# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/898203430:0050
# Permalink to this reading: https://leibnizlegible.com/page/898203430:0050?run=74
# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 22, page id 898203430:0050
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=898203430&page=50
# Source image: https://digitale-sammlungen.gwlb.de/content/898203430/jpgs/default/00000050.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 45 lines, status machine
# Lines: 45 recognised, mean confidence 0.89
# 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.

VINCENTM VIVTANI PROLOCIS,
sux Sectionis; quoniam in triangulo F FTO est F G maior B D, erso a
Modulus EB, ipsI EIC aequalis, codem recto BD maior cA.
Sed idem Modulus aliquando axi crantuerlo requalis cst, aliquando
minor, aliquando maior. Si enim rectum latus B D fueric dinidium axis
cransuer(i BF, etiam AIC, vel EIB, ipsi HIC aequalis, erir dimidium.
ForiuS EIF (in eriangulo G HIF ob aeguidiltantes FIC,BD) nempe MO-
dulus ELB aequalis axi eransuerso B F. 1Si vero sic B D minus dimidio
BE. ob ealdem rationes, HIB erit minor dimidio FIE, Eue II B minor
BF. Si eandem tueric B D dimidio iplius B E maior, _ FIB erie maior
dimidio eOriuS FTE, Sive TIB maior BF. l.lCM it NC
4. In Elliph denique prolata praedictus Modulus ex Lemirecto, aue
requalis, aueminor, aut andior esse porestrecto latero luae Secrionis. Nam,
quum sic D B ad BF rE C7FL, vel VE BIIipsi C H aequalis ad HF; Si fuC-
ric rectum D B, duplum axis EranHCNS B F, crit etiam B H dupla HIF,
ideoque eadem BII dupla reliquae BF; quare Moculus B HI recto BD
aequalis. Si vero rectum B D itueric plus quam duplum aXis CPANSUCKII
BE, ob caldem rationes erir B II plus quam dupla BI L, nempe FIB MiHUS
quam dupla reliquae BF, cuius ponicur BD plus quam dupla, ergo MO-
dulus B II minor estrrecto latere BB. Si aurem rectum B D Cuc minus
duplo axis BF, e B HI eric minor quam dupla HI B, nempe B II pluS
quam dupla BF; quare Modulus B H maior cst recto BD.
Tandem ipse Modulus BH semper maior est axc transuerso B F. sUIX
dectionis; quoniam totum lua parte maius el, adeoque lemimoculus
maior semiaxe cransuerso.
i
L.10
XIV
N quacunque Coni-sectione; Ouadrata ramorum ab
drum axis inter ordinatus ca ramorum terminis, (9
TT SuxCUIque Lom =lECHO A B, cuus axis BC, vertex B, rectum
latus BD axi crectum, atque in eribus vicimis Rguris, videlicet FIIi
Pls oblonsae, prolatae, de Fyperbola, Cu axis transuerlus BR, d in.
omnibus sic reguILaEriX R D, Per reCtAM VerO AB (qua ad sectionis par-
tem cum axe BC lemirectum angulum Faciac) compleatur AOurA MO-
dulum exhibens BC, _ praeter B A Cic quilibet alius ramus BHI, e ex
eorum terminis sint semiordinatae HI, AC. Dico quadrata ramorum
BA, BFI esse inter sC ve rectancula C CB, GTB. 1
Producantur ordinata vsque ad regulatricem in F, L, _ FTP conveniat
eUM AB in M. 11I.
Jam, quum ex constructione angulus ABC Sit SemireCtS; de ad C re
etus, erio e ad A semircetus, ideoque latera AC, CB, d MI, IB
TunE
orisine in vertice, sunt or se et rectanou la sermen-
terminos Moduli ex semirecto intercepiorum.