# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068194:0101
# Permalink to this reading: https://leibnizlegible.com/page/00068194:0101?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 51r, page id 00068194:0101
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 52v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068194&page=101
# Source image: https://digitale-sammlungen.gwlb.de/content/00068194/jpgs/default/00000101.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 58 lines, status machine
# Lines: 58 recognised, mean confidence 0.90
# 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.

Conica
29. + X, X, q = yy
X = gu CA q BR, Y 29
x - 29. + x 298 = Et XZ = XW 2t HXu
BX = 24 +X,  29+ X - + = +: Y
Sumar BXM, sit
X
sit
n lis bk+
 L
XZ = CB: BF
sit anulus rectus CBR sit triangulum ad B rectangulur
preducatur tatus CB in CB, si opus producta des versu B
tumatur punctum quodcunque X, per quod ducntur ipsi BR
 unde educatur ad angulos rectos XZ occurnens ipsi P
parablelae ad CR, en  denique a B ad sumatur
ab s ad versus B sumatur e . la ut _ BWS sit aequalis ipsi XZ
circa I r describatur circut circulus secans BR in F
Comphatuo rectangulum F BX Y eatque Y ad sectionem (onicam; Et quidem
si punctum X cadat intra CB, erit Elipsis (vel Ciiculus; si extra erit
parab Hypertola, Uenique si  purstum C infiniti absit a B incia ent BR erit RC paalletaips BC, et
erit erimiscit BR et XZ et BW, eritque X BW = X B, erique
et Curra erit parabola
reita.
Sit Friangulum datum ad B rectangulum EBR, et sit BCd
datum
dupla ipsias BC, incnta sumaturque in CB si opus producta ultra B,
Pa reet pandum K, et per puncta p et X ducantur parabelae PZ ipsi CR
et XZ ipsi BR, quae R Z occurrat  X L in  ipsi XZ in Z et ipsi NX BR (si opus productae) ta N
Sumatur RX recta BX L, sic ut Y L sit aequalis ipsi XZ
et circa BL deserlnem circulus secans X L in  M B X L Y
Z in Y erit punc punctum Y in curva conica
quae erit Eaipsis vel circulus si X cavat nitra B et D i sed erit
Hyperbola si X cadat B cadat inter P et X: vel
Hyperbola opposita si permutentur B et P quae dixitaus de B. et D in Ellinsi autem haec permulatio non aliam
quod si Na inpin C infinite disteit a B, sit B  duple BR
acet BAA vel X X Z val BM aequalus puntat BBo
fit linea sit parabolam At haec quidem locum habent 
punctum C sit assignabile, sed si ponaur BC) in firsiti distare a B
fit Unea fit paravola, et XZ, sol BM abit in BR BN
duplam ipsius BR quia erim LZ est ad pC a BA ad E
(Id est ad BC) t BR ad BR ad BC, erit val ad PC, ad BC ort ad pC
eruat LZ et BR aequalat, et ob C infinili distantem erit RL
paralleta ipsius Bp ergo et XL = BR Est amtum B P (sou dupla BC
latus rec Est autem BN dimidium latus rectum, BC dimidium BB
litus transversum, quod est Bp vel quae recta etiam dicitur Axis,
C est centrum B est vertex, D vertex oppositus. In parabola ergo
ordinata XY est media proportionlis inter Latus rectin Et absissam BX
it latus rectum BN quod Ellipsi  minuitur in Hyperbola
acgitur ipsa NF (completo rectangulo NBXF) quae est ad ab NF sen ad BX
ut BR a BC, seu quae est ad abscissam ut latus rectum ad transversum
Unde his figuris nomen. Quod si latus rectum et transversum sunt aequalia
ex cllissi sit circulus cui rrspom et Hyperbola aervilatera. Si constructio
generalis ad circulim applicetur is qui describendus est ad punctum determinandum
est ille qu est construtudus Rocta a punctas ad purctum lineae
ducta vocitur chorda
Wd
lineam producit