# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/851387705:0621
# Permalink to this reading: https://leibnizlegible.com/page/851387705:0621?run=74
# Title: [Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica (shelfmarks Leibn. Marg. 100:1/2, Stück 1; Leibn. Marg. 100:1/2)
# Folio 601, page id 851387705:0621
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=851387705&page=621
# Source image: https://digitale-sammlungen.gwlb.de/content/851387705/jpgs/default/00000621.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 57 lines, status machine
# Lines: 57 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.

ti
C
a
l
i alLodc CeCibabe
FO. FL:: FP. FD.
TE DO, Forizontalis recta; FP ad FTorizontem pet
pendicularis; FO, inclinara recta, per quam vel
Descendit vel Ascendit Crare; Ec rectae PO, parallel
DE, (trianguli crura sccans proportionaliter, per 2
Elem. 6.) ErgO: uE FO, ad P L, Longitudo ad Lon
gicudinem; lic FP, ad FD: HIOC CHt, (per 3 _ TOhu
jus,) Descentus ad Descentum (s Deortum,) vel (A
TurCum mOveatuT) ACcentus ad Ascensum. Ouod CraL
Propolicum.
Idem, mutatis mucandis, de moris ab alia Viquaris, similiter octendetur.
SCHOF TV M.
vmie haec Demonstratio: Forironcalis rectae PO, puncta omnia, uE P, C
aeque alta: adeoque PO rectam, quasi in superticie Sphaerica, Perrae concen-
trica, jacere. Sin arerBcs loquamur, pro rectis PO, DL, Substiendi funt arcus
circulares, Perra ce fentrici; (ee quidem pro singulis in FO punctis, mucabitur
Perpendiculi rolicio, ec inclinacio decliris rectae:) Sed rancillum a Rectis differunt
Arcus illi, ut pro Rectis ruro usurpari soleane, ob causas ad DeF. 15. Cap. L. emOrataS.
P R OP. X
Reais, lire ad orizontem perpendicularibus, sire utcunque inclina-
tis; Si per AEquales Longitudines feratur Crare: Descensuum AF
centuumre Alcicudinco, sunc Consicudinibus portionum aque alta
rum reciproce proportionales.
Su per Inaequales Longitudines ferantur: Descensuum Ascensuumre
Alticudines, sunt in ea ratione qua componitur ex ratione Longi
tudinum pex quaS HIcmOtuS, _ reciproca Congirudinum portionum
aeque altarum.
Adeogue; Si emensa Fongitudines, sint Consitudinibus aque altis
proportionales: Descensus Alcentutre sunt aquales.
Idem intellige, mutatis mutandis, de alia Vi motrice.
FO. FP:: FL. = F P. FD: F K. FM.
mL. L:: H = D. = D:: nM. = D.
TTE PP, ad Forirontem recta; FO, inclinata: Per PP, descendat P Crare:
in F O, grave L; per Longicudinem P L, recta PP aequalem. Jungatur PO
Florizontalis recta, (abscindens porciones PP, FO, aque altas:) ec, huic D2
rallela, L. D. Descenlus itaque graris P, tantus est quanta recta F P; pravis L
quanta est recta FD; (per LO hujus.) Eltque (per 2 Elem.: 6.) uc FO (Jonei
cudo porrionis obliguae,) ad F L, vel huic aqualem F P, (longitudinem perpen-
diculi aeque alti:) Sic, rice rerla, F P (alcitudo Delcentus, in perpendiculo de
Ccendentis, P,) ad F D (altidinem descensus, oblique descendentis L, per lon-
picudinem aequalem.) Idemque de ascendenrium per ealdem L. F, PF, Ascen
libus, similicer ostendetur. Ouod crat probandum
Adeoque; Si per Tnaequales Lonsitudines terantur; (puta, per PD; _ FR =
EF P;) erunt Descensus Ascentulre, in ratione quX ex illa, dt longicudinum per
quas feruntur, compolica; (nempe F M = E LD.) Dec praeced. OuOd POTEOPEO.
baltcuim ctal.
Fis. 4
altarum, ee directa longicudinum emenlarum,) Cint inricem reciprocx; IIOc et
( lonsicudines emensa, sint consitdinibus aque altis proportionales; (PUta, F L
FD, longicudines ementae, iplis F O, F P, lonsicudimitis aque altis, proporciona
+88E
Ldeoque; (per 6 Cap. 7. ) Si TaLIOHILS La, (MLMMDC, RCCIPFOCA PONLOMII aGUC