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# Title: Leibniz-Handschriften zur Mathematik LH 35, 10, 1
# Folio 13r, page id 00068154:0025
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seutn - 99- 5r et 1p = 5r  = 2r -9
FO3e OG, Sr FG4n. SYtan = 99. E Trianguli OGF atera
sunt 3e, sr, 4n. Hiuc triangulum  ita fiet
+ 3C + 5Y + 99-5Y = +3C + 99
+3C - Sr +99 -5Y = + 3C +99 - (2)5Y = 3C- 1p
Ergo arca trianguli  Y99 - 3 C in 3C - r p. (4
Ergo depeer Les sit Sy2BB = 55 5. 58
et SBD = S3e- 1 p et Trianguli area S7qB 18D. (1) =672
+ 3C + Sr - 99 + 5r = 3C - 99 +2) 5r = 3 e+ pip : m
AV, 99
3C + 5Y + 99 - 5r = - 3C + 99
jam 24c: (2) 6. T2: 5Y = F_ 12: 5 M porro  FN:  MN: : FG: GM. Ergo
FN + MN,  seu FM: MN:: FG + GM. G Ergo  16. 1s seu NM: GM:: FM: FG+ GM: DL: DG
seu sb: B MN = 16IsGM oportet ergo quaerere FM: FG + GM est autem G_
1b GM b  1b: 5 GM = L 4 n - 12. 5 FM (45 - 12,: 5 = 400 -144, 25 = 256: 25 - 16.5) 44
Exg. F: GM = SA nS N - () 6EFL: =r e suique et 12: 5 FM: FG+ GM :: M 12. SM: a n. 5 mm
Seu::  12:5m: a +n + S4 n - 125 nm :: 1C (12: 5 m) An - (4 n - 12: 5 n, : 12 5 m (12: 5 W
3- 2 = 3166 -2.
30- 25-
(6: 9- 16. 107 2
4: 380
 G ZR + RH = GH. Et GH quia Triangula G2F, et GH) ob angulos FGE et OGH
 aliter.
aequales similia suntofiet GQ: GH(:: FGse. CG: An: 5Y et q R: RH:: 4n = 5Y
4:
a et FQ: OH:: 4n: 5 Y et F2 + QR FR seu 83en: 99 et GH + OH OG seu 57
Ex aequ. 1 et 2. fit GHAn: SYC + gR + RH = GH Ex aeq. 4 et 5 fil OH An: Sr + QK  3e m: 99
seu Qp) Y5CA: 9u .p ON et RH   5r f. . ut prius.  et ZR+ RH = 4n+5r Dus prius 
QH set RK + AH eq e Se ADA  (GH 1 in. 51 ) GH ip. gr et pro Os 
A
substituendo vulorem ex aeg. 6 fiet  e - 5F + GH - Gti qqisr
seu QR = 4n Y 3esr - 9gOH: 5r9q et RH a est AQ ut 5 ad 4n, et
R ZH est ad Re ut 5r + 14n seu ut 94 ad 4n. Er Ergo fiet
25-9 = 16
 R+ RH seu ZH = 3CSr = 99OH : 5Y = (ex aeq. 7) GH, - n: 51) p. 5  9 tatys 3. 5: 1 10
dut
in per 5.
iame  seu (per aeq. 6) 3C5r - 995r + g9 GH = GH ip. et GH = 5Y 99- 3e: 99- 1 mml per 4. dr. Sdi
Ergo OH  Sr 99 - 1p - 99 + 5C
 2r. 4 iP = r- 19)
: 99 - ip et CH: GH: BC - 1p: 194 - 3C:  D: GD
jam si
x3- 5C. seu funt
D- Ba: Y fiet  = da F.
13C- 1 p: V9j - 3C, an. :: n - ( 99 - 55 03e = ipr:
ran
cgran
Y (A)r An- ON: OD
eu O = (2r 4n = (4r4n - (
Erro O (4) _SranO ((4) Sran) = (1) FranZ O2
seu (4) Sran -C2 = D
seu (4) Sran = 9 + D = 99(-38 + 3C) -1 p2
quod verissimum est, itaque consentiunt duo calculi
nam ) 3Y =qr et n = nam (2) 5r =  99 + ep
et (2) an = 9q - 1p
3C- 1p est 3- (99 - 3c est axis transversus
sungatur B ex foco ad terminiaxis linusversi et 
in ea sumatur F3I, = FC fiet fiet BH = dimid: bea
si jam ex 51
scribatur circulus
normaliter educatur 51 et centro _B radio Bse  194 ee
arcus circuli secans st G in h, erit trangulum h5tB simile triangulo C
t 351 = D3e-Ip eritque CB: B.: CB ad hFC ut GD ad DL
si jam trausferatur BC in SYI firt et j  51 B et jungatur 
leut liranguum, ∞B 175)G simile insi GDL
sit DL = dr. jam dp = 2dY et ddr u =a. +se C - 1B2 cui a addatur vis centrifuga
AG tdp = 7Ba  e- p: 2G 9+pjam vis lentrifuga  GD: r - aD: r
pt ser
: 9+ p
ddp =- D a e + D a pP - D a p9  a pD: P q seu p sijam a-ddp aufera
circulationibus existentibus
aequalibus sunt ipsa
descensus proportionales
usis
15I potiylinus secutur
h in C, et fiet jungatur
B. ps
il BCa
Ergo 9+ pdp = Ba sec -pp.  e seu pdap + dp =  p dpba: sec -pp =
Ergo ddp p = d a c p  Da p D’a pqQD’ a
si jam a ddp anferntur aB. +d addatur vis centutuga aD: 1) fiet , BC + 2Y4 - 9GY + 2r - 4
9Sg. 16- 12
4. 12: 5.9 = 16: 15
d. 25-9. 25310
=9. 25 10-9: 10
8: 721.1.9.
cujus latus 1. 3
2Y- 9 - p
q- p = q. 2Y19
=29 - 2r - 2n
qn
24 n = 24 7,
Seu r- 24- L
en