# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00067993:0166
# Permalink to this reading: https://leibnizlegible.com/page/00067993:0166?run=39
# Title: Leibniz-Handschriften zur Mathematik LH 35, 2, 1
# Folio 83v, page id 00067993:0166
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 84r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00067993&page=166
# Source image: https://digitale-sammlungen.gwlb.de/content/00067993/jpgs/default/00000166.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 39, 2026-08-27T09:55:26Z — 80 lines, status machine
# Lines: 80 recognised, mean confidence 0.86
# 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.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

Definitio 3
Figuram egmentorum est quae constituitur, ex tangentits
arcuum dimidiorum diam etro circuli ita ordinatim
applicatis, ut sinibius rectis arcuum inteqrorum in directum
in fig. 2
a quemadmodum arcus, AB dimidiati
translatam videmus in DE sive diametro
ADita applicatam, ut sinui recto BD arcus ipsius integri
AB directum jaceat, Maxmia autem applicatarum
quae irentum tangit,  unde fit figura AEF
quae procurrit in infinitum
versis F. Num et ad
rectam HG. tangentem
circuli, meximam applica.
tarum s inf in infinritu
accedit, ita tamen ut eam
nunquam attingat, quare recta
HG quam velut appli catarum ejus maximam consicerare
possis, est ipsi asymptotos.
Voco autem figniam segmentorum quia postea ostendam portiones ab
ea abscissas, ut ADE perpetuo segmentio circuli respondentibus ABA
duplicatis aequivalere. Quam figuram a Geometris non consideratam
miror, cum Cissoeide parter et C Conchoeide simplicior sit; et
n habeat hoc egregium ut posita AL vel DE ordinata, vel DE ad
em vel diametrum, sive AL, abscissa ex tangente verticis; rationali: etiam
 AD, abscissa ex diametro vel Axe, sive LE applicata ad Tangentem
dverticis futura sit rutionalis.
Quod treviter sic ostendo:
cognita est differ. prop. 3.
Figura quam voco Segmentorum est rationalis
ibe ex quid rpircola positu enim AD asue L et X et DE siveML 1, y fiet:
per prop. 2. est enim per constructionem sive
aefinitio acni figurae segnentoru.au AD sinus versus anus interri, et
ty
DE er sive AL, tangens arcus dimidii. Figum autem
in omnis rationalis a me appellatur ide def. 2. in qua ni cujus
aequatione unjus incognitarum valor simplex purusque habetur.
Habeatue flexum in contrarium, et ita investigabimus: aequatio cjus est:
a X + (Xis p 2ay, unde: al + ly  4ay - 2xy ac
a proinde BB +ay- 2∞5, et pro X posito ejus valoret, fiet:
ras- 4 a
Est ergo L
a+ y
sive: C 4dys ( 4aV - 4ay) vire l
.a + 2ay + yt
curvan
24y2
ui l N au
a ray  uno habet fuit ex
semperque obvertere concavitatem rectae AH,, eum X semper sit major ipsa b
Ab x addater  ra, fiert ras Auferatur X, a a, frei: la = 2a5 sive
rat + ray- 205. sive 2a
a +y
2a - x Dt Eritque Z  CZ in figura et summa
omnium Z aequalis segmento Circuli duplicato. Jucatur Z in y, seu HZ. distantiam ab axes
habetur solidum ex revolutione figurae AEFGH, cucu axem AH. quae erit: L co
unde 2y  a co +s co. Quaeritur ergo hujus figurae quadratura quoundo eum apparea
Satis simplex. Ejus tum tt ejus langens inrestigetur, fiat: eo -rico ssit
si vera sunt quae dianturi de ductibus nom 62 63 habetur absolute
Habetur jam et ipsius figurae integre dimensia ex supposita circuli quadratura,
L-gao et H A. Ergo f
urca alias bass ut De genitum  HYa. seu 
jaceant
n amm. gei.
summ omnium
+ayta
+L Eap + BS adatus s X) S
tia ergo datur et gag, + 2y + 2ay4
Eqet datur ex qoad  aet3
dincusio lnia
qua gest
habebitur ergo e
datus ex
tangense AC
 e quad. Hpil. l. X TI
2ay- 2y
et +y pi gay - 2Y H
pro y pone ejys valore, vel 
s
a X + Xy