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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 230r, page id 00068200:0461
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ars construendi quaeratur facilior observandae sunt Canones  constructiones quaedam parti
culares ab aliis jam inventae ac demonstralae, ubi paucarum linearum ductae ingens
calculi vis praescinditur. Incipiam a facillimis
vel subduplicare
Exempli causa: rationem datam duplicare, seu rectam invenire, quae sit ad alian
dota ratione, duplicata. quod ita fiet si vis duplicare sunto datae AC. AC, ductis in
vel sulidunticata
circulo ordinatis cB. Ed.  juntisus AB. AD, eae erunt in duplicata ipsarum AC. AE
unde vicissim si AB. AD. siut datae, AC. et AE erunt in ratione subduplicata
Eodem modo aliae rationis multiplicationis quaerendae sunt
per
nes in infanitum Temper lineis reometrice ex hiberi posse
non vero suldividi et libuerie possit.
Ex date
Ex Thcorculate Deallii
invenire 24Z vel contra
a-7
pidentur alem submultiplicatio
AB AZ
Esto Tangens circuli tunc
AC tangens arcus dupli
erit 2a 
a- y2
3) Erdatis, a. et C.  ducere La + + a + L S C- La + s t
5)
sit circulus cujus diameter AB. sumatur AC  ap CD productaque DE
seu aequationis hujus:
ad cirulum, jungatur sit AC  CD Y a. AF B C. e 9
CFHCB. et diametro AB radius circulus AEB et juncta
DE, parallela CB, ac denique ducta E EGF AFB c. erit CC
quaesita
constructio problematis pappi, apud Cartes. lib 2.
X4 - 2a X3 + La
VX
-243X + a+.
Unde quod
motabile est, si a sumatur pro indeterminata non minus atque X, locum harum
duarum indeterminatarum AC, CG fore ad circulum uo male: non erit ad circulum
quia alia atque alia sumta AC, alius atque alius sit circulus.
com
datur arcucirculi CB, trisccandus producta diametro dum tangenti
oecurrat in N. Datu AC demissaque CF. dantur: AC , a.
CNHC. AN  nn CF p f. FNj9 Trisectio putetur
facta in punctis D. E. et tangense ducatur EP. DR. CK
rel c
Ex data EP, 7. datur DR, quae est
242
L(vid. num. 2)
a- y2
ducatur AEQ, et gp. pate ACN QNN ess similia pset
et etim esse C, 1+ ex data EP dari GN. item Suiangula
de CFK) ∞
2SN. et ZNB CN = Cg. pitem Q N,, CN 2
es
At 
ob lia imilia QSA, e PEA, erit
Jam ut CN ad CA, ita NZ ad Q N ad QF et
Se CF QN et SN(, FN2QN jam AS( AN - NN. pursusque ob friangula
et ordinando ten et
CN
similia QSA, et DEA fiet CFZ
fiet Ep seu 7 C AEria,
tasc Y cna
- cg L - 249
+cgarL
243F
aequatio
25 unde Zpy afc- 2072
+afC (10.
a- qu
en =cg + 2092
Alii methodo institeramque expuncto Eidcunttendo perpendicularem EH.
a - 50
eanque ponendo incognilam. Ex quo d sequitur AH eEK B HA seu MFB FA EH X
eCM  CF - nF. AM 1 SAF v MF
LG1
MI
AGX
AH.
C(B DGF, AHCCM
DL. 1DG- 2G Jam aliunde
DK r  AG
DL
F
H A
LGIY AG∞ NDG= aV
habetur ergo
qua resoluta, et abarratio nalibus viberata, ain quibus incognita continetur
liberata, brietur aequatio octo graduum. Cum tamen non sit, nisi trium sive
A cartesius clgarlissene, sunta imoguita, issa sitensa
past.
50
Ert
asi
ut similit
Ergo CN- C2
a
ob slasimi
ex
estet
eN
Ne CFN fiet
AC
ad eA eF