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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 215r, page id 00068194:0429
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 214v); this page is its right half.
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 79 lines, status machine
# Lines: 79 recognised, mean confidence 0.81
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# After the first blank line: the recognised lines in reading order, one per line.

ABq BC aqu g
pet  X - 5 + bs + et aequ. 0
2at + a x - yt aequ. 0.  fiat X aequ. 1Z + b. et y aaqui B tC
adeoque + rax aqu.
2a 1Z rua
+ a X aqu. 4 x   + 24 1 b.
y aqu
+2a 12b
+  b
R.. 13 I4CV. 44e
cometria tota constitui potest, sine ulla mentione magnitudinum
seu figurarum similitudine Be situ
rationum atque proporti ma soto cangulotum adhibilis tantum angulis et rectarum
unte linearum intersectionibus seu adhibito tantum situ e motu. Quando autem
magnitudo aut ratio problema inredietur, poterimus in problema ad alios reducere
termines ut non ingrediantur.
leris A ret colculo inventa facilius construantur, utile erit condi theoremata
quaedam apta, ex ut in circulo utilisimum est theorema, quod do
rectangula segnentorum in eo sempero aequalia sunt ita lenui si detur
ratio incognati redae incognitae ad incognitam equalis rationi quantitatis
cognitae ad cogrutam. Eodem modo excogitanda theoremata
ubi cubi rationi rectangulio ad rectangulum aequetur ratior ratio
rectae ad rectam, haec ex. P. Gregorio S. Viacentio polerunt duci.
Nunc obiter istud colligemus: annotabimus
sit circulus AB AEBC, circa diametrum AB. patet esse
ADB caequ. CdE, seu Ae aqu. _eDC.
CBD
Hinc modo ipsarum AD, BD summa cetur locus erit ad circulum datum
et sit Bla 1 X + 2y + 3 (1) 7X + 87 + 9 H Cd cus AB u lot3
aequ
DEp. 4 X + 5.y + 6 - 1 X~-2y + 10 , AD
Sint tres aecuationes: X sit runtus aequatio  X + 5y .  aqu. 0.
+8
ita ut sit 9+  aequ. CE. Dabebimus moblena solutum.
298.9
sint aequationes  19 e0 19 X 4 20 y + 21 rqu. 0.
(+
comparando 2. 3
et 31X + 21 + 14XY +15X + 26 Y + 2Y aqu. 0. sit 4) qd 19-7
aequationem t  analogiam 1. redueendo ad aquationem fet.
4, 7 X + 4, 8 Xy _ A 
+152 xy 468y
h P X + 12 Xy +ey
+4,9 X vo
+519 V
2tau
1 -y
+6,7 X +6, 86 y +6, 9
+13 X +23, Y
=81, 10X 12, 10 y 3, 10
22 fier. per X  aqu. (19,  - 7 + 22
(equa 20-8
6 rq t9
per etfiet   aqu 20, 8 - 9 + 23 per 19 fier 2, 1, ae qu 13 3, 8i7. 13 3 i 4
exautt.9 q sit.
+ ngX +I,2OXY
= 1 21X
41 19.. +oy +1,I
.
4 13, 19X, + 13, 20V 4 13, 2)
per _. fit: 119, (+ 1 + 19, 7 (=7) - 22 aequo ponams P Agu. 5. et fer: 114Z dju 22 (Erx nab, ee uqu. 2
per s. fit: 1, 20 (+ 2) + 20, 8(= 8) = 23 aequ.o ponamus 2 aquo et fiet 12 1 liqu. 
per 3X fiti : 12. 19, + 11, 20 (+ 2, 1. 2. + 20,7 (-8, 7 4. 19,. 8(7, 8) - 24 aegulo per
2 -2
20
o  +se  alis  pe u  dll o rus .  res
19
1 + F19 +v per ultimot temimos sit aec _3, + 310 + 2.9 + 27 gd 3
+ aequ. 19-7
6 aequ - 21 - 9
19X + 20y + 21
IX 1 12 y 13
His Missis vie
reg per elegantur
S aequ 20 - 8
absolu
seqventi na
XVIISZ
posto XAV () a. Kjo. AB.