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# Piece: https://leibnizlegible.com/api/records/155/text
# Catalogue record: 155 — Leibniz an Johann Balthasar Wernher
# Incipit: Notae Algebraicae usitatiores Additio: a+b Substractio a- b
# Date: 1697-10-16
# Sender: Leibniz — Addressee: Werner
# Akademie-Ausgabe: AA III,7 N. 148
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=155&katnr=59125
# AA III,7: the volume in the Repositorium des Leibniz-Archivs (CC BY-NC 4.0): https://www.gwlb.de/leibniz/digitale-ressourcen/repositorium-des-leibniz-archivs/laa-bd-iii-7
# In the Akademie-Ausgabe: AA III,7, p. 54 (PDF, Repositorium des Leibniz-Archivs, CC BY-NC 4.0): https://www.gwlb.de/fileadmin/Leibniz/repositorium-des-leibniz-archivs/III7B.pdf#page=54
# Work: https://leibnizlegible.com/work/00068230
# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 17
# Folios: Bl. 2 (from the shelfmark LH 35, 3 A 17 Bl. 2): 2 pages, canvases 3–4, page ids 00068230:0003 to 00068230:0004
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068230&page=3
# Lines: 133 recognised on 2 of 2 pages, mean confidence 0.89
# 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.
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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 2r — 00068230:0003
# Source image: https://digitale-sammlungen.gwlb.de/content/00068230/jpgs/default/00000003.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 54 lines, status machine
a + b
a = b
Vincula et Y
Notae Algebraicae usitatiores
a2b ides vel ab,  vel 2.3.  id est 6, vel 2. 3. 5 id est 30
a: b vel . Eodem modo exprimitur ratio a ad b
(3Ja id est a vel cubus ab a
Ia id est radix cubica de a, vel (3) a
a = b
a p b id est a majus quam b
a e b id est a minus quam b
a: b = c: d, significat a esse ad b, ut c ad d
3 :5 = 6:10, seu ratio 3 ad S,  aequalis est rationi 6 ad 10
pro renata
 pro his adhibeo mta, lineas, parentheses commata
a + bC vel a+ b, c, vel (a +b) C significat a+ multiplicari in c
a+b: C vel a+ b,:c vel A+ b) c significat a+b dividi perc
ab: C, vel 3 4:5 significat factum ex a in b dividi per c
2.3: 5 significat factum ex 2 in 3 dividi per 5
a: b vel (a: C) b vel a: c, b significat idem quidem efficit quod ab: c
sed alium indicat ordinem operationis, ut prius a dividatur
per c, et proveniens multiplicetur per b.
a+ BC taa +bb ab
vel (a + bc + aa + bb) ab
vel (a + b)c + aa + bb al
vel ((a + b) C + aa + b1) ab
vel a +bC + aa + bb, ab
vel (a+b) C + aa +bb, ab 
Haec omnia idem significant, nempe
a+b multiplicari per c, ad productum
addi aa+bb; denique quae summam
provenientem multiplicari per ab
saepe autem utile est commata et parentheses adhiberi pro
Lineolis, qi linec quoties una lineola super aliam esset
ducenda, quod praesertim in typis incommodum est, facitque
lineas nimis spatiin occupari nimium spatii occupari
 sunt et aliae nota ut ambiguitatis, disjunctivorum, rela
tionis, similitudinis, r congruentiae coincidentiae. Et pro
calculo infinitesimali, differentiarum summarumque varii grudus,
cerrinotis utimur sed has ut minus ordinarias, hic omitto.
Additio:
Subtractio
Multiplicatio
Aequalitas
Majoritas
Duitio in se seu
divisio.
potentia
Extractio
Minoritas
Analogia vel
proportio
verb. gr.
distinctiones

## Folio 2v — 00068230:0004
# Source image: https://digitale-sammlungen.gwlb.de/content/00068230/jpgs/default/00000004.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 79 lines, status machine
a + b, a -b = aa - bb
a + b aa - ab + bb = a+ b3
a + b a - ab + db - b3 = a - b
ete ita porro
mia- nsa
mna-nnb
mnulaa -mndab = un 3bb
Ma + nb
ma- mn V ab + mn V ab - n3 + 63
mt a - n b
ma-mn Vab + mu ab - mn Sab +n b
d
ma + n5 b
Ma =nn Vab + mn Vab-mn  a b+ mn Vab = n 
mia +ni ma - 16b
Et ita porro. Hinc enim apparet progressus in infinitum.
Nota: possunt m et n negligi, seu poni = 1, quasi esset tantum Sa + N
Facile enim ex calculo pro solis, sa + ib duci potest calculus proma +n Vb. idemque est
in Trinemiis aut pluribus ad huc nominibus
Qui casculum eundem pro Trinomiis peragere volet,
pro praesenti Algebraestatu
n sextigradus
poterit nunc quidem subsistere in quati gradus irrationalibus
seu in fu
lem A ad or
.Nam lonus procedendo, calculus
ultra
nimis prolixus orietur Nam ad sudeaidas procedendo a
a Ba LY6+ DC
Calculus nimis prolixus orjetur donec Tabulae quaedam combi-
natoriae prius sint praeparatae ad praeimovendam Algebram
po sed
et procedi
 erdoolexe
ad cubicas qe qua
unt pl nassis plurmomiiis in ruditibus quadraticis sbst potent subsisti nis
neessariae praeparentur.
sit a+b +C =0 seu a = 0
fiet (quadralius at - 2aabb = 0
pro tollendis caliuis a + 3a63 - 21 ab c = 0
irvationalibus
usque ad Cubicas; pro pento quinomiis aut
senomiis potert in quadratics radicibus
subsisti
Diguintiais a - 44 64 6a b5- 124 abEt = 0
a  ab + ab
+ d b-- abe+ b
Uo. Haec Methodus tollludi rctio aales
non tantum usum habet pro fractionum
denominatoribus, sed etiam po aequa
tionibus in universum
2
ut MVa+
seu in L
ac
pro quadrimonio sit arb+c +d =0 fiit -a - b = ct d et a + b + 240 = c + d + 2cd. seu arb - c - d 4 2 2cd
6d
et ita res ad trinomium reducta. unde si a +b - c- d boletur ee fint +C
Ex Tabula illa mea combi formarem  reductoria poteatiaum
ad forgas X, y Z es seu a, ab abc videtur haberi pss
Ba
meralis redectid Prationalium. A
torte iiuc melus se sota adesset Z Miirquia X00 firiit o ne pent.  + 2at +b
Nam
pudrato. quadra sicis per solas
a eu
a
y et Z, ut rtitet solum aeui. pro co quae densi eptitibi
hibe
ad 
eito X=0
invenientur
preo quadralicis persolas ac, a, a, pro cubicis persolas a, a, as 1s 2d quarum opetollenda literae  y, L. cdB
suffecert autem rem tructari per modum equationiem, ex quibus tollantur irrationales, Et
imo qua co est smplit abis sipeut 
eamque in rem ex hiberi cheoremata etsi enim methodus tallendi irrationales jam ab aliis est explicata
a X- 1X NZ Hloqu ae sd pu y liamio ajpugendi  ab, tionral s, aqu utit Aes alabid deniq sond tr d a tinemvet 82, EB, eoq9, i atta 5
ipsam tamen sublationem non actu ipso exhibueri
pro quadrinomit