maximam seu ultimam in secunda
in ultiman et penultimam; tertia in ultimam penultimam t
antepenultimam et schema hoc erit:
1 4   16 ()0 0
2
4+ 3 14)
3 4+312 A1) =
4 (ap 12+1 
eo
4 + b 1b f - b
2b. 0,
22
9 16 (+ (48
4 4 16
mejus
4 9
9 4
 te
i
0- 2b 1b 0 - 2d. Nota siquia croscad i dascenta chordami ratione,
26 c6 2
atb. erd
a +bFa 
atbyu
uga minim
Cycloeis ita crscit: chorda maxima pene maximia, et c.
fien evoluta ita crescunt: Choria maxima: chorda maxima
et pene maxima 3. chorda maximgus pene manimo
pertia; et B. eo ipso fita ista cresunt in in versa
remimima
Nc. Videndum anhoc
chordam, ut minima,  ipis universale, an prope
differentravel.
lnvestigandum exacte qua sieratio hujus (a16 a16 ad ho. (16d1
Jam a D. quod aequale est ipsi A.
ouferatur quod lincola duplici
circumdatum est intra d. aequale
ipsi B. restabit a
differentiar ider Aec B. B
9
c 4
b9
d 1 d 1.
b9 sea ot i
c4 19
E4
o
64 64 (c4
49 4g ag A9 (49 49
36
s  
36
2el25l2s
16 16 16 16 16
9
a + d - b = c
d mb-
Item a +d - c = b Ergo
Hinc jam sequitur opendium fieri
posse ratiocinationis nostrae, nam
auc = b - d
choidae infinilae cytoci didengponentes
creseant an a. versus
per
esqu ut chorde circuli, etc.
 Porro fila crescuntceodem modo seu
4 4 4 + 4 e cycloeides evolatae, sunt, ut patit exschem
i
1
Hugen. prop. 5. part. 3. Ergo sunt ut
crescunt ut quadrata chordarum multiplicatar
ultiplicata per cocori basin, peu ut
Summahorum est dimeditisumerus, quadiator e putum sa
maxime
ili calcrum per hungum
aoridem, ut guadiatu e aliquod ad lum
xchnis, ut dictum conflatam ejudem basis et altitudinis. Et.
si numeri sint progressionis Arithmeticae, et primus per ultimum haec linca contitorm
secundus per penultimum et: multiplicetur, summa recta horum osc ub si g cyclandu
rectangulorum, erit dinidium summae quadratorum numerorum. Mponentes cicus non 25 i2s
Regula generalis si in quacunque progressione vel serie derscerent est 225
primi per postremos numerenur mul vel peneprini pehpene: circularis diametri 104
duplicati, ut A ato 354
postrenos multiplicentur, sucmma rectangulorum inverse circulus loco provolulionis
productorum aequabut summae directe productorum aliquod punctum in circi
irca
seu quadralorum, si scilicet quadrata differentiarum tia immobiliter circumaser
aut primus ei p ultimum perc primum secundim
et oenultimum eH. adjiciantur. Quae cum infinito
Aut puncta negligi possunt
ejus aequatarhue 2bC
d Y a 16.)  a. 6-  au d 15)
2b. c9 B, = b - c, se. = b - c:  b -c
100 100 100 100 100 100  100 100 100,
49 (29 49
36
c 4
ta-d, a-d, a, - a - d, d = a- d, a - d.
+ b-c
cb c
64 (64 6+ 64 64 64
Eg
36
a + d = b +C. En
6
5