# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/898203430:0161
# Permalink to this reading: https://leibnizlegible.com/page/898203430:0161?run=74
# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 133, page id 898203430:0161
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=898203430&page=161
# Source image: https://digitale-sammlungen.gwlb.de/content/898203430/jpgs/default/00000161.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 47 lines, status machine
# Lines: 47 recognised, mean confidence 0.88
# 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.

GRDTHATIONNM COMTC. LIMITIBVS LIB. L.
OE erie in ratione transuersi ad summam laterum; quum sC ergO FOIZ:
OD ad totam OR vE parS OP ad partem OB, eric reliqua PD ad reli-
quam L. R ve toca ad totam, e ve pais ad parcem, nempe ve transuei-
sum dacae Fyperbolae ad la crun summam, livre, ex Fypocheti, veNI trans-
versum descripiae Hypctbolae L. F Y ad suum rectum LI; sed P D ad F. R,
sumpta communi alticudine DF, est ve rectangulum P D F, CIVC VE re-
ctangulum ipsi aequale 2 N DL. ad rectangulum liib R F, FD, CivC ad 2 19. huius
quacrarum mediae proporrionalis F. A in exiangulo rectangulo P AR sectO ad num. 2.
per AD in criansula libi, ac inrer se similia, vel ad quadraum lemibalis
DS, ip(i E A aequalis ( ex Moduli inventione) _ NL ad L I est (ob HI7-
perbolam L F Y) ve b idem rectansuum NDL. ad quacra um semiordi- p 2L. primi
natae ex D in eadem Hyperbola, ergo ipsa semiordinata ex D aequaur Conic.
semibali DS, ac ideo Hyperpola L. L. Y necellario transic per Si eadem
Paricer ratione octendetur transire per Y. Fc quum rectangulum B P F
aequale LIC C quadrato semiAXIS PL, FCCL SF, TF LIyperbOlam SLF c rg. buius
Concingen d ad S, F. Ouare haec criansulo circumaucte S P P eAt in- adnum, 2.
Scripta.
dex coner
Insuper, sit in Fyperbola S L. T a puncto axis B ordinata BF, _ Cx ConC.
orisine F alius quicuique ramus F. V ad dacum ABC, de per V ordine.
tuE X Y.
Tam, quadrata FaMOTUM FV, E A, F B sINE ve C rectangula NXL., ay, Buivs
NDT, N BL, vel ob Fyperbolam SL T re E quadrata semiordinata F21. prim
rUI XY, DS, BF. Sed horum quadratorum hoinolosa F A, DS sunE ConIC.
aequalia, ob poluam aequalitatem rectaruur . A, D S, ergo ee reliqua.
reliquis homolose lumpia, adeoque de iplorum latera, nempe ipsi rami
ipsis semiordinatis, singuli singulis, hoc est ramns LV lemiordinatae XY,
S raUS minimuS E B, semiordinatae BF EqualiS erIF _C. CONCAMLI eF-
eo huusmodi descriprae Ayperbola est Limes propolicaxe Ordinationis.
Quod erac _c.
(0 37. primi
e.
1
X Otenis, OP ad PL. en re canuertum latus datae FIyper.
Dea A LI LCCIMLE, COPOHCHAO IGITIE OR ad F. P est
et lumma corundem laterum ad rectum: Quare P F. distancia a CeNETO Li-
miris vlque ad originem est quarca proporcionalium, si hac ve lumma.
lacerum datae FIrperbolae ad suum rectum, ita distantia inCer CentrUm
eiuldem, de originem ad aliam.
2. Onunque P B CONSCE CX P F, E B, eric P B, distancia inter cen
erum Limiris de verricem datae Hyperbolae, aequalis aGGrCSatO Cx GUaKA
inVenta PF, d ramo minimo F B.
3. Fc quoniam quadralum P L ostensum est eequale rectangulo (uB
DP, PB, ipse PL Cemiaxis Zimiris pocerie rectangulum sub distancia sui
cenri a bali trianguli circumseripei, in distantiam eiusdem centri, ab
origine, vel a vertice ipsius criansuli.