# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/898203430:0269
# Permalink to this reading: https://leibnizlegible.com/page/898203430:0269?run=74
# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 77, page id 898203430:0269
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=898203430&page=269
# Source image: https://digitale-sammlungen.gwlb.de/content/898203430/jpgs/default/00000269.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 43 lines, status machine
# Lines: 43 recognised, mean confidence 0.92
# 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.

VARIAR: DISPOSITIOMNM LIMIT. LIBEK HII.
eSi denique perpendicularis ex D super A B inciderit in focum B, vE in
terria sioura, quum demonstratum sic rectangulum AF C suberiplum qua
draci DF, erie de ABC suberiplun quadrari DB, sed idem A ei C TubEri
plum est. quadrati AB, quum sic A B cripla BC, ex hyporhest, ergo quan
draca BD, D A lunc requalia, adeoque d latera, e anculi ad D, A, aequa-
les, led reliquus B est rectus, ergo angulus ad A est semirectus, sive ay.
culus ad B duplus anguli ad A. Duod tandem er ic demonstrandum.
Tlinc est quod Locus verricum eorundem criangulorum, super eadem
bali constituiorum, _ quorum anguli ad vrum balis terminum dupli sine
anguli ad terminum reliquum, est curua Hyperbolae qualem diximus.
Duod erat _c.
A D Propositionem xxii. Libri quarri sC Circa Locos Solidos persit
L  PappuIs.
3 C22 recta A B positione data, atque à daro extra puncto C ipse occurat
sL recta quaedam linea CD, es ipsi A B ad rectos anculos ducatur D F;
 sit aurem proporrio CD ad D E data. Dico punctum F esse ad Typerbolam.
Ouod ipse Pappus per datorum doctrinam faeilé ostendie, et Comn
mandinus elesanter illustrat, addens, quod ( dum perpendicularis CF
ad produeta FHI sIt VE CD ad D E, sIEgue F R aequalis FH) interval
tum KI est cransuersum lacus Flyperbolae HF, punctum F cenerum, de
FH lemicransuertum lacus, vel pocius lemiaxis eranuersus, nihil agens de
Temiaxe coniugato: led ex eius dictis ta
tim collisicur calem esse perpendiculum
CF, necape à purcto C emissionis dia.
gonalium, vsque ad rectam A B Limitem
carundem: quoniam quum sit C V 2d
DE, VE C F ad F EI, erie quadratum
CD, vel duo C F, FD, vel duo OF,
GF. ad quadratum DF, vel ad quadra
EUM F C, vel ad rectangulum RC II cum
Quadrato FFI, ve quadracum C F ad qua-
draTUm FFI, vel ve religuum ad reliquum, hoc est ve quadratum LC, ad
rectangulum R C FT, vel re semirectum latus ad semiaxem eranluerlum
HIF: quum isitur sic quadratum CP ad PII ve lemirectum latus ad iplam
FFI, erir C F media incer semilarera, adeoque semiaxi coniugaro aequalis,
ve constat ex Conicis Flementis: quamobrem, ( data ratio CD ad DF
fuerit aequalitatis, latera quoque FIyperbolae HD aequalia crune, quod pro
sequentibus animaduereisse opporcunum exir.
Insignis vero quidam Mathemaricus, de mazimi Geomerricorum Libro-
rum Auctor ab hac Forre Pappi lumpro arsumento, hoc idem, sed pro
speciali rancum Hyperbola exempliticas in Prop. cluxurvi. lui de cadem
aautatos