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# Piece: https://leibnizlegible.com/api/records/25871/text
# Catalogue record: 25871 — [Ductus-Methode]
# Incipit: Sit AX,x XY,y XV,v.
# Date: 1678-02
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=25871&katnr=57026
# Work: https://leibnizlegible.com/work/00068196
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folios: Bl. 323 (from the shelfmark LH 35, 13, 1 Bl. 323): 2 pages, canvases 641–642, page ids 00068196:0641 to 00068196:0642
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068196&page=641
# Lines: 120 recognised on 2 of 2 pages, mean confidence 0.71
# Catalogue: Leibniz-Katalog / Arbeitskatalog der Leibniz-Edition (https://leibniz-katalog.bbaw.de/), ed. Arbeitsstelle Potsdam I der Berlin-Brandenburgischen Akademie der Wissenschaften, CC BY 4.0.
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
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# After the first blank line, page by page: a "## Folio <label> — <page id>" line ("## Canvas <n>" where no folio label is recorded), "# " lines naming its source image and model, then its recognised lines in reading order, one per line.

## Folio 323r — 00068196:0641
# Source image: https://digitale-sammlungen.gwlb.de/content/00068196/jpgs/default/00000641.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 64 lines, status machine
sit AX, X XY, y XV, V. et d sit figur
ABCTA in plano pagina, et ABEVM, pependiculariter
ad paginam erecta. Perveneritque ductus usque ad Y8, pacal-
lelam usque ad ipsi AB. cui YC insistet  perpendiculariter
VX BE V huc translata. ad ductum jam factum ipsius
AXVA in AXYA, applicetur area ipsius AXVA, proveniatt
recta AP. parellela ipsi XH et ad easdem partes.  In AX
sumatur AG, designans GX distantiam centri gravitatis, figurae
AXVA, ab XY. compoletoque rectangulo AGa erit Q locus
centri gravitatis mobilis AXVA partibus dispersis, ad quam
pervenit per ductum. At distantia centri gravitatis figuri
VXBE) a plano ABE, quae est cum ad Y8 perveneris
est eadem quae ipsa XY. Ergo sumendo in Y8, punctum V
sie ut p sit distantia centrigravitatis figurae VXBEV a baso
BE; fiet Y locus centrigravitatis ipsius VXBEY quo pervenit
hactenus inductu. jungatur V9, et secetur sic in K, ut sit Gk ad VK
ut figura YX BEY ad figuram AXVA. eritque V locus centri gravitutis
totius mobilis ABEVA. Nunc pars VXBEY nondum dispersa ad continuati
onem ductus ulterius promoveatur, usque ad AS, aequalem et parel-
lam ipsi Y8, cadente s in DC, erit oolidum sub rectangulo YS et sub figura ei perpendicularitur
insistente VX BEV, elementum ductus novum. Centrumque dictae figurae Cdemissa ex eo normali
in R5 cadet in T, quod habemus completo rectangulo 56) T. jungatur T9, seceturue g7 ut
prius semimus L) nempe in puncto (X) sic ut sit Z(K) ad X T(K), ut figura VX BEV ad fiu AXVA
du ut gK ad KG, est ergo K(K) parallela ipsi VT et erit K(K) progressus centri gravitatis
otalis in ductu continuato ad YT vel ad 45. et K (H) ducea _ in totum mobile ABEVA
dabit rectangulum RY∞S, elementum ductus. sit ductus fatati totius mobilis t. Ductus
p ex AXVA in AXYA est s syvax. Ductus ipsius VXBEV in XY est fCyspax ductus
totulis t est syxax 1 ysvdx Cts ysV ax = ysvaX. Ductus totatus L est YsYdx + huc ustue
SyDdx + y Nax -y srax
AG= fod IXvat = svax G9 =5∞y+x: Suax.
in AB sit B F aequ. 8) erit AF = SXVdx = SXVdX, :, SVdx - sudx. Cx y
in FVagatur normalis QH, cui occurrat (HX in I. et esit IK ad H H) ut NVde- secX
ad SV ax. est autem HG H) = y = svyax: Six. Ergo erit Ik = 3- 5vy dx, Sy dx - svdx
seu IK = 3sVax -y seax AV svya
Vdx
suax
Svyax
svax
vax et GGtik = ySV dx -y)vdr t svycu 
ax.
quae recta ducta in ABEVA, sent in sVax dabit ductum F, qualem habuimus supra, in quo
hademus consistit calculi comprobatione. porro investiganda jam est, K(K) quae est ad VT seu ad du
ut (Vde = (vax ad Si dx, erit 7 eritque K(K) = dy (sVdx - sBax, : (V aX)
et, K(K) ductam in mobile monifestum est seu in (Vex, manis estium est
paltot
esse rectangulum R, seu 5 vet dus in XB femin facit elementum ducus
facere du (SVdx = Sedx) Elemento a ductus, serit VX BEY ductomin 85 seu in dus
et poteramus habere sine omni illo
apparatu centrorum. Itaque Fiet t- yf+ t fiet + ductus aliquousque totalis
= (du V, = ((dy svax). Est autem suda constans totm figura ABEYA, et fiet tnde
idus srax) = sVax say = ySVax, et + = ysVdx - s(dy Svax). Videndum
quid det Calculus eliunde sit a sydx fvix = co yax soda A vds fydx X ded
exvidemur nihil
novi discere, fit eninli ysvdx = co fit  dy svax) + 5d vax = ysudx
taque nihil hinc discimus, nisi quando sedy sedx) est tractabilius quam syvax
sit v = +0 y -4 fed 5 70+x 
E0ro sol Z
fiet (. ly svex = d = N B dG + EdD, sep si et fuix Aay vdx =
(D dei p q 2174)
2, 4 + 5, C, Yog
loco duchus rectilinei possit similis concipi curvilinent, veluti si figura
ABC esset  no superfica sphaerae, et AB linea arcustis irculi in sphaera aui
perpendi culaniter ab vsea sprbrae insisterent VX. la rotando prodiret ductus sprarius, cudus elcm
daretur Elementum

## Folio 323v — 00068196:0642
# Source image: https://digitale-sammlungen.gwlb.de/content/00068196/jpgs/default/00000642.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 56 lines, status machine
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